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Powered by Question2AnswerAnswered: CAT2018-2: 98
https://aptitude.gateoverflow.in/6119/cat2018-2-98?show=8215#a8215
Given that,<br />
<br />
DIAGRAM<br />
<br />
<br />
<br />
<br />
<br />
In drum$1,$ $A$ and $B$ are in the ratio of $18 : 7.$<br />
<br />
So, the quantity of $A = \frac{18}{25}$<br />
<br />
The quantity of $B = \frac{7}{25}$<br />
<br />
In final mixture, $A$ and $B$ are in the ratio of $13 : 7.$<br />
<br />
So, the quantity of $A = \frac{13}{20}$<br />
<br />
The quantity of $B = \frac{7}{20}$<br />
<br />
In drum$2,$ let us assume the proportion of $B$ with respect to the overall mixture is $x.$<br />
<br />
So, $ \frac{ \frac{7}{25} \times 3 + x \times 4}{7} = \frac{7}{20}$<br />
<br />
$\Rightarrow \frac{21}{25} + 4x = \frac{49}{20}$<br />
<br />
$\Rightarrow 20 (21 + 100x) = 25 \times 49$<br />
<br />
$\Rightarrow 420 + 2000x = 1225$<br />
<br />
$\Rightarrow 2000x = 805 $<br />
<br />
$ x = \frac{805}{2000} $<br />
<br />
$ \boxed{x = \frac{161}{400}} $<br />
<br />
In drum$2, \; B$ is $\frac{161}{400} $<br />
<br />
So, $A$ should be the remaining.<br />
<br />
Thus, $A$ is $\frac{239}{400}. $<br />
<br />
$\therefore$ In drum$2, \; A$ and $B$ are in the ratio of $239 : 161.$<br />
<br />
Correct Answer$: \text{C}$Quantitative Aptitudehttps://aptitude.gateoverflow.in/6119/cat2018-2-98?show=8215#a8215Mon, 18 Oct 2021 06:52:25 +0000Answered: CAT2018-2: 83
https://aptitude.gateoverflow.in/6134/cat2018-2-83?show=8214#a8214
Given that, <br />
<br />
Total mixture $ = 175 \; \text{ml} + 700 \; \text{ml} $<br />
<br />
$ = 875 \; \text{ml} $<br />
<br />
Gopal takes out $10\%$ of the mixture and substitutes it by water of the same amount.<br />
<br />
We know that,<br />
<br />
A container contains $\text{x} \; \text{units}$ of the liquid from which $\text{y} \; \text{units}$ are taken out and replaced by water.<br />
<br />
Again from this mixture $\text{y} \; \text{units}$ are taken out and replaced by water. If this process is repeated $\text{‘n’}$ times.<br />
<br />
Then,<br />
<br />
The liquid left in the container after<br />
<br />
$\frac{ \text{n}^{th} \text{operation}}{ \text{Original quantity of the liquid in the container}} = \left( \frac{\text{x -y}}{\text{x}} \right)^{\text{n}}$ <br />
<br />
$\Rightarrow \text{Quantity of liquid left after n}^{th} \text{operation} = \text{x} \ast \left( 1 – \frac{\text{y}}{\text{x}} \right)^{\text{n}} $<br />
<br />
Here, $\text{n} = 2$<br />
<br />
Final quantity of alcohol in the mixture $ = 700 \times \left( 1 – \frac{70}{700} \right)^{2} $<br />
<br />
$ = 700 \times \left( 1 – \frac{1}{10} \right)^{2} $<br />
<br />
$ = 700 \times \frac{9}{10} \times \frac{9}{10} = 7 \times 81 = 567 \; \text{ml} $<br />
<br />
Therefore, Final quantity of water in the mixture $ = 875 – 567 = 308 \; \text{ml} $<br />
<br />
Hence, the percentage of water in the mixture $ = \frac{308}{875} \times 100 \% $<br />
<br />
$ = 0 \cdot 352 \times 100 \% $<br />
<br />
$ = 35 \cdot 2 \% $<br />
<br />
Correct Answer $: \text{A}$Quantitative Aptitudehttps://aptitude.gateoverflow.in/6134/cat2018-2-83?show=8214#a8214Sun, 17 Oct 2021 17:10:12 +0000Answered: CAT2018-1: 95
https://aptitude.gateoverflow.in/6016/cat2018-1-95?show=8212#a8212
Let the cost price per kg of type $A,$ and $B$ be $\text{Rs.} x$ and $\text{Rs.} y$ respectively.<br />
<br />
When, $A$ and $B$ are mixed in the ratio of $3:2,$ then the profit is $10\%,$<br />
<br />
So, selling price $:$<br />
<br />
$ \left( \frac{3x+2y}{5} \right) \times \frac{110}{100} = 40 $<br />
<br />
$ \Rightarrow \left( \frac{3x+2y}{5} \right) \times \frac{11}{10} = 40 \quad \longrightarrow (1) $<br />
<br />
When, $A$ and $B$ are mixed in the ratio of $2:3,$ then the profit is $5\%.$<br />
<br />
So, selling price $:$<br />
<br />
$ \left( \frac{2x+3y}{5} \right) \times \frac{105}{100} = 40 $<br />
<br />
$ \Rightarrow \left( \frac{2x+3y}{5} \right) \times \frac{21}{20} = 40 \quad \longrightarrow (2) $<br />
<br />
On equalling equation $(1),$ and $(2),$ we get<br />
<br />
$ \left( \frac{3x+2y}{5} \right) \times \frac{11}{10} = \left( \frac{2x+3y}{5} \right) \times \frac{21}{20} $<br />
<br />
$ \Rightarrow (3x+2y) \times 22 = (2x+3y) \times 21 $<br />
<br />
$ \Rightarrow 66x + 44y = 42x + 63y $<br />
<br />
$ \Rightarrow 24x = 19y $<br />
<br />
$ \Rightarrow \boxed{\frac{x}{y} = \frac{19}{24}} $<br />
<br />
$\therefore$ The cost price per kg of $A$ and $B$ is $19 : 24.$<br />
<br />
Correct Answer $: \text{B}$Quantitative Aptitudehttps://aptitude.gateoverflow.in/6016/cat2018-1-95?show=8212#a8212Fri, 01 Oct 2021 11:22:05 +0000Answered: CAT2018-1: 85
https://aptitude.gateoverflow.in/6026/cat2018-1-85?show=8211#a8211
Let the cost price of peanuts per kg be $\text{Rs}. x.$<br />
<br />
Then, the cost price of walnuts per kg be $\text{Rs}. 3x.$<br />
<br />
A wholesaler sold $8 \; \text{kg}$ of peanuts at a profit of $10\%.$<br />
<br />
So, the cost price of $8 \; \text{kg}$ peanuts $ = \text{Rs}. 8x.$<br />
<br />
Therefore, selling price of $8 \; \text{kg}$ peanuts $ = 8x \times \frac{110}{100} = \text{Rs.} \frac{88x}{10} $<br />
<br />
And, he also sold $16 \; \text{kg}$ walnuts at a profit of $20 \%.$<br />
<br />
So, the cost price of $16 \; \text{kg}$ walnuts $ = 16 \times 3x = \text{Rs.} 48x $<br />
<br />
Therefore, selling price of $16 \; \text{kg}$ walnuts $ = 48x \times \frac{120}{100} = \text{Rs.} \frac{288x}{5} $<br />
<br />
The shopkeeper who bought the products from the wholesaler lost $5 \; \text{kg}$ of walnuts, and $3 \; \text{kg}$ of peanuts in transit.<br />
<br />
So, he finally have $11 \; \text{kg}$ of walnuts, and $5 \; \text{kg}$ of peanuts. He then mixed the remaining nuts, and this brought the total quantity $ = (11 \; \text{kg} + 5 \; \text{kg}) = 16 \; \text{kg}.$<br />
<br />
Shopkeeper sold $16 \; \text{kg}$ of mixture at the rate of $\text{Rs.} 166 \; \text{per kg}.$<br />
<br />
So, total amount earned by shopkeeper of $16 \; \text{kg} = 16 \times 166 = \text{Rs.} 2656 $<br />
<br />
Now, since the shopkeeper made a profit of $25 \%$ on his entire purchase of $8 \; \text{kg}$ of peanuts and $16 \; \text{kg}$ of walnuts.<br />
<br />
Thus, $125 \% \left( \frac{88x}{10} + \frac{288x}{5} \right) = 2656 $<br />
<br />
$ \Rightarrow \frac{125}{100} \left( \frac{88x}{10} + \frac{288x}{5} \right) = 2656 $<br />
<br />
$ \Rightarrow \frac{5}{4} \left ( \frac{88x + 576x}{10} \right) = 2656 $<br />
<br />
$ \Rightarrow \frac{664x}{8} = 2656 $<br />
<br />
$ \Rightarrow 83x = 2656 $<br />
<br />
$ \Rightarrow x = \frac{2656}{83} $<br />
<br />
$ \Rightarrow \boxed{x = 32} $<br />
<br />
$ \therefore$ The cost price of walnuts per kg $ = 3x = 3 \times 32 = \text{Rs.} 96 $<br />
<br />
Correct Answer $: \text{B}$Quantitative Aptitudehttps://aptitude.gateoverflow.in/6026/cat2018-1-85?show=8211#a8211Fri, 01 Oct 2021 10:50:05 +0000Answered: CAT2018-2: 88
https://aptitude.gateoverflow.in/6129/cat2018-2-88?show=8210#a8210
<p>Given that, points $A$ and $B$ are $150 \; \text{km}$ apart.</p>
<p><img alt="" height="198" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=8191531806366313400" width="630"><br>
<br>
Each car travel at a speed of $100 \; \text{km/hr}$ for the first $50 \; \text{km}.$<br>
<br>
$ \boxed{\text{Time} = \frac{\text{Distance}}{\text{Speed}}} $<br>
<br>
So, $ t_{1} = \frac{50}{100} $<br>
<br>
$ \Rightarrow \boxed{t_{1} = \frac{1}{2} \; \text{hour}} $<br>
<br>
And, each car travel at a speed of $ 50 \; \text{kmph}$ for the $50 \; \text{km}.$<br>
<br>
So, $ t_{2} = \frac{50}{50} $<br>
<br>
$ \Rightarrow \boxed{t_{2} = 1 \; \text{hour}} $<br>
<br>
And, each travel at a speed of $25 \; \text{kmph}$ for the last $50 \; \text{km}. $<br>
<br>
So, $t_{3} = \frac{50}{25} $<br>
<br>
$ \Rightarrow \boxed{t_{2} = 2 \; \text{hours}} $<br>
<br>
Thus, total time for $\text{car 1}$ and $\text{car 2}$ to reach from $A$ to $ B = t_{1} + t_{2} + t_{3} = \frac{1}{2} + 1 + 2 = 3.5 \; \text{hours} $<br>
<br>
$\text{Car 1}$ is $20 \; \text{km}$ away from $A\;\text{(car 2)}.$<br>
<br>
So, time taken by $\text{car 1}$ to cover first $20 \; \text{km} = \frac{20}{10} = \frac{1}{5} \; \text{hours} = 0 \cdot 2 \; \text{hours} = \frac{1}{5} \times 60 = 12 \; \text{minutes} $<br>
<br>
So, $\text{car 2}$ is lagging by $12 \; \text{minutes}$ when $\text{car 1}$ reach point $B.$<br>
<br>
If $\text{car 1}$ reaches $B,$ $\text{car 2}$ will take $12 \; \text{minutes}$ to reach $B.$<br>
<br>
The distance between $\text{car 2}$ and $B = 25 \times \frac{1}{5} = 5 \; \text{km}.$<br>
<br>
$\therefore$ The distance between $\text{car 2}$ and $B,$ when $\text{car 1}$ reaches $B$ is $5 \; \text{km}.$</p>
<hr>
<p>$\textbf{Short Method} :$<br>
<br>
Each part of the distance covers by both the cars, the speed is the same.<br>
<br>
So, if both the cars start from the same point, and the start time is also the same, then they reach the destination at the same time.<br>
<br>
But, here $\text{car 1}$ is $20 \; \text{km}$ ahead of $\text{car 2}.$<br>
<br>
So, time taken by $\text{car 1}$ to travel first $ 20 \; \text{k} = \frac{20}{100} = \frac{1}{5} \; \text{hour} = \frac{1}{5} \times 60 = 12 \; \text{minutes} $<br>
<br>
Thus, $\text{car 2}$ will reach $B, 12 \; \text{minutes}$ after $\text{car 1 }$ reach.<br>
<br>
$\therefore$ The distance between $\text{car 2}$ and $ B = 25 \times \frac{1}{5} = 5 \; \text{km}. $</p>
<p>Correct Answer $: 5$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6129/cat2018-2-88?show=8210#a8210Thu, 30 Sep 2021 14:18:13 +0000Answered: CAT2018-2: 71
https://aptitude.gateoverflow.in/6146/cat2018-2-71?show=8209#a8209
<p>Given that, $A$ and $B$ are two points such that $B$ is $350 \; \text{km}$ of $A.$</p>
<p>Let $`x\text{’}$ and $`y\text{’}$ be the speed $(\text{in km/hr})$ of cars starting from both $A$ and $B$ respectively.</p>
<p><img alt="" height="212" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=4758642415910467700" width="584"></p>
<p>Let us assume $\text{car 2}$ traveled $ d\;\text{km}$ and meet $\text{car 1},$ after $1 \; \text{hour}.$ </p>
<p>$\boxed{\text{Speed} = \frac{\text{Distance}}{\text{Time}}}$</p>
<p>So, $ S_{\text{car 1}} = \frac{350-d}{1} $</p>
<p>$\Rightarrow \boxed{x = 350 – d} \quad \longrightarrow (1) $</p>
<p>And, $ S_{\text{car 2}} = \frac{d}{1} $</p>
<p>$ \Rightarrow \boxed {y = d} $</p>
<p>From the equation $(1),$ we get</p>
<p>$ x = 350 – d $</p>
<p>$ \Rightarrow x = 350 – y $</p>
<p>$\Rightarrow \boxed{x+y = 350} \quad \longrightarrow (2) $</p>
<p><img alt="" height="216" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=1113078051704362232" width="626"></p>
<p>Let us assume, when they move toward east, they meet at point $P$ and distance traveled by $\text{car 1}$ is $`p\text{’} \; \text{km},$ and distance traveled by $\text{car 2}$ is $`350+p\text{’} \; \text{km}$ in $7 \; \text{hours}.$</p>
<p>So, $S_{\text{car 1}} = \text{p}{7} $</p>
<p>$ \Rightarrow x = \frac{p}{7} $</p>
<p>$ \Rightarrow \boxed{p = 7x} \quad \longrightarrow (3) $</p>
<p>And, $S_{\text{car 2}} = \frac{350+p}{7} $</p>
<p>$ \Rightarrow y = \frac{350+7x}{7} \quad [\because \text{From equation} (3)] $</p>
<p>$ \Rightarrow 7y = 350 + 7x $</p>
<p>$ \Rightarrow 7y – 7x = 350 $</p>
<p>$ \Rightarrow 7(y – x) = 350 $</p>
<p>$ \Rightarrow y – x = \frac{350}{7} $</p>
<p>$ \Rightarrow \boxed{y – x = 50 \; \text{km/hr}} $</p>
<p>$\textbf{PS:}$ If they both move in east direction, then $B$ will overtake $A$ only if $y>x.$</p>
<hr>
<p>$\textbf{Short Method: }$</p>
<p>Concept of relative speed ;</p>
<ul>
<li>When two bodies moves in the same direction then the $ \boxed{\text{Relative speed = Difference of speeds}} $</li>
<li>When two bodies move in opposite direction, then the $ \boxed { \text {Relative speed = Sum of speeds}} $</li>
</ul>
<p>Let $`x\text{’}$ and $`y\text{’}$ be the speed ( in km/hr) of cars starting from both $A$ and $B$ respectively.</p>
<p><img alt="" height="152" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=11530151385817762430" width="646"></p>
<p>$\text{Relative speed} = (y – x) \; \text{km/hr} \quad [\because y > x] $</p>
<p>They travel $350 \; \text{km}$ in $7 \; \text{hours}$ with a relative speed of $(y – x) \; \text{km/hr}.$</p>
<p>So, $(y -x) = \frac{350}{7} $</p>
<p>$ \Rightarrow \boxed{ y – x = 50 \; \text{km/hr}} $</p>
<p>Correct Answer $: 50$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6146/cat2018-2-71?show=8209#a8209Thu, 30 Sep 2021 13:34:31 +0000Answered: CAT2018-2: 77
https://aptitude.gateoverflow.in/6140/cat2018-2-77?show=8208#a8208
<p>Given that,</p>
<ul>
<li>$ 2x^{2} – ax + 2 > 0 \quad \longrightarrow (1) $</li>
<li>$ x^{2} – bx + 8 \geqslant 0 \quad \longrightarrow (2) $</li>
</ul>
<p>For any quadratic equation $ax^{2} + bx + c > 0 $<br>
If $a$ is greater than zero then this means that the quadratic equation will always be above $x\text{-axis}$ and will never intersect it at any real value of $x.$ Thus the solutions to this equation will be imaginary.</p>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=7760155586414348091" width="400"><br>
<br>
So, here discriminant $\boxed{\text{D<0}}$<br>
<br>
$ \Rightarrow \boxed{ b^{2} – 4ac < 0} $<br>
<br>
On the other hand for an inequality $ ax^{2} + bx + c < 0 $ for $a < 0$ the expression will always be below the $x\text{-axis}.$Similarly, the solutions will be imaginary.</p>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=6008161801507174221" width="400"><br>
<br>
So, here discriminant $\boxed{D<0}$<br>
<br>
$ \Rightarrow \boxed{b^{2} – 4ac} $<br>
<br>
For the equation $(1),$ graph will be :</p>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=2275779146737219027" width="400"><br>
<br>
Here, $\boxed{\text{D}<0}$<br>
<br>
$ \Rightarrow \boxed{ b^{2} – 4ac < 0} $<br>
<br>
$ \Rightarrow (-a)^{2} – 4(2)(2) < 0 $<br>
<br>
$ \Rightarrow a^{2} – 16 < 0 $<br>
<br>
$ \Rightarrow a^{2} < 16 $<br>
<br>
$ \Rightarrow \boxed{ -4 < a < 4} $<br>
<br>
For the equation $(2),$ graph will be</p>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=13593144565332005721" width="400"><br>
<br>
In this case, the graph can touch $x – \text{axis}$, so it can have at most one root.<br>
<br>
Thus discriminant $\boxed{\text{D} \leqslant 0} $<br>
<br>
$ \Rightarrow \boxed{ b^{2} – 4ac \leqslant 0}$<br>
<br>
$ \Rightarrow (-b)^{2} – 4(1)(8) \leq 0$<br>
<br>
$ \Rightarrow b^{2} – 32 \leq 0$<br>
<br>
$ \Rightarrow b^{2} \leq 32 $<br>
<br>
$ \Rightarrow b \leq \sqrt{32} $<br>
<br>
$ \Rightarrow b \leq \sqrt{16 \times 2} $<br>
<br>
$ \Rightarrow \boxed{-4\sqrt{2} \leqslant b \leqslant 4 \sqrt{2}} $<br>
<br>
As $b$ is an integer.<br>
<br>
So, $\boxed{ -5 \leqslant b \leqslant 5} $<br>
<br>
For the largest value of $ 2a – 6b,$ we can take $a = 3,$ and $b = -5.$<br>
<br>
$\therefore$ The largest possible value of $ 2a – 6b = 2(3) – 6(-5) = 6 + 30 = 36.$<br>
<br>
Correct Answer $:36$<br>
<br>
$\textbf{PS :}$ For equation $ax^{2} + bx + c = 0,$ expression $b^{2} – 4ac$ is called discriminant and denoted by $\text{D}.$</p>
<p>$\begin{array}{cl|l}\hline & \textbf{Value of discrimimant} & \textbf{Nature of roots}\\\hline 1. & D<0 & \text{Unequal and imaginary}\\ 2. & D = 0 & \text{Real and equal}\\ 3. & D>0, \;\text{and is a perfect square} & \text{Real, unequal, and rational}\\ 4. & D>0,\;\text{and not a perfect square} & \text{Real. unequal, and irrational}\\\hline \end{array}$</p>
<p>Reference: <a href="https://brilliant.org/wiki/jee-quadratic-roots/" rel="nofollow">https://brilliant.org/wiki/jee-quadratic-roots/</a></p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6140/cat2018-2-77?show=8208#a8208Mon, 27 Sep 2021 16:19:54 +0000Answered: CAT2018-2: 69
https://aptitude.gateoverflow.in/6148/cat2018-2-69?show=8207#a8207
<p>Given that, $n^{3} – 11n^{2} + 32n – 28 > 0 \quad \longrightarrow (1) $</p>
<p>For, the factorazation, let us assume</p>
<p>$ n^{3} – 11n^{2} + 32n – 28 = 0 \quad \longrightarrow (2) $</p>
<p>Now, put the various of $n,$ and check</p>
<ul>
<li>$ n = – 1 \Rightarrow (-1)^{3} – 11(-1)^{2} + 32(-1) – 28 = 0 $</li>
</ul>
<p>$ \qquad \qquad \quad \; \Rightarrow -1 -11 -32 -28 = 0 $</p>
<p>$ \qquad \qquad \quad \; \Rightarrow \boxed{ -72 \neq 0} $</p>
<ul>
<li>$n=0 \Rightarrow (0)^{3} – 11 (0)^{2} + 32(0) – 28 = 0 $</li>
</ul>
<p>$ \qquad \qquad \quad \; \Rightarrow \boxed{ -28 \neq 0} $</p>
<ul>
<li>$n=1 \Rightarrow (1)^{3} – 11 (1)^{2} + 32(1) – 28 = 0 $</li>
</ul>
<p>$ \qquad \qquad \quad \; \Rightarrow 1 – 11 + 32 – 28 = 0 $</p>
<p>$ \qquad \qquad \quad \; \Rightarrow \boxed{ – 6 = 0} $</p>
<ul>
<li>$n=2 \Rightarrow (2)^{3} – 11 (2)^{2} + 32(2) – 28 = 0 $</li>
</ul>
<p>$ \qquad \qquad \quad \; \Rightarrow 8 – 44 + 64 – 28 = 0 $</p>
<p>$ \qquad \qquad \quad \; \Rightarrow 72 – 72 = 0 $</p>
<p>$ \qquad \qquad \quad \; \Rightarrow \boxed{0 = 0} $</p>
<p>So, $(n-2)$ is the factor.</p>
<p>Now, we can divide the whole expression by $ n-2.$ </p>
<p><img alt="" height="328" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=13845981271777842374" width="505"></p>
<p>We can write, $ (n-2) (n^{2} -9n + 14) = 0 $</p>
<p>$ \Rightarrow (n-2) ( n^{2} – 7n – 2n + 14) = 0 $</p>
<p>$ \Rightarrow (n -2) \left[n (n-7) -2 (n – 7) \right] $</p>
<p>$ \rightarrow (n – 2)(n – 2)(n – 7) = 0 $</p>
<p>$ \Rightarrow \boxed{n = 2, 2, 7} $</p>
<p>The $n = 7$, makes the whole expression zero.</p>
<p>So, $n = 8$ is the smallest integer which make expression greater than zero.</p>
<p>Put the value of $n = 8,$ in the equation $(1),$ we get</p>
<p>$ n^{3} – 11n^{2} + 32n – 28 > 0 $</p>
<p>$ \Rightarrow (8)^{3} – 11 (8)^{2} + 32 (8) – 28 > 0 $</p>
<p>$ \Rightarrow 512 – 704 + 256 – 28 > 0 $</p>
<p>$ \Rightarrow 768 – 732 > 0 $</p>
<p>$ \Rightarrow \boxed{36 > 0} $ (Satisfied)</p>
<p>$\therefore$ The value of smallest integer is $8.$</p>
<p>Correct Answer $:8$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6148/cat2018-2-69?show=8207#a8207Mon, 27 Sep 2021 15:30:57 +0000Answered: CAT2018-2: 67
https://aptitude.gateoverflow.in/6150/cat2018-2-67?show=8206#a8206
<p>Let $ S = 7 \times 11 + 11 \times 15 + 15 \times 19 + \dots + 95 \times 99$<br>
<br>
We can write first series as :<br>
<br>
$ S_{1} = \underbrace{7 + 11 + 15 + \dots + 95}_{\text{Arithmetic Progression (AP)}}$<br>
<br>
Here, first term $ a = 7,$ common difference $d = 11 – 7 = 4,$ last term $l = 95$<br>
<br>
The $n^{th}$ term of the series $t_{n} = l = a+(n-1)d \;,$ where $n =$ number of terms<br>
<br>
$ \Rightarrow 95 = 7+(n-1)4 $<br>
<br>
$ \Rightarrow 4n – 4 + 7 = 95 $<br>
<br>
$ \Rightarrow 4n + 3 = 95 $<br>
<br>
$ \Rightarrow 4n = 92 $<br>
<br>
$ \Rightarrow \boxed{ n= 23} $<br>
<br>
The $n^{th}$ term of the series $\boxed{t_{n} = 4n + 3} $<br>
<br>
Similarly, we can write second series as :<br>
<br>
$S_{2} = \underbrace{11 + 15 + 19 + \dots + 99}_{\text{Arithmetic Progression (AP)}}$<br>
<br>
Here, $ a = 11, \; d = 15 – 11 = 4, \; l = 99, \; n = 23 $<br>
<br>
The $n^{th}$ term of the series $ t_{n} = l = a + (n-1)d $<br>
<br>
$ \Rightarrow t_{n} = 11 + (n-1)4 $<br>
<br>
$ \Rightarrow t_{n} = 11 + 4n – 4 $<br>
<br>
$ \Rightarrow \boxed{t_{n} = 4n + 7} $<br>
<br>
Now, we can write $T_{n} = (4n+3)(4n+7) \;, \text{where} \; n = 1, 2, \dots, 23 $<br>
<br>
$ \Rightarrow T_{n} = 16n^{2} + 28n + 12n + 21 $<br>
<br>
$ \Rightarrow T_{n} = 16n^{2} + 40n + 21 $<br>
<br>
$ \Rightarrow \sum T_{n} = \sum (16n^{2} + 40n + 21) $<br>
<br>
$ \Rightarrow S_{n} = 16 \sum n^{2} + 40 \sum n + 21 \sum 1 $<br>
<br>
$ \Rightarrow S_{n} = 16 \left[ \frac{n(n+1)(2n+1)}{6} \right] + 40 \left[ \frac{n(n+1)}{2} \right] + 21n $<br>
<br>
The sum of the series $S = 16 \left[\frac{(23)(24)(47)}{6} \right] + 40 \left[ \frac{(23)(24)}{2} \right] + 21 \times 23 $<br>
<br>
$ \Rightarrow S = 69184 + 11040 + 483 $<br>
<br>
$ \Rightarrow \boxed{S = 80707} $<br>
<br>
Correct Answer $: \text{A}$</p>
<p>$\textbf{PS :}$</p>
<p>If $ S_{n} = 1 + 2 + 3 + \dots + n $</p>
<p>$ \Rightarrow S_{n} = \displaystyle{}\sum_{k=1}^{n} k $</p>
<p>$ \Rightarrow \boxed{S_{n} = \frac{n(n+1)}{2}} $</p>
<p>If $S_{n} = 1^{2} + 2^{2} + 3^{2} + \dots + n^{2} $<br>
<br>
$ \Rightarrow S_{n} = \displaystyle{}\sum_{k=1}^{n}k^{2} $<br>
<br>
$ \Rightarrow \boxed{S_{n} = \frac{n(n+1)(2n+1)}{6}} $<br>
<br>
If $S_{n} = 1^{3} + 2^{3} + 3^{3} + \dots + n^{3} $<br>
<br>
$ \Rightarrow S_{n} = \displaystyle{}\sum_{k=1}^{n} k^{3} $<br>
<br>
$ \Rightarrow \boxed{S_{n} = \left[ \frac{n(n+1)}{2} \right]^{2}} $</p>
<p>Reference: <a href="https://brilliant.org/wiki/sum-of-n-n2-or-n3/" rel="nofollow">https://brilliant.org/wiki/sum-of-n-n2-or-n3/</a></p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6150/cat2018-2-67?show=8206#a8206Mon, 27 Sep 2021 14:51:35 +0000Answered: CAT2018-2: 73
https://aptitude.gateoverflow.in/6144/cat2018-2-73?show=8205#a8205
<p>Given that, a chord length $5 \; \text{cm}$ subtends an angle of $60^{\circ}$ at the centre of a circle.<br>
<br>
Let the radius of a circle be $`r\text{’} \; \text {cm}.$<br>
<br>
So, $\boxed{OA = OB = OC = r}$</p>
<p><img alt="" height="417" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=5455723960823898261" width="402"><br>
<br>
In $\triangle OAB,$ two sides are equal $(OA = OB = r).$<br>
<br>
So, $\angle A = \angle B = 60^{\circ}$<br>
<br>
Thus, $\triangle ABC$ is an equilateral triangle.<br>
<br>
$OABC$ is a rhombus.<br>
<br>
Area of rhombus $= \frac{d_{1} \times d_{2}}{2} \; \text{sq. units},$ where $d_{1}, d_{2}$ are the diagonal of the rhombus.</p>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=9728690996253513526" width="400"></p>
<p>Diagonals are perpendicular, to each other. $ \boxed{d^{2}_{1} + d^{2}_{2} = 4a^{2}} $</p>
<p>So, $ (OB)^{2} + (AC)^{2} = 4r^{2} $<br>
<br>
$ \Rightarrow (5)^{2} + (AC)^{2} = 4(5)^{2} $<br>
<br>
$ \Rightarrow 25 + (AC)^{2} = 100 $<br>
<br>
$ \Rightarrow (AC)^{2} = 75 $<br>
<br>
$ \Rightarrow AC = \sqrt{75} = \sqrt{25 \times 3} $<br>
<br>
$ \Rightarrow AC = 5 \sqrt{3} \; \text{cm} $<br>
<br>
$\therefore$ The length of a chord that subtends an angle of $120^{\circ}$ at the center of the circle is $5 \sqrt{3} \; \text{cm}.$<br>
<br>
Correct Answer $:\text{C}$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6144/cat2018-2-73?show=8205#a8205Sat, 25 Sep 2021 15:18:35 +0000Answered: CAT2018-2: 97
https://aptitude.gateoverflow.in/6120/cat2018-2-97?show=8204#a8204
<p>Given that, $\triangle ABC$ has area $ = 32 \; \text{sq units.}$<br>
<br>
Length of $BC = 8 \; \text{units},$ and it lies on the line $x=4.$<br>
<br>
Since we want the shortest distance possible between $A$ and the point $(0,0).$<br>
<br>
So, we can assume point $A$ lie on the $x\text{-axis}$ and its coordinates be $(p,0).$<br>
<br>
<img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=17542712008761182014" width="400"></p>
<p><br>
Since $|x_{1} – x_{2}|$ is the distance between the $x\text{-coordinates}$ of the two points.<br>
<br>
So, the height of the $\triangle ABC:\; \boxed {AD = |p-4| \; \text{units}} $<br>
<br>
$\text{The area of triangle} = \frac{1}{2} \times \text{Base} \times \text{Height} $<br>
<br>
The area of $\triangle ABC = \frac{1}{2} \times 8 \times |p-4| $<br>
<br>
$ \Rightarrow 4 \times |p-4| = 32 $<br>
<br>
$ \Rightarrow |p-4| = 8 $<br>
<br>
$ \Rightarrow p-4 = 8 \; (\text{or}) \; – (p-4) = 8 $<br>
<br>
$ \Rightarrow \boxed{ p=12} \; (\text{or}) \; -p+4 = 8 \Rightarrow \boxed{p= -4} $<br>
<br>
$\therefore$ The shortest possible distance between $A(p,0) = A(-4,0)$ and the point $O(0,0) = |-4-0| = |-4| = 4 \; \text{units.} $<br>
<br>
Correct Answer $: \text{A}$<br>
<br>
$\textbf{PS:}$ For any real number $x,$ the absolute value or modulus of $x$ is denoted by $|x|.$<br>
<br>
$$|x| = \left\{\begin{matrix} x\;, & \text{if} \; x \geq 0 & \\ -x\;, & \text{if} \; x <0. & \end{matrix}\right.$$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6120/cat2018-2-97?show=8204#a8204Sat, 25 Sep 2021 14:33:15 +0000Answered: CAT2018-2: 96
https://aptitude.gateoverflow.in/6121/cat2018-2-96?show=8203#a8203
<p>Given that, area of rectangle ${ABCD} = 768 \; \text{cm}^{2}.$</p>
<p>Let the radius of semicircle be $`r\text{’} \; \text{cm}.$</p>
<p><img alt="" height="267" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=1991921897048556741" width="301"><br>
<br>
$\text{Area of semicircle} = \dfrac{\pi r^{2}}{2},$ where $`r\text{’}$ is the radius of semicircle.<br>
<br>
$ \Rightarrow \frac{\pi r^{2}}{2} = 72 \pi $<br>
<br>
$ \Rightarrow r^{2} = 144 $<br>
<br>
$ \Rightarrow \boxed{r = 12 \; \text{cm}} $<br>
<br>
$ \Rightarrow \boxed{ AB = 2r = 24 \; \text{cm}} $<br>
<br>
$\text{Area of rectangle} = AB \times BC $<br>
<br>
$ \Rightarrow 24 \; BC = 768 $<br>
<br>
$ \Rightarrow BC = \frac{768}{24} $<br>
<br>
$ \Rightarrow \boxed{ BC = 32 \; \text{cm}} $<br>
<br>
A semicircular part is removed from the rectangle. The figure will be :</p>
<p><img alt="" height="262" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=15576979463383859350" width="340"><br>
<br>
The perimeter of the remaining portion $ = AD + DC + BC + \text{arc} (AB) $<br>
<br>
$\quad = 32 + 24 + 32 + $ Perimeter of semicircle<br>
<br>
$\quad = 88 + \frac{2 \pi (12)} {2} \quad [\because \text{Perimeter of semicircle} = \frac {2 \pi r}{2} = \pi r] $<br>
<br>
$ \quad = (88 + 12 \pi) \; \text{cm}. $<br>
<br>
Correct Answer $: \text{D} $</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6121/cat2018-2-96?show=8203#a8203Sat, 25 Sep 2021 13:30:35 +0000Answered: CAT2018-2: 99
https://aptitude.gateoverflow.in/6118/cat2018-2-99?show=8202#a8202
<p>Given that, $A,P,Q$ and $B$ lie on the same line such that $P,Q$ and $B$ are respectively, $100 \; \text{km}, 200 \; \text{km}$ and $300 \; \text{km}$ away from $A.$</p>
<p><img alt="" height="177" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=6076925569588580180" width="668"><br>
Let the speed of $\text{car1, car2}$ and $\text{car3}$ be $x,y$ and $z \; \text{km/hr}.$</p>
<p>After some time, $\text{car3}$ meets $\text{car1}$ at $Q.$<br>
<img alt="" height="110" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=8469227390895479812" width="687"><br>
We know that, $ \boxed{\text{Speed} = \frac{\text{Distance}}{\text{Time}}} $<br>
<br>
$ \Rightarrow \boxed{\text{Speed} \propto \text{Distance}} \text{(Time constant)} $<br>
<br>
$ \Rightarrow \boxed{\frac{S_{1}}{S_{2}} = \frac{D_{1}}{D_{2}}} $<br>
<br>
We can say that, if time is constant, speed is directly proportional to distance.</p>
<ul>
<li>Distance traveled by $\text{car1} = 200 \; \text{km} $</li>
<li>Distance traveled by $ \text{car3} = 100 \; \text{km} $</li>
</ul>
<p>So, $\frac{x}{z} = \frac{200}{100} $<br>
<br>
$ \Rightarrow \frac{x}{z} = \frac{2}{1} $<br>
<br>
$ \Rightarrow \boxed{x : z = 2 : 1} \quad \longrightarrow (1) $<br>
<br>
After some time, $\text{car3}$ meets $\text{car2}$ at $P.$</p>
<p><img alt="" height="148" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=5723641429343761136" width="631"></p>
<ul>
<li>Distance traveled by $\text{car2} = 100 \; \text{km} $</li>
<li>Distance traveled by $ \text{car3} = 200 \; \text{km} $</li>
</ul>
<p>So, $\frac{y}{z} = \frac{100}{200} $<br>
<br>
$ \Rightarrow \frac{y}{z} = \frac{1}{2} $<br>
<br>
$ \Rightarrow \boxed{y : z = 1 : 2} \quad \longrightarrow (2) $<br>
<br>
Now, combine the ratios, from equation $(1),$ and $(2),$ we get.</p>
<ul>
<li>$ x:z = (2:1) \times 2 = 4:2 $</li>
<li>$ y:z = (1:2) \times 1 = 1:2 $</li>
<li>$x:y:z = 4:1:2 $</li>
</ul>
<p>$\therefore$ The ratio of the speed of $\text{car2}$ to that of $\text{car1} = y:x = 1:4.$<br>
<br>
Correct Answer $: \text{C}$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6118/cat2018-2-99?show=8202#a8202Sat, 25 Sep 2021 11:45:20 +0000Answered: CAT2018-2: 95
https://aptitude.gateoverflow.in/6122/cat2018-2-95?show=8201#a8201
<p>Given that, the ratio of Amal and Bimal scores is $11:14.$</p>
<ul>
<li>Let, the score of Amal $ = 11x$</li>
<li>Then, the score of Bimal $ = 14x$</li>
<li>Where $x$ is some constant.</li>
</ul>
<p>Let their scores increases by $k.$<br>
<br>
So, $\frac{11x+k}{14x+k} = \frac{47}{56} $<br>
<br>
$ \Rightarrow 56(11x+k) = 47(14x+k) $<br>
<br>
$ \Rightarrow 616x+56K = 658x+47k $<br>
<br>
$ \Rightarrow 56k – 47k = 658x – 616x $<br>
<br>
$ \Rightarrow 9k = 42x $<br>
<br>
$ \Rightarrow \boxed{k = \frac{42}{9}x} $</p>
<p>Now, the score of Bimal:</p>
<ul>
<li>Bimal new score $ = 14x + k = 14x + \frac{42}{9}x $</li>
<li>Bimal original score $ = 14x $</li>
</ul>
<p>$\therefore$ The ratio of Bimal’s new score to that of his original score $ = \frac{14x+\frac{42x}{9}}{14x} = \frac{14x \left(1+\frac{3}{9} \right)}{14x}= \frac{9+3}{9} = \frac{12}{9} = \frac{4}{3} $</p>
<p>Therefore, the ratio of Bimal's new score to that of his original score is $4:3.$</p>
<p>Correct Answer $: \text{C}$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6122/cat2018-2-95?show=8201#a8201Sat, 25 Sep 2021 11:40:40 +0000Answered: CAT2018-2: 76
https://aptitude.gateoverflow.in/6141/cat2018-2-76?show=8200#a8200
<p>For easy understanding we can assume $24 \; \text{hours}$ clock.<br>
<br>
Let $`t\text{’}$ be the time when the tank is emptied.<br>
<br>
On Monday $\text{A}$ alone completed filling the tank at $8 \; \text{pm} \; (20 \; \text{in 24 hours clock}).$<br>
<br>
So, time taken by $\text{A}$ to fill the tank $ = (20 – t) \; \text{hours}.$<br>
<br>
On Tuesday $\text{B}$ alone completed filling the tank at $ 6 \; \text{pm} ( 18 \text{ in 24 hours clock}).$<br>
<br>
So, time taken by $\text{B}$ to fill the tank $ = (18 – t) \; \text{hours}.$<br>
<br>
On Wednesday $\text{A}$ alone worked till $ 5 \; \text{pm} \; (17 \; \text{in 24 hours clock}),$ and then $\text{B}$ worked alone from $5 \; \text{pm}$ to $ 7 \; \text{pm} \; ( 2 \; \text{hours}) $<br>
<br>
So, time taken by $\text{A} = (17 – t) \; \text{hours},$ and time taken by $ \text{B} = 2 \; \text{hours}$ to fill the tank.<br>
<br>
Let $\text{A}$ and $\text{B}$ be the rate of works (efficiency) of $\text{A}$ and $\text{B}$ respectively.We can that, the capacity of the tank will be the same each day.<br>
<br>
So, $(20-t) \text{A} = (18-t) \text{B} = (17-t) \text{A+2B}\quad \longrightarrow (1) $<br>
<br>
Taking first two terms,<br>
<br>
$(20-t) \text{A} = (18-t) \text{B} $<br>
<br>
$ \Rightarrow 20 \text{A – At} = 18 \text{B – Bt} $<br>
<br>
$ \Rightarrow \text{At – Bt} = 20\text{A} – 18\text{B} \quad \longrightarrow (2) $<br>
<br>
Taking last two terms.<br>
<br>
$(18 – t) \text{B} = (17-t) \text{A+2B} $<br>
<br>
$ \Rightarrow \text{18B – B}t = 17 \text{A- A}t + 2 \text{B} $<br>
<br>
$ \Rightarrow \text{A}t – \text{B}t = 17 \text{A} – 16 \text{B} $<br>
<br>
$ \Rightarrow \text{20A – 18B = 17A – 16B} \quad [ \because \text{From equation (2)}] $<br>
<br>
$ \Rightarrow \text{3A = 2B} $<br>
<br>
$ \Rightarrow \frac{\text{A}}{\text{B}} = \frac{2}{3} = k \; \text{(let)}$<br>
<br>
$ \Rightarrow \boxed {\text{A} = 2k, \; \text{B} = 3k} $<br>
<br>
Now, from equation $(1),$ we get<br>
<br>
$ (20-t) \text{A} = (18-t) \text{B} $<br>
<br>
$ \Rightarrow (20 -t) 2k = (18 -t) 3k $<br>
<br>
$ \Rightarrow 40 – 2t = 54 – 3t $<br>
<br>
$ \Rightarrow \boxed{t=14 = 2\; \text{pm}} $<br>
<br>
Total work $ = 2k \times (20 – t) = 3k (18 – t) $<br>
<br>
$ = 2k \times (20 – 14) = 3k \times (18 – 14) $<br>
<br>
$ = 12k = 12k \; \text{units} $<br>
<br>
On Thursday, when both pumps were used simultaneously, time taken $ = \frac{12k}{5k} = \frac{12}{5} = 2.4 \; \text{hours} $<br>
<br>
We know that,</p>
<ul>
<li>$ 1 \; \text{hour} \longrightarrow 60 \; \text{minutes} $</li>
<li>$ 0.4 \; \text{hour} \longrightarrow 60 \times \frac{0.4}{10} = 24 \; \text{minutes} $</li>
</ul>
<p>So, time taken by $\text{A and B} = 2 \; \text{hours 24 minutes}. $<br>
<br>
$\therefore$ The total time taken by both the pumps to fill the tank $ = 14 + 2 \;\text{hours 24 minutes}$<br>
<br>
$\quad = 2 \; \text{pm + 2 hours 24 minutes} $<br>
<br>
$\quad = \boxed{4 : 24 \; \text{pm}} $<br>
<br>
Correct Answer $: \text{C}$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6141/cat2018-2-76?show=8200#a8200Sat, 25 Sep 2021 07:27:30 +0000Answered: CAT2018-2: 84
https://aptitude.gateoverflow.in/6133/cat2018-2-84?show=8199#a8199
Given that, in a tournament, there are $43$ junior level and $51$ senior-level participants ( Boys + Girls).<br />
<br />
Let the number of girls in junior-level be $ \text{‘G’}. $<br />
<br />
And, the number of boys in senior-level be $ \text{‘B’}.$<br />
<br />
The number of girl Vs girl matches in junior-level $ = 153$<br />
<br />
$ \Rightarrow \;^{\text{G}}c_{2} = 153 $<br />
<br />
$ \Rightarrow \frac{\text{G!}}{(\text{G-2})! \; 2!} = 153 $<br />
<br />
$ \Rightarrow \frac{\text{G (G-1) (G-2)!}} { \text{(G-2)}! \; 2!} = 153 $<br />
<br />
$ \Rightarrow \text{G (G-1)} = 306 $<br />
<br />
$ \Rightarrow \text{G}^{2} – \text{G} – 306 = 0 $<br />
<br />
$ \Rightarrow \text{G}^{2} – 18 \text{G} + 17 \text{G} – 306 = 0 $<br />
<br />
$ \Rightarrow \text{G(G-18)} + 17 \text{(G-18)} = 0 $<br />
<br />
$ \Rightarrow \text{(G-18)(G+17)} = 0 $<br />
<br />
$ \Rightarrow \boxed{ \text{G} = 18, \; – 17} $<br />
<br />
Thus, the number of girls in junior level $ \boxed {\text{G}= 18} $<br />
<br />
So, the number of boys in junior level $ = 43 – 18 = 25.$<br />
<br />
The number of matches played between a boy and a girl $ = 25 \times 18 = 450 $<br />
<br />
The number of boy Vs boy matches in senior-level $ = 276 $<br />
<br />
$ \Rightarrow \;^{ \text{B}}c_{2} = 276 $<br />
<br />
$ \Rightarrow \frac{\text{B}!}{(\text{B-2})! \; 2!} = 276 $<br />
<br />
$ \Rightarrow \frac{\text{B(B-1)(B-2)!}} {(\text{B} – 2)! \; 2!} = 276 $<br />
<br />
$ \Rightarrow \text{B}^{2} – \text{B} = 552 $<br />
<br />
$ \Rightarrow \text{B}^{2} – \text{B} – 552 = 0 $<br />
<br />
$ \Rightarrow \text{B}^{2} – 24\text{B} + 23 \text{B} – 552 = 0 $<br />
<br />
$ \Rightarrow \text{B(B-24)} + 23 \text{(B-24)} = 0 $<br />
<br />
$ \Rightarrow \text{(B-24)(B+23)} = 0 $<br />
<br />
$ \Rightarrow \boxed{\text{B} = 24, \; -23 } $<br />
<br />
Thus, the number of boys in senior level $ \boxed{ \text{B} = 24} $<br />
<br />
So, the number of girls in senior level $ = 51 – 24 = 27.$<br />
<br />
The number of matches played between a boy and a girl $ = 27 \times 24 = 648.$<br />
<br />
$\therefore$ The number of matches a boy plays against a girl $ = 450 + 648 = 1098.$<br />
<br />
Correct Answer $:1098$<br />
<br />
$\textbf{PS:}$ Among a group of $n$ person, number of matches played between them $ = \;^{n}c_{2} $<br />
<br />
$\quad = \frac{n!}{(n-2)! \; 2 \times1} $<br />
<br />
$\quad = \frac{n(n-1)(n-2)!}{(n-2)! \; 2 \times 1} $<br />
<br />
$\quad = \frac{n(n-1)}{2} $Quantitative Aptitudehttps://aptitude.gateoverflow.in/6133/cat2018-2-84?show=8199#a8199Sat, 25 Sep 2021 05:43:39 +0000Answered: CAT2018-2: 82
https://aptitude.gateoverflow.in/6135/cat2018-2-82?show=8198#a8198
<p>Let, the efficiency of Ramesh is $\text{‘R’} \; \text{unit/day}. $<br>
<br>
And, the efficiency of Ganesh is $\text{‘G’} \; \text{unit/day}.$<br>
<br>
We know that, $ \boxed{\text{Total work done = Total time} \times \text{Efficiency}} $<br>
<br>
Now, Total work $ = 16 (\text{R + G}) \; \text{units} $<br>
<br>
Work done in $ 7 \; \text{days},$ when they working together $ = 7 (\text{R+G}) \; \text{units} $<br>
<br>
Remaining work $ = 16 \left(\text{R+G}) – 7( \text{R+G}\right) = 9\left( \text{R+G}\right) \; \text{units} $<br>
<br>
Ramesh got sick and his efficiency fell by $30 \%.$ That means he will work $70\% \left( \frac{70}{100} = \frac{7}{10} \right)$ of his efficiency.<br>
<br>
Now, they worked together and complete the work in $17 \; \text{days}.$<br>
<br>
Remaining days they worked $ = 17 – 7 = 10 \; \text{days}.$<br>
<br>
So, $ 10 \times \left( \frac{7}{10}\text{R + G} \right) = 9 ( \text{R+G}) $<br>
<br>
$ \Rightarrow 10 \times \left( \frac{\text{7R+10G}} {10} \right) = \text{9R+9G} $<br>
<br>
$ \Rightarrow \text{G} = \text{2R} $<br>
<br>
$ \Rightarrow \boxed{\text{R} = \frac{\text{G}}{2}} $<br>
<br>
If Ganesh had worked alone after Ramesh got sick. Then,</p>
<ul>
<li>Remaining work $ = 9( \text{R+G}) \; \text{units}$</li>
<li>Efficiency $ = \text{G} \; \text{unit/day} $</li>
</ul>
<p>So, $ 9( \text{R+G}) = \text{Time} \times \text{G} $<br>
<br>
$ \Rightarrow 9 \left( \frac{\text{G}}{2} + \text{G}\right) = \text{Time} \times \text{G} $<br>
<br>
$ \Rightarrow 9 \times \frac{3\text{G}}{2} = \text{Time} \times \text{G} $<br>
<br>
$ \Rightarrow \text{Time} = \frac{27}{2} $<br>
<br>
$ \Rightarrow \boxed{ \text{Time} = 13 . 5 \; \text{days}} $<br>
<br>
$\therefore$ The Ganesh had worked alone after Ramesh got sick. Then time taken by him to complete the remaining work is $ 13.5 \; \text{days}.$<br>
<br>
Correct Answer $: \text{A}$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6135/cat2018-2-82?show=8198#a8198Sat, 25 Sep 2021 05:03:54 +0000Answered: CAT2018-2: 78
https://aptitude.gateoverflow.in/6139/cat2018-2-78?show=8197#a8197
<p>If $M_{1}$ person can do $W_{1}$ work in $D_{1}$ days working $T_{1}$ hours in a day and $M_{2}$ person can do $W_{2}$ work in $D_{2}$ days working $T_{2}$ hours in a day then the relationship between them is :<br>
$$ \boxed {\frac{M_{1} \ast D_{1} \ast T_{1}}{W_{1}} = \frac{M_{2} \ast D_{2} \ast T_{2}}{W_{2}}} $$</p>
<p>Let $` W\text{’} \; \text{unit}$ be the capacity of the tank.</p>
<p>Now, $ \frac{(10A + 45B) \ast 30}{W} = \frac{(8A + 18B) \ast 60}{W} $</p>
<p>$ \Rightarrow 10A + 45B = 16A + 36B $<br>
<br>
$ \Rightarrow 6A = 9B $<br>
<br>
$ \Rightarrow 2A = 3B $<br>
<br>
$ \Rightarrow \frac{A}{B} = \frac{3}{2} = k \;(\text{let}) $<br>
<br>
$ \Rightarrow \boxed{ A = 3k, \; B = 2k} $<br>
<br>
And, $\frac{(7A +27B) \ast \text{Time}}{W} = \frac{(8A+18B) \ast 60}{W} $<br>
<br>
$ \Rightarrow [ 7(3k) + 27(2k)] \ast \text{Time} = [ 8(3k) + 18(2k) \ast 60] $<br>
<br>
$ \Rightarrow (21k + 54k) \ast \text{Time} = (24k + 36k) \ast 60 $<br>
<br>
$ \Rightarrow 75k \ast \text{Time} = 60k \ast 60 $<br>
<br>
$ \Rightarrow \boxed{ \text{Time} = 48 \; \text{minutes}} $<br>
<br>
Correct Answer $:48$</p>
<p>$\textbf{PS:}$</p>
<ul>
<li>Work Done $=$ Time Taken $\ast$ Rate of work</li>
<li>Total Work Done $=$ Total Time $\ast$ Efficiency </li>
</ul>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6139/cat2018-2-78?show=8197#a8197Fri, 24 Sep 2021 17:52:09 +0000Answered: CAT2018-2: 79
https://aptitude.gateoverflow.in/6138/cat2018-2-79?show=8196#a8196
Given that, ${N}^{N} = 2^{160} $<br />
<br />
$ \Rightarrow N^{N} = \left( 2^{10} \right)^{16} $<br />
<br />
$ \Rightarrow N^{N} = \left( 2^{5} \right)^{32} $<br />
<br />
$ \Rightarrow N^{N} = (32)^{32} $<br />
<br />
$\therefore \; \boxed{N = 32} $<br />
<br />
Now, $ N^{2} + 2^{N} = 32^{2} + 2^{32} $<br />
<br />
$ = \left( 2^{5} \right)^{2} + 2^{32} $<br />
<br />
$ = 2^{10} + 2^{32} $<br />
<br />
$ = 2^{10} (1+2^{22}) $<br />
<br />
Here, $N^{2} + 2^{N}$ is a integral multiple of $2^{x}.$<br />
<br />
So, $ 2^{x} = 2^{10} $<br />
<br />
$ \Rightarrow \boxed{ x = 10} $<br />
<br />
$\therefore$ The largest possible value of $x$ is $10.$<br />
<br />
Correct Answer $:10$Quantitative Aptitudehttps://aptitude.gateoverflow.in/6138/cat2018-2-79?show=8196#a8196Fri, 24 Sep 2021 17:20:04 +0000Answered: CAT2018-2: 72
https://aptitude.gateoverflow.in/6145/cat2018-2-72?show=8195#a8195
<p>Given that,</p>
<p>$\text{BC}$ is a diameter of circle, the lengths of $\text{AB} = 30 \; \text{cm}, \text{AC} = 25 \; \text{cm},$ and $\text{CP} = 20 \; \text{cm}.$<br>
<br>
Now, we can draw the diagram :</p>
<p><img alt="" height="390" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=10341962592378710563" width="341"><br>
<br>
The angle inscribed in a semicircle is always a right angle.<br>
<br>
So, $ \triangle \text{BPC},$ and $ \triangle \text{BQC}$ are right angle triangle.<br>
<br>
Now, we can draw the $ \triangle \text{ABC}$ as :</p>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=203554204645992151" width="400"><br>
<br>
Area of the $\triangle \text{ABC} = \frac{1}{2} \times \text{Base} \times \text{Height} $<br>
<br>
$\quad = \frac{1}{2} \times \text{AB} \times \text{CP} $<br>
<br>
$\quad = \frac{1}{2} \times 30 \times 20 $<br>
<br>
$\quad = 300 \; \text{cm}^{2} $<br>
<br>
Again, we can draw the $ \triangle \text{ABC}$ as :</p>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=15628280607169980849" width="400"><br>
<br>
Area of the $ \triangle \text{ABC} = \frac{1}{2} \times \text{AC} \times \text{BQ} $<br>
<br>
$ \Rightarrow 300 = \frac{1}{2} \times 25 \times \text{BQ} $<br>
<br>
$ \Rightarrow 25 \; \text{BQ} = 600 $<br>
<br>
$ \Rightarrow \text{BQ} = \frac{600}{25} $<br>
<br>
$ \Rightarrow \boxed{\text{BQ} = 24 \; \text{cm}} $<br>
<br>
$\therefore$ The length of $\text{BQ}$ is $24 \; \text{cm}.$<br>
<br>
Correct Answer $: 24 $</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6145/cat2018-2-72?show=8195#a8195Fri, 24 Sep 2021 17:01:48 +0000Answered: CAT2018-2: 68
https://aptitude.gateoverflow.in/6149/cat2018-2-68?show=8193#a8193
<p>Let $`xy\text{’}$ be the two-digit number.<br>
<br>
The two-digit number can be expressed as $10x+y,$ where $ y \neq 0 $<br>
<br>
On interchanging the digits, the number will be $`yx\text{’},$ and can be expressed as $ 10y + x $<br>
<br>
The two-digit number is more than thrice the number formed by interchanging the positions of its digits.<br>
<br>
So, $ 10x + y > 3(10y + x) $</p>
<p>$ \Rightarrow 10x + y > 30y + 3x $</p>
<p>$ \Rightarrow \boxed{7x > 29y} \quad \longrightarrow (1) $<br>
<br>
Minimum possible value of $ y = 1.$ So,</p>
<ul>
<li>$ x = 5 \Rightarrow 35 > 29 $</li>
<li>$ x = 6 \Rightarrow 42 > 29 $</li>
<li>$ x = 7 \Rightarrow 49 > 29 $</li>
<li>$ x = 8 \Rightarrow 56 > 29 $</li>
<li>$ x = 9 \Rightarrow 63 > 29 $ </li>
</ul>
<p>And, now we take $ y = 2, $ So,</p>
<ul>
<li>$ x = 9 \Rightarrow 63 > 58 $</li>
</ul>
<p>For $ y = 3,$ no value of $`x\text{’}$ is possible.</p>
<p>$\therefore$ The two digits numbers are $: 51, 61, 71, 81, 91,92.$<br>
<br>
Correct Answer $: \text{B}$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6149/cat2018-2-68?show=8193#a8193Fri, 24 Sep 2021 16:39:38 +0000Answered: CAT2018-2: 80
https://aptitude.gateoverflow.in/6137/cat2018-2-80?show=8192#a8192
<p>Given that,<br>
Let, $ t_{1}, t_{2}, \dots$ be a real numbers.<br>
And,</p>
<ul>
<li>$ t_{1} + t_{2}+ \dots + t_{n} = 2n^{2} + 9n + 13 \quad \longrightarrow (1) $</li>
<li>$ t_{1} + t_{2} + \dots + t_{n-1} = 2(n-1)^{2} + 9(n-1) + 13 \quad \longrightarrow (2) $</li>
</ul>
<p>From the equation $(1),$ subtract the equation $(2),$ we get<br>
<br>
$ (t_{1} + t_{2} + \dots + t_{n-1} + t_{n}) – ( t_{1} + t_{2} + \dots + t_{n-1}) = 2n^{2} + 9n +13 – [ 2(n-1)^{2} + 9(n-1) +13] $</p>
<p>$ \Rightarrow t_{n} = 2n^{2} + 9n +13 – [ 2(n^{2}+ 1 -2n) +9n – 9 + 13] $<br>
<br>
$ \Rightarrow t_{n} = \require{cancel} {\color{Red} {\cancel{2n^{2}}}} + {\color{Teal} {\cancel{9n}}} + {\color{Blue} {\cancel{13}}} – {\color{Red} {\cancel{2n^{2}}}} – 2 + 4n – {\color{Teal} {\cancel{9n}}} + 9 – {\color{Blue} {\cancel{13}}} $<br>
<br>
$ \Rightarrow t_{n} = 4n + 7 \quad \longrightarrow (3) $<br>
<br>
We have, $ t_{k} = 103 $<br>
<br>
From the equation $(3),$ we get<br>
<br>
$ t_{k} = 4k + 7 $<br>
<br>
$ \Rightarrow 103 = 4k + 7 $<br>
<br>
$ \Rightarrow 4k = 96 $<br>
<br>
$ \Rightarrow \boxed {k = 24} $<br>
<br>
Correct Answer $: 24 $</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6137/cat2018-2-80?show=8192#a8192Fri, 24 Sep 2021 14:52:06 +0000Answered: CAT2018-2: 86
https://aptitude.gateoverflow.in/6131/cat2018-2-86?show=8191#a8191
<p>Given that, area of parallelogram $\text{ABCD}$ is $48 \; \text{sq cm.} $<br>
<br>
And, $ \text{CD} = 8 \; \text{cm}, \; \text{AD} = s \; \text{cm} $<br>
<br>
We can draw the parallelogram :</p>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=5122761987008266958" width="400"><br>
<br>
The area of parallelogram $\text{ABCD} = 2 \times \text {The area of triangle ACD} $<br>
<br>
$ \Rightarrow 2 \times \text{The area of triangle ACD = 48} $<br>
<br>
$ \Rightarrow \text{The area of triangle ACD} = 24 $<br>
<br>
$ \Rightarrow \frac{1}{2} \times \text{AD} \times \text{CD} \times \sin \theta = 24 $<br>
<br>
$ \Rightarrow s \times 8 \times \sin \theta = 48 $<br>
<br>
$ \Rightarrow s \times \sin \theta = 6 $<br>
<br>
$ \Rightarrow \sin \theta = \frac{6}{s} $<br>
<br>
As, $– 1 \leq \sin \theta \leq 1 $<br>
<br>
But length can’t be negative.<br>
<br>
So, $ 0 < \sin \theta \leq 1 $<br>
<br>
$ \Rightarrow 0 < \frac{6}{s} \leq 1 $<br>
<br>
$ \Rightarrow 6 \leq s $<br>
<br>
$ \Rightarrow \boxed {s \geq 6\; \text{cm}} $<br>
<br>
Correct Answer $: \text{A}$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6131/cat2018-2-86?show=8191#a8191Fri, 24 Sep 2021 14:20:15 +0000Answered: CAT2018-2: 87
https://aptitude.gateoverflow.in/6130/cat2018-2-87?show=8190#a8190
Given that, $ a_{1}, a_{2}, \dots , a_{52} $ be a positive integers, such that $ a_{1} < a_{2} < \dots < a_{52}.$<br />
<br />
Now, $ \dfrac{a_{1}+a_{2}+ \dots +a_{52}}{52} = \dfrac{a_{2}+a_{3}+ \dots + a_{52}}{51} – 1 $<br />
<br />
$ \Rightarrow \dfrac{a_{1}+a_{2}+ \dots +a_{52}}{52} = \dfrac{a_{2}+a_{3}+ \dots + a_{52}-51}{51} $<br />
<br />
$ \Rightarrow 51( a_{1}+a_{2}+ \dots + a_{52}) = 52 (a_{2}+a_{3}+ \dots + a_{52} – 51) $<br />
<br />
$ \Rightarrow 51( a_{1}+a_{2}+ \dots + a_{52}) = 52 (a_{2}+a_{3}+ \dots + a_{52}) -(51 \times 52)$<br />
<br />
$ \Rightarrow 51a_{1} – (a_{2}+a_{3}+ \dots + a_{52}) = -51 \times 52 $<br />
<br />
$ \Rightarrow a_{2}+a_{3}+ \dots + a_{52} = 51a_{1}+ (51 \times 52)$<br />
<br />
$ \Rightarrow a_{2}+a_{3}+ \dots + 100 = 51(a_{1}+52) \quad \longrightarrow (1)\quad [ \because a_{52} = 100] $<br />
<br />
For largest possible value of $a_{1}:$<br />
<br />
$a_{2} = 50, a_{3} = 51, a_{4} = 52, \dots $<br />
<br />
From the equation $(1),$ we get<br />
<br />
$ 50+51+52+ \dots + 100 = 51 (a_{1}+52) $<br />
<br />
$ \Rightarrow 51(a_{1}+52) = \frac{51}{2} (50 + 100)$<br />
<br />
$ \Rightarrow a_{1} + 52 = \frac{150}{2} $<br />
<br />
$ \Rightarrow a_{1} + 52 = 75 $<br />
<br />
$ \Rightarrow a_{1} = 75 – 52 $<br />
<br />
$ \Rightarrow \boxed{a_{1} = 23} $<br />
<br />
$\therefore$ The largest possible value of $a_{1}$ is $23.$<br />
<br />
Correct Answer $: \text{B}$Quantitative Aptitudehttps://aptitude.gateoverflow.in/6130/cat2018-2-87?show=8190#a8190Fri, 24 Sep 2021 13:46:40 +0000Answered: CAT2018-2: 89
https://aptitude.gateoverflow.in/6128/cat2018-2-89?show=8189#a8189
<p>Given that,<br>
<br>
$ \frac{x+y+z}{3} = 80 $<br>
<br>
$ \Rightarrow x+y+z = 240 \quad \longrightarrow (1) $<br>
<br>
And, $\frac{x+y+z+u+v}{5} = 75 $<br>
<br>
$ \Rightarrow x+y+z+u+v = 375 \quad \longrightarrow {2} $<br>
<br>
Also, $ u = (x+y)/2 \; , \; v = (y+z)/2 $<br>
<br>
Put the value of $u$ and $v$ in the equation $(2),$ we get<br>
<br>
$ x+y+z+\frac{x+y}{2}+\frac{y+z}{2} = 375 $<br>
<br>
$ \Rightarrow \frac{2(x+y+z) + x+y+z+y}{2} = 375 $<br>
<br>
$ \Rightarrow 2(240) + 240 + y = 750 $<br>
<br>
$ \Rightarrow 720 + y = 750 $<br>
<br>
$ \Rightarrow \boxed{y = 30} $<br>
<br>
Put the value of $y$ in equation $(1),$ we get<br>
<br>
$ x+y+z = 240 $<br>
<br>
$ \Rightarrow x+30+z = 240 $<br>
<br>
$ \Rightarrow x+z = 240 – 30 $<br>
<br>
$ \Rightarrow x+z = 210 \quad \longrightarrow (3) $<br>
<br>
Since, $ x \geqslant z, \; x $ takes the minimum possible value, when $ x = z.$<br>
<br>
From equation $(3),$<br>
<br>
$ x+z = 210 $<br>
<br>
$ \Rightarrow x+x = 210 $<br>
<br>
$ \Rightarrow 2x = 210 $<br>
<br>
$ \Rightarrow \boxed{x = 105} $<br>
<br>
$\therefore$ The minimum possible value of $x$ is $105.$</p>
<p>Correct Answer $:105$</p>
<p>$\textbf{PS:}$ The <strong>arithmetic mean</strong> is the sum of all the numbers in a data set divided by the quantity of numbers in that set.</p>
<p>The arithmetic mean $\overline{x}$ of a collection of $n$ numbers $(\text{from}\; a_1$ through $a_n)$ is given by the formula:</p>
<p>$$\overline{x}=\displaystyle \frac{1}{n}\sum_{i=1}^n a_i = \frac{a_1+a_2+a_3+\dots + a_n}{n}.\ _\square$$</p>
<p>Reference: <a href="https://brilliant.org/wiki/arithmetic-mean/" rel="nofollow">https://brilliant.org/wiki/arithmetic-mean/</a></p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6128/cat2018-2-89?show=8189#a8189Fri, 24 Sep 2021 10:42:56 +0000Answered: CAT2018-2: 92
https://aptitude.gateoverflow.in/6125/cat2018-2-92?show=8188#a8188
<p>Given that,<br>
<br>
$ 4^{n} > 17^{19} $<br>
<br>
Taking the $ \log_{10}$ both sides.<br>
<br>
$ \log_{10}4^{n} > \log_{10} 17^{19} $<br>
<br>
$ \Rightarrow n \log_{10}4 > 19 \log_{10}17 \quad [ \because \log_{b}a^{x} = x \log_{b}a] $<br>
<br>
$ \Rightarrow n > 19 \left( \frac{\log_{10}17}{ \log_{10}4} \right) $<br>
<br>
$ \Rightarrow n > 19 ( \log_{4}17) \quad \left[ \because \log_{b}a = \frac{ \log_{x}a}{ \log_{x}b} \right] $<br>
<br>
For easy calculation, let us assume $17 \approx 16.$<br>
<br>
Now, $ n > 19 ( \log_{4} 16)$<br>
<br>
$ \Rightarrow n > 19 ( \log_{4} 4^{2})$<br>
<br>
$ \Rightarrow n > 19 \times 2 ( \log_{4}4)$<br>
<br>
$ \Rightarrow \boxed{n >38} \quad [ \because \log_{a}a = 1 ] $<br>
<br>
$ \Rightarrow \boxed{n \simeq 39} $<br>
<br>
$\therefore$ The small integer $n$ is closed to $39.$</p>
<hr>
<p>$\textbf{Short Method :}$<br>
<br>
Given that, $ 4^{n} > 17^{19} $<br>
<br>
$ \Rightarrow \left( 4^{2} \right)^{\frac{n}{2}} > 17^{19} $<br>
<br>
$ \Rightarrow (16)^{\frac{n}{2}} > 17^{19} $<br>
<br>
Here, $ 16 < 17 ,$ so $ \frac{n}{2}$ must be greater than $19.$<br>
<br>
Thus, $ \frac{n}{2} > 19 $<br>
<br>
$ \Rightarrow n > 38 $<br>
<br>
$ \Rightarrow \boxed{n \simeq 39} $<br>
<br>
Correct Answer $:\text{C}$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6125/cat2018-2-92?show=8188#a8188Thu, 23 Sep 2021 16:41:02 +0000Answered: CAT2018-2: 100
https://aptitude.gateoverflow.in/6117/cat2018-2-100?show=8187#a8187
Let, $ \text{S} = \frac{1}{ \log_{2}100} – \frac{1}{ \log_{4}100} +\frac{1}{\log_{5}100} – \frac{1}{\log_{10}100} + \frac{1}{\log_{20}100} – \frac{1}{\log_{25}100} + \frac{1}{\log_{50}100} $<br />
<br />
$ \Rightarrow \text{S} = \log_{100}2 – \log_{100}4 + \log_{100}5 – \log_{100}10 + \log_{100}20 – \log_{100}25 + \log_{100}50 \quad \left[ \because \log_{b}a = \frac{1}{\log_{a}b} \right] $<br />
<br />
$ \Rightarrow \text{S} = \log_{100}2 – \log_{100}4 + \log_{100}5 – \log_{100}10 + \log_{100}(5 \cdot 4) – \log_{100}(5 \cdot 5) + \log_{100}(5 \cdot 10) $<br />
<br />
$ \Rightarrow \text{S} = \require{cancel}\log_{100}2 – {\color{Red}{\cancel{\log_{100}4}}} + \log_{100}5 – {\color{Blue}{\cancel{\log_{100}10}}} + {\color{Magenta}{\cancel{\log_{100}5}}} +{\color{Red}{\cancel{\log_{100}4}}} – {\color{Magenta}{\cancel{\log_{100}5}}} – {\color{Magenta}{\cancel{\log_{100}5}}} + {\color{Magenta}{\cancel{\log_{100}5}}} + {\color{Blue}{\cancel{\log_{100}10}}} \quad \left[ \because \log_{x}(ab) = \log_{x}a + \log_{x}b \right] $<br />
<br />
$ \Rightarrow \text{S} = \log_{100}2 + \log_{100}5 $<br />
<br />
$ \Rightarrow \text{S} = \log_{100}(2 \cdot 5) $<br />
<br />
$ \Rightarrow \text{S} = \log_{100}10 $<br />
<br />
$ \Rightarrow \text{S} = \log_{10^{2}} 10 $<br />
<br />
$ \Rightarrow \text{S} = \frac{1}{2} \; \log_{10}10 \quad \left[ \because \log_{b^{x}}a = \frac{1}{x} \; \log_{b}a \right] $<br />
<br />
$ \Rightarrow \boxed{\text{S} = \frac{1}{2}} \quad [ \because \log_{a}a = 1 ] $<br />
<br />
Correct Answer $ : \text{A}$Quantitative Aptitudehttps://aptitude.gateoverflow.in/6117/cat2018-2-100?show=8187#a8187Thu, 23 Sep 2021 16:27:58 +0000Answered: CAT2018-2: 91
https://aptitude.gateoverflow.in/6126/cat2018-2-91?show=8186#a8186
<p>Given that,</p>
<ul>
<li>$ \text{T} = \{ 1,2,3,4\} $</li>
<li>$ \text{Q} = \{ 2,3,5,6 \} $</li>
<li>$ \text{R} = \{ 1,3,7,8,9\} $</li>
<li>$ \text{S} = \{ 2,4,9,10\} $</li>
</ul>
<p>$ \boxed{ \text{A} \triangle \text{B} = ( \text{A} \cup \text{B}) – ( \text{A} \cap \text{B})} $</p>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=1327312873496265385" width="400"></p>
<p>$ \boxed {\text{A} \triangle \text{B} = ({ \text{A} – \text{B}) \cup (\text{B} – \text{A})}} $ </p>
<p>Now, $ \text{P} \triangle \text{Q} = \{ 1,2,3,4\} \triangle \{ 2,3,5,6\} $</p>
<p>$ \Rightarrow \text{P} \triangle \text{Q} = \{ 1, 4, 5,6 \} $</p>
<p>And, $ \text{R} \triangle \text{S} = \{ 1,3,7,8,9 \} \triangle \{ 2,4,9,10 \} $</p>
<p>$ \Rightarrow \text{R} \triangle \text{S} = \{ 1,2,3,4,7,8,10 \} $</p>
<p>Thus, $ ( \text{P} \triangle \text{Q}) \triangle ( \text{R} \triangle \text{S}) = \{ 1,4,5,6 \} \triangle \{ 1,2,3,4,7,8,10 \} $</p>
<p>$ \Rightarrow ( \text{P} \triangle \text{Q}) \triangle ( \text{R} \triangle \text{S}) = \{ 2,3,5,6,7,8,10 \} $</p>
<p>$\therefore$ The number of elements in $( \text{P} \triangle \text{Q}) \triangle (\text{R} \triangle \text{S})$ is $7.$</p>
<p>Correct Answer $: \text{B}$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6126/cat2018-2-91?show=8186#a8186Thu, 23 Sep 2021 16:01:54 +0000Answered: CAT2018-2: 90
https://aptitude.gateoverflow.in/6127/cat2018-2-90?show=8185#a8185
Let $x$ and $y$ be the two numbers.<br />
<br />
$ x^{2} + y^{2} = 97 \quad \longrightarrow (1) $<br />
<br />
The geometric mean cannot exceed the arithmetic mean. $ \boxed{ \text{AM} \geqslant \text{GM}} $<br />
<br />
$ \Rightarrow \boxed{\frac{a_{1} + a_{2} + \dots + a_{n} } {n} \geqslant \sqrt[n]{a_{1} a_{2} \dots a_{n}}} $<br />
<br />
Now$, \frac{x^{2} + y^{2}}{2} \geqslant \sqrt{x^{2} \cdot y^{2}} $<br />
<br />
$ \Rightarrow \frac{x^{2} + y^{2}}{2} \geqslant \sqrt{(xy)^{2}} $<br />
<br />
$ \Rightarrow \frac{x^{2} + y^{2}}{2} \geqslant xy $<br />
<br />
$ \Rightarrow x^{2} + y^{2} \geqslant 2xy $<br />
<br />
$ \Rightarrow 97 \geqslant 2xy \quad [\because \text{From equation (1)}]$<br />
<br />
$ \Rightarrow 2xy \leqslant 97 $<br />
<br />
$ \Rightarrow xy \leqslant \frac{97}{2} $<br />
<br />
$ \Rightarrow \boxed{xy \leqslant 48. 5}$<br />
<br />
So$,xy$ cannot be more than $48. 5.$<br />
<br />
$\therefore$ Only option $\text{(C)}$ not possible.<br />
<br />
Correct Answer $: \text{C}$Quantitative Aptitudehttps://aptitude.gateoverflow.in/6127/cat2018-2-90?show=8185#a8185Thu, 23 Sep 2021 15:39:50 +0000Answered: CAT2018-2: 81
https://aptitude.gateoverflow.in/6136/cat2018-2-81?show=8184#a8184
<p>Let say $, \;p^{3} = q^{4} = r^{5} = s^{6} = k$</p>
<p>Now,</p>
<ul>
<li> $ p^{3} = k \Rightarrow p = k^{\frac{1}{3}} $</li>
<li>$ q^{4} = k \Rightarrow q = k^{\frac{1}{4}} $</li>
<li>$ r^{5} = k \Rightarrow r = k^{\frac{1}{5}} $</li>
<li>$ s^{6} = k \Rightarrow s = k^{\frac{1}{6}} $</li>
</ul>
<p>Now, $ \log_{s} (pqr) = \log_{k^{\frac{1}{6}}} \left( k^{\frac{1}{3}} \cdot k^{\frac{1}{4}} \cdot k^{\frac{1}{5}} \right) $</p>
<p>$ \quad = \log_{k^{\frac{1}{6}}} \left[ k^{\left( \frac{1}{3} + \frac{1}{4} + \frac{1}{5}\right)} \right] $ </p>
<p>$ \quad = \log_{k^{\frac{1}{6}}} \left[ k^{\left(\frac{ 20+15+12}{60}\right)} \right] $</p>
<p>$ \quad = \log_{k^{\frac{1}{6}}} \left( k^{\frac{47}{60}} \right) $</p>
<p>$ \quad = \frac{47}{60} \; \log_{k^{\frac{1}{6}}} k \quad [ \because \log_{b} a^{x} = x\log_{b} a ] $</p>
<p>$ \quad = \frac{47}{60} \times 6 \log_{k} k \quad \left[ \because \log_{b^{x}} a = \frac{1}{x} \log_{b} a \right] $</p>
<p>$ \quad = \frac{47}{10} \quad [ \because \log_{a} a = 1 ] $</p>
<p>Correct Answer $ : \text{D}$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6136/cat2018-2-81?show=8184#a8184Thu, 23 Sep 2021 11:24:45 +0000Answered: CAT2018-2: 74
https://aptitude.gateoverflow.in/6143/cat2018-2-74?show=8183#a8183
<p>Given that, $ f(x) = \max \{ 5x, 52-2x^{2} \} \quad \longrightarrow (1) $</p>
<p>And, $x$ is a positive real number.</p>
<p>The minimum value occurs when both the graphs intersect.</p>
<ul>
<li>Let $ y_{1} = 5x \quad \longrightarrow (2) $</li>
<li>And, $ y_{2} = 52 – 2x^{2} \quad \longrightarrow (3) $</li>
</ul>
<p>From equation $(2),$</p>
<p>$ y_{1} = 5x$ is an equation of line.</p>
<p>$ y = mx+c\,,$ where $m =$ slope of the line , $c =$ intercept on the $y$ – axis.</p>
<p><img alt="" height="437" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=12136042819295506478" width="332"><br>
From equation $(3),$</p>
<p>$ y_{2} = 52 – 2x^{2}$ is a quadractic equation.</p>
<p>$ y_{2} = 0 \Rightarrow x = \sqrt{26} = \pm 5 \cdot 09 $</p>
<p>$ x = 0 \Rightarrow y_{2} = 52 $</p>
<p><img alt="" height="409" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=3464424983177913505" width="378"><br>
Now, combine both graphs, we get</p>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=14182808778878042355" width="400"><br>
From the above graph,</p>
<p>$ 5x = 52 – 2x^{2} $</p>
<p>$ \Rightarrow – 2x^{2} + 52 – 5x = 0 $</p>
<p>$ \Rightarrow 2x^{2} + 5x – 52 = 0 $</p>
<p>$ \Rightarrow 2x^{2} + 13x – 8x – 52 = 0 $</p>
<p>$ \Rightarrow x( 2x+13) – 4(2x+13) = 0 $</p>
<p>$ \Rightarrow (2x+13) (x-4) = 0 $</p>
<p>$ \Rightarrow 2x+13 = o , x-4 = 0 $</p>
<p>$ \Rightarrow \boxed{x = \frac{-13}{4}} , \boxed{x=4}$</p>
<p>Since, $x$ is positive real number, so we take $x = 4.$</p>
<p>Now, from equation $(1),$</p>
<p>$ f(x) = \max \{ 5(4), 52 – 2(4)^{2} \}$</p>
<p>$ \Rightarrow f(x) = \max \{ 20, 52 – 32 \} $</p>
<p>$ \Rightarrow f(x) = \max \{ 20, 20 \} $</p>
<p>$ \Rightarrow \boxed{f(x) = 20} $</p>
<p>$\therefore$ The minimum possible value of $f(x)$ is $20.$</p>
<p>Correct Answer $: 20 $</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6143/cat2018-2-74?show=8183#a8183Thu, 23 Sep 2021 10:41:36 +0000Answered: CAT2018-1: 90
https://aptitude.gateoverflow.in/6021/cat2018-1-90?show=8182#a8182
<p>Given that, radius $ = \text{OA} = \text{OB} = 1 \; \text{cm},$ and $ \boxed{\text{OC} = \text{OD}} $</p>
<p>So, the $\triangle \text{OCD},$ is isosceles triangle.</p>
<p>An isosceles triangle is a triangle that :</p>
<ul>
<li>Have two sides equal </li>
<li>The base angles are also equal</li>
<li>The perpendicular from the apex angle bisects the base</li>
</ul>
<p>We can draw the diagram,</p>
<p><img alt="" height="346" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=12134598642071328937" width="413"></p>
<p>We know that, sum of all the angles of a triangle $ = 180^ {\circ}$</p>
<p>Now, the sum of all the angles of a $ \triangle \text{OCD} = 180^{\circ}$</p>
<p>$ \Rightarrow 60^{\circ} + x + x = 180^{\circ} $</p>
<p>$ \Rightarrow 2x = 120^{\circ} $</p>
<p>$ \Rightarrow x = 60^{\circ} $</p>
<p>So, $ \triangle \text{OCD}$ is a equilateral triangle.</p>
<p>Area of $\triangle \text{OCD} = \frac{1}{2} \text{(area of R)} \quad \longrightarrow (1) $</p>
<p>Area of sector $ = \frac{Q}{360^{\circ}} \times \pi \times (\text{radius})^{2};$ where $Q$ is the angle subtended at the center.</p>
<p>Area of $ R = \frac{60^{\circ}}{360^{\circ}} \times \pi \times (1)^{2} = \frac{\pi}{6} \; \text{cm}^{2} $</p>
<p>Now, the area of $\triangle \text{OCD} = \frac{\sqrt{3}}{4} \; \text{(side)}^{2} = \frac{\sqrt{3}}{4} \; \text{OC}^{2} \; \text{cm}^{2} $</p>
<p>From the equation $(1),$ we get </p>
<p>$ \frac{\sqrt{3}}{4} \; \text{OC}^{2} = \frac{1}{2} \times \frac{\pi}{6} $</p>
<p>$ \Rightarrow \text{(OC)}^{2} = \frac{\pi}{3 \sqrt{3}} $</p>
<p>$ \Rightarrow \text{OC} = \sqrt{\frac{\pi}{3 \sqrt{3}}} = \left( \frac{\pi}{3 \sqrt{3}} \right)^{\frac{1}{2}} \; \text{cm}.$</p>
<p>Correct Answer $: \text{A}$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6021/cat2018-1-90?show=8182#a8182Sat, 18 Sep 2021 04:29:51 +0000Answered: CAT2018-1: 75
https://aptitude.gateoverflow.in/6036/cat2018-1-75?show=8181#a8181
Let the number of people below $51 \; (<51) \; \text {years}$ be $x.$<br />
<br />
The total number of people in an apartment complex $ =$ The number of people whose ages $51 \; \text{years}$ and above $( \geq 51) + $ the number of people whose ages below $ 51 \; (<51) \; \text{years} = 30 + x $ <br />
<br />
The average age of all the people in the apartment complex $ = 38 \; \text {years}.$<br />
<br />
The total age of people in apartment complex $ = (30+x) \times 38 $<br />
<br />
The smallest possible average age of people above $51 \; \text{years}$ is $51,$ and it gives the largest value for the other group.<br />
<br />
The total age of people above $51 \; \text{years} = 30 \times 51 = 1530$<br />
<br />
Now, the total age of people below $51 \; \text{years} = (30+x) \times 38 – 1530$<br />
<br />
$\quad = 1140 + 38x – 1530 = 38x – 390 $<br />
<br />
The average age people below $51 \; \text{years} = \frac{38x – 390}{x} \quad \longrightarrow (1) $<br />
<br />
The number of people whose ages are below $51 \; \text{years}$ is almost $39 \; (\leqslant 39).$<br />
<br />
For getting the largest possible average age, the number of people should be $ x = 39 .$<br />
<br />
$\therefore$ The average age people below $51 \; \text{years} = \frac{(38 \times 39) – 390}{39} = \frac{39(38-10)}{39} = 28 \; \text{years}.$<br />
<br />
Correct Answer $: \; \text{B}$Quantitative Aptitudehttps://aptitude.gateoverflow.in/6036/cat2018-1-75?show=8181#a8181Sat, 18 Sep 2021 03:11:40 +0000Answered: CAT2018-1: 91
https://aptitude.gateoverflow.in/6020/cat2018-1-91?show=8180#a8180
<p>Given that, the digits $:1,2,3,4,5,6,7,8,9 $<br>
<br>
We know that, the number of ways to pick $k$ unordered elements from an $n$ element set $ = \;^{n}C_{k} = \frac{n!}{k!(n-k)!} $<br>
<br>
After selecting the number from the given digits, there is only one way to arrange it.<br>
<br>
So, the total number of ways $ = \;^{9} C_{2} + \;^{9} C_{3} + \;^{9} C_{4} + \dots + \;^{9} C_{9} \quad \longrightarrow (1)$</p>
<p>We know that, $^{n} C_{0} + \;^{n} C_{1} + \;^{n} C_{2} + \dots + \;^{9} C_{n} = 2^{n}$</p>
<p>Here, $^{9}C_{0} + \;^{9}C_{1} + \;^{9} C_{2} + \;^{9} C_{3} + \;^{9} C_{4} + \dots + \;^{9} C_{9} = 2^{9}$<br>
<br>
$\Rightarrow \; ^{9} C_{2} + \;^{9} C_{3} + \;^{9} C_{4} + \dots + \;^{9} C_{9} = 2^{9} – \;^{9}C_{0} - \;^{9}C_{1}$<br>
<br>
From the equation $(1),$ we get<br>
<br>
$\therefore$ The total number of ways $ = 2^{9} – \;^{9}C_{0} – \;^{9}C_{1}$<br>
<br>
$\quad = 512 – \frac{9!}{0! \cdot 9!} – \frac{9!}{1! \cdot 8!} $<br>
<br>
$\quad = 512 – 1 – \frac{9 \times 8!}{1! \cdot 8!} $<br>
<br>
$\quad = 512 – 1 – 9 $<br>
<br>
$\quad = 512 – 10 $<br>
<br>
$\quad = 502 \; \text{ways}.$<br>
<br>
Correct Answer $: 502$<br>
<br>
$ \textbf{PS}:\text{Important Properties:}$</p>
<ul>
<li>$n! = n(n-1)(n-2) \dots 1 = n(n-1)!$</li>
<li>$0! = 1 $</li>
<li>$1! = 1 $</li>
<li>$ ^{n}C_{n} = \frac{n!}{n! \; 0!} = 1 $</li>
<li>$ ^{n}C_{0} = \frac{n!}{0! \; n!} $</li>
<li>$ ^{n}C_{1} = \frac{n!}{1!(n-1)!} = \frac{n(n-1)!}{1!(n-1)!} = n $</li>
</ul>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6020/cat2018-1-91?show=8180#a8180Fri, 17 Sep 2021 16:47:22 +0000Answered: CAT2018-1: 86
https://aptitude.gateoverflow.in/6025/cat2018-1-86?show=8179#a8179
Let $`n\text{’}$ be the total number of tests taken by a $ \text{CAT}$ aspirant, and his average score be $`x\text{’}.$<br />
<br />
His average score increase by $1,$ if the first $10$ tests are not considered, and his average score for the first $10$ tests is $20.$<br />
<br />
So$, (n-10) (x+1) + 10 \times 20 = n \times x $<br />
<br />
$ \Rightarrow nx + n – 10x – 10 + 200 = nx $<br />
<br />
$ \Rightarrow -10x + n + 190 = 0 $<br />
<br />
$ \Rightarrow 10x - n - 190 = 0 \quad \longrightarrow (1) $<br />
<br />
His average score decreased by $1$ if the last tests are not considered, and his average score for the last $10$ tests is $30.$<br />
<br />
So, $ (n-10)(x-1) + 10 \times 30 = n \times x $<br />
<br />
$ \Rightarrow nx – n – 10x + 10 + 300 = nx $<br />
<br />
$ \Rightarrow -10x – n + 310 = 0 $<br />
<br />
$ \Rightarrow 10x + n – 310 = 0 \quad \longrightarrow (2) $<br />
<br />
Adding the equation $(1)$ and $(2),$ we get<br />
<br />
$\begin{array} {cc}10x - n - 190 = 0 \\ 10x + n – 310 = 0 \\\hline 20x – 500 = 0 \end{array}$<br />
<br />
$ \Rightarrow 20x = 500 $<br />
<br />
$ \Rightarrow x = \frac{500}{20} $<br />
<br />
$ \Rightarrow \boxed{x = 25}$<br />
<br />
From, the equation $(2),$ we get<br />
<br />
$ 10x + n – 310 = 0 $<br />
<br />
$ \Rightarrow 10(25) + n – 310 = 0 $<br />
<br />
$ \Rightarrow 250 + n – 310 = 0 $<br />
<br />
$ \Rightarrow \boxed {n = 60} $<br />
<br />
$\therefore$ The number of tests taken by $\text{CAT}$ aspirant is $60.$<br />
<br />
Correct Answer $: 60 $Quantitative Aptitudehttps://aptitude.gateoverflow.in/6025/cat2018-1-86?show=8179#a8179Fri, 17 Sep 2021 16:07:00 +0000Answered: CAT2018-1: 84
https://aptitude.gateoverflow.in/6027/cat2018-1-84?show=8178#a8178
<p>Given that,</p>
<ul>
<li>$ n(H \cup E \cup P) = 74 $</li>
<li>$ n( H \cap E \cap P) = 10 $</li>
<li>$ n(H \cap E) = 20 $</li>
<li>Only $ P = 0 $</li>
</ul>
<p>We can draw the Venn diagram,</p>
<p><img alt="" src="https://aptitude.gateoverflow.in/?qa=blob&qa_blobid=947970516015480734" width="400"></p>
<p>Here, given that $ : b=20, g=10, d=0 $</p>
<p>The number of students studying $ H = $ The number of students studying $E$</p>
<p>$ a + b + e + g = b + c + g + f $</p>
<p>$ \Rightarrow a + 20 + e + 10 = 20 + c + 10 + f $</p>
<p>$ \Rightarrow \boxed{a + e = c + f} \quad \longrightarrow (1) $</p>
<p>We have, $ a + b + c + d + e + f + g = 74 $</p>
<p>$ \Rightarrow a + 20 + c + 0 + e + f + 10 = 74 $</p>
<p>$ \Rightarrow a + e + c + f = 44 $</p>
<p>$ \Rightarrow 2(a+e) = 44 \quad [ \because \text{From equation (1)}]$</p>
<p>$ \Rightarrow \boxed{a + e = 22} $</p>
<p>$\therefore$ The number of students who studies $ H = a + b + e + g = 22 + 20 + 10 = 52.$</p>
<p>Correct Answer $: 52$</p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6027/cat2018-1-84?show=8178#a8178Fri, 17 Sep 2021 15:39:51 +0000CAT2020-3: 1
https://aptitude.gateoverflow.in/8177/cat2020-3-1
<p>[There is] a curious new reality: Human contact is becoming a luxury good. As more screens appear in the lives of the poor, screens are disappearing from the lives of the rich. The richer you are, the more you spend to be off-screen$\dots$</p>
<p>The joy – at least at first – of the internet revolution was its democratic nature. Facebook is the same Facebook whether you are rich or poor. Gmail is the same Gmail. And it’s all free. There is something mass market and unappealing about that. And as studies show that time on these advertisement-support platforms is unhealthy, it all starts to seem declasse, like drinking soda or smoking cigarettes, which wealthy people do less than poor people. The wealthy can afford to opt out of having their data and their attention sold as a product. The poor and middle class don’t have the same kind of resources to make that happen.</p>
<p>Screen exposure starts young. And children who spent more than two hours a day looking at a screen got lower scores on thinking and language tests, according to early results of a landmark study on brain development of more than $11,000$ children that the National Institutes of Health is supporting. Most disturbingly, the study is finding that the brains of children who spend a lot of time on screens are different. For some kids, there is premature thinning of their cerebral cortex. In adults, one study found an association between screen time and depression$\dots$</p>
<p>Tech companies worked hard to get public schools to buy into programs that required schools to have one laptop per student, arguing that it would better prepare children for their screenbased future. But this idea isn’t how the people who actually build the screen-based future raise their own children. In Silicon Valley, time on screens is increasingly seen as unhealthy. Here, the popular elementary school is the local Waldorf School, which promises a back-to nature, nearly screen-free education. So as wealthy kids are growing up with less screen time, poor kids are growing up with more. How comfortable someone is with human engagement could become a new class marker.</p>
<p>Human contact is, of course, not exactly like organic food$\dots$ But with screen time, there has been a concerted effort on the part of Silicon Valley behemoths to confuse the public. The poor and the middle class are told that screens are good and important for them and their children. There are fleets of psychologists and neuroscientists on staff at big tech companies working to hook eyes and minds to the screen as fast as possible and for as long as possible. And so human contact is rare$\dots$</p>
<p>There is a small movement to pass a “right to disconnect” bill, which would allow workers to turn their phones off, but for now a worker can be punished for going offline and not being available. There is also the reality that in our culture of increasing isolation, in which so many of the traditional gathering places and social structures have disappeared, screens are filling a crucial void.</p>
<p>The author is least likely to agree with the view that the increase in screen-time is fuelled by the fact that:</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>there is a growth in computer-based teaching in public schools.</li>
<li>some workers face punitive action if they are not online.</li>
<li>with falling costs, people are streaming more content on their devices.</li>
<li>screens provide social contact in an increasingly isolating world.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8177/cat2020-3-1Fri, 17 Sep 2021 13:45:05 +0000CAT2020-3: 2
https://aptitude.gateoverflow.in/8176/cat2020-3-2
<p>[There is] a curious new reality: Human contact is becoming a luxury good. As more screens appear in the lives of the poor, screens are disappearing from the lives of the rich. The richer you are, the more you spend to be off-screen$\dots$</p>
<p>The joy – at least at first – of the internet revolution was its democratic nature. Facebook is the same Facebook whether you are rich or poor. Gmail is the same Gmail. And it’s all free. There is something mass market and unappealing about that. And as studies show that time on these advertisement-support platforms is unhealthy, it all starts to seem declasse, like drinking soda or smoking cigarettes, which wealthy people do less than poor people. The wealthy can afford to opt out of having their data and their attention sold as a product. The poor and middle class don’t have the same kind of resources to make that happen.</p>
<p>Screen exposure starts young. And children who spent more than two hours a day looking at a screen got lower scores on thinking and language tests, according to early results of a landmark study on brain development of more than $11,000$ children that the National Institutes of Health is supporting. Most disturbingly, the study is finding that the brains of children who spend a lot of time on screens are different. For some kids, there is premature thinning of their cerebral cortex. In adults, one study found an association between screen time and depression$\dots$</p>
<p>Tech companies worked hard to get public schools to buy into programs that required schools to have one laptop per student, arguing that it would better prepare children for their screenbased future. But this idea isn’t how the people who actually build the screen-based future raise their own children. In Silicon Valley, time on screens is increasingly seen as unhealthy. Here, the popular elementary school is the local Waldorf School, which promises a back-to nature, nearly screen-free education. So as wealthy kids are growing up with less screen time, poor kids are growing up with more. How comfortable someone is with human engagement could become a new class marker.</p>
<p>Human contact is, of course, not exactly like organic food$\dots$ But with screen time, there has been a concerted effort on the part of Silicon Valley behemoths to confuse the public. The poor and the middle class are told that screens are good and important for them and their children. There are fleets of psychologists and neuroscientists on staff at big tech companies working to hook eyes and minds to the screen as fast as possible and for as long as possible. And so human contact is rare$\dots$</p>
<p>There is a small movement to pass a “right to disconnect” bill, which would allow workers to turn their phones off, but for now a worker can be punished for going offline and not being available. There is also the reality that in our culture of increasing isolation, in which so many of the traditional gathering places and social structures have disappeared, screens are filling a crucial void.</p>
<p>The author claims that Silicon Valley tech companies have tried to “confuse the public” by:</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>promoting screen time in public schools while opting for a screen-free education for their own children.</li>
<li>pushing for greater privacy while working with advertisement-support platforms to mine data</li>
<li>concealing the findings of psychologists and neuroscientists on screen-time use from the public.</li>
<li>developing new work-efficiency programmes while lobbying for the “right to disconnect” bill. </li>
</ol>Othershttps://aptitude.gateoverflow.in/8176/cat2020-3-2Fri, 17 Sep 2021 13:45:05 +0000CAT2020-3: 3
https://aptitude.gateoverflow.in/8175/cat2020-3-3
<p>[There is] a curious new reality: Human contact is becoming a luxury good. As more screens appear in the lives of the poor, screens are disappearing from the lives of the rich. The richer you are, the more you spend to be off-screen$\dots$</p>
<p>The joy – at least at first – of the internet revolution was its democratic nature. Facebook is the same Facebook whether you are rich or poor. Gmail is the same Gmail. And it’s all free. There is something mass market and unappealing about that. And as studies show that time on these advertisement-support platforms is unhealthy, it all starts to seem declasse, like drinking soda or smoking cigarettes, which wealthy people do less than poor people. The wealthy can afford to opt out of having their data and their attention sold as a product. The poor and middle class don’t have the same kind of resources to make that happen.</p>
<p>Screen exposure starts young. And children who spent more than two hours a day looking at a screen got lower scores on thinking and language tests, according to early results of a landmark study on brain development of more than $11,000$ children that the National Institutes of Health is supporting. Most disturbingly, the study is finding that the brains of children who spend a lot of time on screens are different. For some kids, there is premature thinning of their cerebral cortex. In adults, one study found an association between screen time and depression$\dots$</p>
<p>Tech companies worked hard to get public schools to buy into programs that required schools to have one laptop per student, arguing that it would better prepare children for their screenbased future. But this idea isn’t how the people who actually build the screen-based future raise their own children. In Silicon Valley, time on screens is increasingly seen as unhealthy. Here, the popular elementary school is the local Waldorf School, which promises a back-to nature, nearly screen-free education. So as wealthy kids are growing up with less screen time, poor kids are growing up with more. How comfortable someone is with human engagement could become a new class marker.</p>
<p>Human contact is, of course, not exactly like organic food$\dots$ But with screen time, there has been a concerted effort on the part of Silicon Valley behemoths to confuse the public. The poor and the middle class are told that screens are good and important for them and their children. There are fleets of psychologists and neuroscientists on staff at big tech companies working to hook eyes and minds to the screen as fast as possible and for as long as possible. And so human contact is rare$\dots$</p>
<p>There is a small movement to pass a “right to disconnect” bill, which would allow workers to turn their phones off, but for now a worker can be punished for going offline and not being available. There is also the reality that in our culture of increasing isolation, in which so many of the traditional gathering places and social structures have disappeared, screens are filling a crucial void.</p>
<p>The statement “The richer you are, the more you spend to be off-screen” is supported by which other line from the passage$?$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>“Gmail is the same Gmail. And it’s all free.”</li>
<li>“$\dots$screens are filling a crucial void.”</li>
<li>“How comfortable someone is with human engagement could become a new class marker.”</li>
<li>“$\dots$studies show that time on these advertisement-support platforms is unhealthy.”</li>
</ol>Othershttps://aptitude.gateoverflow.in/8175/cat2020-3-3Fri, 17 Sep 2021 13:45:05 +0000CAT2020-3: 4
https://aptitude.gateoverflow.in/8174/cat2020-3-4
<p>[There is] a curious new reality: Human contact is becoming a luxury good. As more screens appear in the lives of the poor, screens are disappearing from the lives of the rich. The richer you are, the more you spend to be off-screen$\dots$</p>
<p>The joy – at least at first – of the internet revolution was its democratic nature. Facebook is the same Facebook whether you are rich or poor. Gmail is the same Gmail. And it’s all free. There is something mass market and unappealing about that. And as studies show that time on these advertisement-support platforms is unhealthy, it all starts to seem declasse, like drinking soda or smoking cigarettes, which wealthy people do less than poor people. The wealthy can afford to opt out of having their data and their attention sold as a product. The poor and middle class don’t have the same kind of resources to make that happen.</p>
<p>Screen exposure starts young. And children who spent more than two hours a day looking at a screen got lower scores on thinking and language tests, according to early results of a landmark study on brain development of more than $11,000$ children that the National Institutes of Health is supporting. Most disturbingly, the study is finding that the brains of children who spend a lot of time on screens are different. For some kids, there is premature thinning of their cerebral cortex. In adults, one study found an association between screen time and depression$\dots$</p>
<p>Tech companies worked hard to get public schools to buy into programs that required schools to have one laptop per student, arguing that it would better prepare children for their screenbased future. But this idea isn’t how the people who actually build the screen-based future raise their own children. In Silicon Valley, time on screens is increasingly seen as unhealthy. Here, the popular elementary school is the local Waldorf School, which promises a back-to nature, nearly screen-free education. So as wealthy kids are growing up with less screen time, poor kids are growing up with more. How comfortable someone is with human engagement could become a new class marker.</p>
<p>Human contact is, of course, not exactly like organic food$\dots$ But with screen time, there has been a concerted effort on the part of Silicon Valley behemoths to confuse the public. The poor and the middle class are told that screens are good and important for them and their children. There are fleets of psychologists and neuroscientists on staff at big tech companies working to hook eyes and minds to the screen as fast as possible and for as long as possible. And so human contact is rare$\dots$</p>
<p>There is a small movement to pass a “right to disconnect” bill, which would allow workers to turn their phones off, but for now a worker can be punished for going offline and not being available. There is also the reality that in our culture of increasing isolation, in which so many of the traditional gathering places and social structures have disappeared, screens are filling a crucial void.</p>
<p>Which of the following statement about the negative effects of screen time is the author least likely to endorse $?$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>It is designed to be addictive.</li>
<li>It is shown to have adverse effects on young children’s learning.</li>
<li>It increases human contact as it fills an isolation void.</li>
<li>It can cause depression in viewers.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8174/cat2020-3-4Fri, 17 Sep 2021 13:45:05 +0000CAT2020-3: 5
https://aptitude.gateoverflow.in/8173/cat2020-3-5
<p>I’ve been following the economic crisis for more than two years now. I began working on the subject as part of the background to a novel, and soon realized that I had stumbled across the most interesting story I’ve ever found. While I was beginning to work on it, the British bank Northern Rock blew up, and it became clear that, as I wrote at the time, “If our laws are not extended to control the new kinds of super-powerful, super-complex, and potentially superrisky investment vehicles, they will one day cause a financial disaster of global-systemic proportions.”$\dots$ I was both right and too late, because all the groundwork for the crisis had already been done – though the sluggishness of the world’s governments, in not preparing for the great unraveling of autumn $2008,$ was then and still is stupefying. But this is the first reason why I wrote this book: because what’s happened is extraordinarily interesting. It is an absolutely amazing story, full of human interest and drama, one whose byways of mathematics, economics, and psychology are both central to the story of the last decades and mysteriously unknown to the general public. We have heard a lot about “the two cultures” of science and the arts – we heard a particularly large amount about it in $2009$, because it was the fiftieth anniversary of the speech during which C. P. Snow first used the phrase. But I’m not sure the idea of a huge gap between science and the arts is as true as it was half a century ago – it’s certainly true, for instance, that a general reader who wants to pick up education in the fundamentals of science will find it easier than ever before. It seems to me that there is a much bigger gap between the world of finance and that of the general public and that there is a need to narrow that gap, if the financial industry is not to be a kind of priesthood, administering to its own mysteries and feared and resented by the rest of us. Many bright, literate take as elementary facts of how the world works. I am an outsider to finance and economics, and my hope is that I can talk across that gulf.</p>
<p>My need to understand is the same as yours, whoever you are. That’s one of the strangest ironies of this story: after decades in which the ideology of the Western world was personally and economically individualistic, we’ve suddenly been hit by a crisis which shows in the starkest terms that whether we like it or not – and there are large parts of it that you would have to be crazy to like – we’re all in this together. The aftermath of the crisis is going to dominate the economics and politics of our societies for at least a decade to come and perhaps longer. </p>
<p>Which one of the following best captures the main argument of the last paragraph of the passage $?$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>The aftermath of the crisis will strengthen the central ideology of individualism in the Western world.</li>
<li>Whoever you are, you would be crazy to think that there is no crises.</li>
<li>In the decades to come, other ideologies will emerge in the aftermath of the crisis.</li>
<li>The ideology of individualism must be set aside in order to deal with the crisis.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8173/cat2020-3-5Fri, 17 Sep 2021 13:45:05 +0000CAT2020-3: 6
https://aptitude.gateoverflow.in/8172/cat2020-3-6
<p>I’ve been following the economic crisis for more than two years now. I began working on the subject as part of the background to a novel, and soon realized that I had stumbled across the most interesting story I’ve ever found. While I was beginning to work on it, the British bank Northern Rock blew up, and it became clear that, as I wrote at the time, “If our laws are not extended to control the new kinds of super-powerful, super-complex, and potentially superrisky investment vehicles, they will one day cause a financial disaster of global-systemic proportions.”$\dots$ I was both right and too late, because all the groundwork for the crisis had already been done – though the sluggishness of the world’s governments, in not preparing for the great unraveling of autumn $2008,$ was then and still is stupefying. But this is the first reason why I wrote this book: because what’s happened is extraordinarily interesting. It is an absolutely amazing story, full of human interest and drama, one whose byways of mathematics, economics, and psychology are both central to the story of the last decades and mysteriously unknown to the general public. We have heard a lot about “the two cultures” of science and the arts – we heard a particularly large amount about it in $2009$, because it was the fiftieth anniversary of the speech during which C.P. Snow first used the phrase. But I’m not sure the idea of a huge gap between science and the arts is as true as it was half a century ago – it’s certainly true, for instance, that a general reader who wants to pick up education in the fundamentals of science will find it easier than ever before. It seems to me that there is a much bigger gap between the world of finance and that of the general public and that there is a need to narrow that gap, if the financial industry is not to be a kind of priesthood, administering to its own mysteries and feared and resented by the rest of us. Many bright, literate take as elementary facts of how the world works. I am an outsider to finance and economics, and my hope is that I can talk across that gulf.</p>
<p>My need to understand is the same as yours, whoever you are. That’s one of the strangest ironies of this story: after decades in which the ideology of the Western world was personally and economically individualistic, we’ve suddenly been hit by a crisis which shows in the starkest terms that whether we like it or not – and there are large parts of it that you would have to be crazy to like – we’re all in this together. The aftermath of the crisis is going to dominate the economics and politics of our societies for at least a decade to come and perhaps longer. </p>
<p>Which one of the following, if true, would be an accurate inference from the first sentence of the passage $?$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>The author has witnessed many economic crises by travelling a lot for two years.</li>
<li>The author’s preoccupation with the economic crisis is not less than two years old.</li>
<li>The author is preoccupied with the economic crisis because he is being followed.</li>
<li>The economic crisis outlasted the author’s preoccupation with it.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8172/cat2020-3-6Fri, 17 Sep 2021 13:45:04 +0000CAT2020-3: 7
https://aptitude.gateoverflow.in/8171/cat2020-3-7
<p>I’ve been following the economic crisis for more than two years now. I began working on the subject as part of the background to a novel, and soon realized that I had stumbled across the most interesting story I’ve ever found. While I was beginning to work on it, the British bank Northern Rock blew up, and it became clear that, as I wrote at the time, “If our laws are not extended to control the new kinds of super-powerful, super-complex, and potentially superrisky investment vehicles, they will one day cause a financial disaster of global-systemic proportions.”. . . I was both right and too late, because all the groundwork for the crisis had already been done – though the sluggishness of the world’s governments, in not preparing for the great unraveling of autumn $2008,$ was then and still is stupefying. But this is the first reason why I wrote this book: because what’s happened is extraordinarily interesting. It is an absolutely amazing story, full of human interest and drama, one whose byways of mathematics, economics, and psychology are both central to the story of the last decades and mysteriously unknown to the general public. We have heard a lot about “the two cultures” of science and the arts – we heard a particularly large amount about it in $2009$, because it was the fiftieth anniversary of the speech during which C.P. Snow first used the phrase. But I’m not sure the idea of a huge gap between science and the arts is as true as it was half a century ago – it’s certainly true, for instance, that a general reader who wants to pick up education in the fundamentals of science will find it easier than ever before. It seems to me that there is a much bigger gap between the world of finance and that of the general public and that there is a need to narrow that gap, if the financial industry is not to be a kind of priesthood, administering to its own mysteries and feared and resented by the rest of us. Many bright, literate take as elementary facts of how the world works. I am an outsider to finance and economics, and my hope is that I can talk across that gulf.</p>
<p>My need to understand is the same as yours, whoever you are. That’s one of the strangest ironies of this story: after decades in which the ideology of the Western world was personally and economically individualistic, we’ve suddenly been hit by a crisis which shows in the starkest terms that whether we like it or not – and there are large parts of it that you would have to be crazy to like – we’re all in this together. The aftermath of the crisis is going to dominate the economics and politics of our societies for at least a decade to come and perhaps longer. </p>
<p>Which one of the following, if false, could be seen as supporting the author’s claims$?$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>The economic crisis was not a failure of collective action to rectify economic problems.</li>
<li>Most people are yet to gain any real understanding of the workings of the financial world.</li>
<li>The huge gap between science and the arts has steadily narrowed over time.</li>
<li>The global economic crisis lasted for more than two years.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8171/cat2020-3-7Fri, 17 Sep 2021 13:45:04 +0000CAT2020-3: 8
https://aptitude.gateoverflow.in/8170/cat2020-3-8
<p>I’ve been following the economic crisis for more than two years now. I began working on the subject as part of the background to a novel, and soon realized that I had stumbled across the most interesting story I’ve ever found. While I was beginning to work on it, the British bank Northern Rock blew up, and it became clear that, as I wrote at the time, “If our laws are not extended to control the new kinds of super-powerful, super-complex, and potentially superrisky investment vehicles, they will one day cause a financial disaster of global-systemic proportions.”$\dots$ I was both right and too late, because all the groundwork for the crisis had already been done – though the sluggishness of the world’s governments, in not preparing for the great unraveling of autumn $2008,$ was then and still is stupefying. But this is the first reason why I wrote this book: because what’s happened is extraordinarily interesting. It is an absolutely amazing story, full of human interest and drama, one whose byways of mathematics, economics, and psychology are both central to the story of the last decades and mysteriously unknown to the general public. We have heard a lot about “the two cultures” of science and the arts – we heard a particularly large amount about it in $2009$, because it was the fiftieth anniversary of the speech during which C.P. Snow first used the phrase. But I’m not sure the idea of a huge gap between science and the arts is as true as it was half a century ago – it’s certainly true, for instance, that a general reader who wants to pick up education in the fundamentals of science will find it easier than ever before. It seems to me that there is a much bigger gap between the world of finance and that of the general public and that there is a need to narrow that gap, if the financial industry is not to be a kind of priesthood, administering to its own mysteries and feared and resented by the rest of us. Many bright, literate take as elementary facts of how the world works. I am an outsider to finance and economics, and my hope is that I can talk across that gulf.</p>
<p>My need to understand is the same as yours, whoever you are. That’s one of the strangest ironies of this story: after decades in which the ideology of the Western world was personally and economically individualistic, we’ve suddenly been hit by a crisis which shows in the starkest terms that whether we like it or not – and there are large parts of it that you would have to be crazy to like – we’re all in this together. The aftermath of the crisis is going to dominate the economics and politics of our societies for at least a decade to come and perhaps longer. </p>
<p>All of the following, if true, could be seen as supporting the arguments in the passage, $\text{EXCEPT}$:</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>The failure of economic systems does not necessarily mean the failure of their ideologies.</li>
<li>The story of the economic crisis is also one about international relations, global financial security, and mass psychology.</li>
<li>The difficulty with understanding financial matters is that they have become so arcane.</li>
<li>Economic crises could be averted by changing prevailing ideologies and beliefs.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8170/cat2020-3-8Fri, 17 Sep 2021 13:45:04 +0000CAT2020-3: 9
https://aptitude.gateoverflow.in/8169/cat2020-3-9
<p>I’ve been following the economic crisis for more than two years now. I began working on the subject as part of the background to a novel, and soon realized that I had stumbled across the most interesting story I’ve ever found. While I was beginning to work on it, the British bank Northern Rock blew up, and it became clear that, as I wrote at the time, “If our laws are not extended to control the new kinds of super-powerful, super-complex, and potentially superrisky investment vehicles, they will one day cause a financial disaster of global-systemic proportions.”$\dots$ I was both right and too late, because all the groundwork for the crisis had already been done – though the sluggishness of the world’s governments, in not preparing for the great unraveling of autumn $2008,$ was then and still is stupefying. But this is the first reason why I wrote this book: because what’s happened is extraordinarily interesting. It is an absolutely amazing story, full of human interest and drama, one whose byways of mathematics, economics, and psychology are both central to the story of the last decades and mysteriously unknown to the general public. We have heard a lot about “the two cultures” of science and the arts – we heard a particularly large amount about it in $2009$, because it was the fiftieth anniversary of the speech during which C.P. Snow first used the phrase. But I’m not sure the idea of a huge gap between science and the arts is as true as it was half a century ago – it’s certainly true, for instance, that a general reader who wants to pick up education in the fundamentals of science will find it easier than ever before. It seems to me that there is a much bigger gap between the world of finance and that of the general public and that there is a need to narrow that gap, if the financial industry is not to be a kind of priesthood, administering to its own mysteries and feared and resented by the rest of us. Many bright, literate take as elementary facts of how the world works. I am an outsider to finance and economics, and my hope is that I can talk across that gulf.</p>
<p>My need to understand is the same as yours, whoever you are. That’s one of the strangest ironies of this story: after decades in which the ideology of the Western world was personally and economically individualistic, we’ve suddenly been hit by a crisis which shows in the starkest terms that whether we like it or not – and there are large parts of it that you would have to be crazy to like – we’re all in this together. The aftermath of the crisis is going to dominate the economics and politics of our societies for at least a decade to come and perhaps longer. </p>
<p>According to the passage, the author is likely to be supportive of which one of the following programmes$?$ark</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>An educational curriculum that promotes developing financial literacy in the masses.</li>
<li>The complete nationalisation of all financial institutions.</li>
<li>An educational curriculum that promotes economic research.</li>
<li>Economic policies that are more sensitively calibrated to the fluctuations of the market.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8169/cat2020-3-9Fri, 17 Sep 2021 13:45:04 +0000CAT2020-3: 10
https://aptitude.gateoverflow.in/8168/cat2020-3-10
<p>Mode of transportation affects the travel experience and thus can produce new types of travel writing and perhaps even new “identities.” Modes of transportation determine the types and duration of social encounters; affect the organization and passage of space and time; $\dots$ and also affect perception and knowledge – how and what the traveler comes to know and write about. The completion of the first $\text{U.S.}$ transcontinental highway during the $1920 \text{s} \dots$ for example, inaugurated a new genre of travel literature about the United States – the automotive or road narrative. Such narratives highlight the experiences of mostly male protagonists “discovering themselves” on their journeys, emphasizing the independence of road travel and the value of rural folk traditions.</p>
<p>Travel writing’s relationship to empire building – as a type of “colonialist discourse” – has drawn the most attention from academicians. Close connections have been observed between European (and American) political, economic, and administrative goals for the colonies and their manifestations in the cultural practice of writing travel books. Travel writers’ descriptions of foreign places have been analysed as attempts to validate, promote, or challenge the ideologies and practices of colonial or imperial domination and expansion. Mary Louise Pratt’s study of the genres and conventions of $18 \text{th} – $ and $19 \text{th} – \text{century} $ exploration narratives about South America and Africa (e.g., the “monarch of all I survey” trope) offered ways of thinking about travel writing as embedded within relations of power between metropole and periphery, as did Edward Said’s theories of representation and cultural imperialism. Particularly Said’s book, Orientalism, helped scholars understand ways in which representations of people in travel texts were intimately bound up with notions of self, in this case, that the Occident defined itself through essentialist, ethnocentric, and racist representations of the Orient. Said’s work became a model for demonstrating cultural forms of imperialism in travel texts, showing how the political, economic, or administrative fact of dominance relies on legitimating discourses such as those articulated through travel writing$\dots$</p>
<p>Feminist geographers’ studies of travel writing challenge the masculinist history of geography by who and what are relevant subjects of geographic study and, indeed, what counts as geographic knowledge itself. Such questions are worked through ideological constructs that posit men as explorers and women as travelers – or, conversely, men as travelers and women as tied to the home. Studies of Victorian women who were professional travel writers, tourists, wives of colonial administrators, and other (mostly) elite women who wrote narratives about their experiences abroad during the $19 \text{th}$ century have been particularly revealing. From a “liberal” feminist perspective, travel presented one means toward female liberation for middle – and upper–class Victorian women. Many studies from the $1970 \text{s}$ onward demonstrated the ways in which women’s gendered identities were negotiated differently “at home” than they were “away,” thereby showing women’s self–development through travel. The more recent poststructural turn in studies of Victorian travel writing has focused attention on women’s diverse and fragmented identities as they narrated their travel experiences, emphasizing women’s sense of themselves as women in new locations, but only as they worked through their ties to nation, class, whiteness, and colonial and imperial power structures.</p>
<p>According to the passage, Said’s book, “Orientalism”:</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>illustrated how narrow minded and racist westerners were.</li>
<li>demonstrated how cultural imperialism was used to justify colonial domination.</li>
<li>explained the difference between the representation of people and the actual fact.</li>
<li>argued that cultural imperialism was more significant than colonial domination.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8168/cat2020-3-10Fri, 17 Sep 2021 13:45:04 +0000CAT2020-3: 11
https://aptitude.gateoverflow.in/8167/cat2020-3-11
<p>Mode of transportation affects the travel experience and thus can produce new types of travel writing and perhaps even new “identities.” Modes of transportation determine the types and duration of social encounters; affect the organization and passage of space and time; $\dots$ and also affect perception and knowledge – how and what the traveler comes to know and write about. The completion of the first $\text{U.S.} transcontinental highway during the $1920 \text{s} \dots$ for example, inaugurated a new genre of travel literature about the United States – the automotive or road narrative. Such narratives highlight the experiences of mostly male protagonists “discovering themselves” on their journeys, emphasizing the independence of road travel and the value of rural folk traditions.</p>
<p>Travel writing’s relationship to empire building – as a type of “colonialist discourse” – has drawn the most attention from academicians. Close connections have been observed between European (and American) political, economic, and administrative goals for the colonies and their manifestations in the cultural practice of writing travel books. Travel writers’ descriptions of foreign places have been analysed as attempts to validate, promote, or challenge the ideologies and practices of colonial or imperial domination and expansion. Mary Louise Pratt’s study of the genres and conventions of $18 \text{th} – $ and $19 \text{th} – \text{century} $ exploration narratives about South America and Africa (e.g., the “monarch of all I survey” trope) offered ways of thinking about travel writing as embedded within relations of power between metropole and periphery, as did Edward Said’s theories of representation and cultural imperialism. Particularly Said’s book, Orientalism, helped scholars understand ways in which representations of people in travel texts were intimately bound up with notions of self, in this case, that the Occident defined itself through essentialist, ethnocentric, and racist representations of the Orient. Said’s work became a model for demonstrating cultural forms of imperialism in travel texts, showing how the political, economic, or administrative fact of dominance relies on legitimating discourses such as those articulated through travel writing$\dots$</p>
<p>Feminist geographers’ studies of travel writing challenge the masculinist history of geography by who and what are relevant subjects of geographic study and, indeed, what counts as geographic knowledge itself. Such questions are worked through ideological constructs that posit men as explorers and women as travelers – or, conversely, men as travelers and women as tied to the home. Studies of Victorian women who were professional travel writers, tourists, wives of colonial administrators, and other (mostly) elite women who wrote narratives about their experiences abroad during the $19 \text{th}$ century have been particularly revealing. From a “liberal” feminist perspective, travel presented one means toward female liberation for middle – and upper–class Victorian women. Many studies from the $1970 \text{s}$ onward demonstrated the ways in which women’s gendered identities were negotiated differently “at home” than they were “away,” thereby showing women’s self–development through travel. The more recent poststructural turn in studies of Victorian travel writing has focused attention on women’s diverse and fragmented identities as they narrated their travel experiences, emphasizing women’s sense of themselves as women in new locations, but only as they worked through their ties to nation, class, whiteness, and colonial and imperial power structures.</p>
<p>From the passage, it can be inferred that scholars argue that Victorian women experienced self-development through their travels because:</p>
<p> </p>
<ol start="1" style="list-style-type:upper-alpha">
<li>their identity was redefined when they were away from home.</li>
<li>they were from the progressive middle- and upper-classes of society.</li>
<li>they were on a quest to discover their diverse identities.</li>
<li>they developed a feminist perspective of the world.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8167/cat2020-3-11Fri, 17 Sep 2021 13:45:04 +0000CAT2020-3: 12
https://aptitude.gateoverflow.in/8166/cat2020-3-12
<p>Mode of transportation affects the travel experience and thus can produce new types of travel writing and perhaps even new “identities.” Modes of transportation determine the types and duration of social encounters; affect the organization and passage of space and time; $\dots$ and also affect perception and knowledge – how and what the traveler comes to know and write about. The completion of the first $\text{U.S.}$ transcontinental highway during the $1920 \text{s} \dots$ for example, inaugurated a new genre of travel literature about the United States – the automotive or road narrative. Such narratives highlight the experiences of mostly male protagonists “discovering themselves” on their journeys, emphasizing the independence of road travel and the value of rural folk traditions.</p>
<p>Travel writing’s relationship to empire building – as a type of “colonialist discourse” – has drawn the most attention from academicians. Close connections have been observed between European (and American) political, economic, and administrative goals for the colonies and their manifestations in the cultural practice of writing travel books. Travel writers’ descriptions of foreign places have been analysed as attempts to validate, promote, or challenge the ideologies and practices of colonial or imperial domination and expansion. Mary Louise Pratt’s study of the genres and conventions of $18 \text{th} – $ and $19 \text{th} – \text{century} $ exploration narratives about South America and Africa (e.g., the “monarch of all I survey” trope) offered ways of thinking about travel writing as embedded within relations of power between metropole and periphery, as did Edward Said’s theories of representation and cultural imperialism. Particularly Said’s book, Orientalism, helped scholars understand ways in which representations of people in travel texts were intimately bound up with notions of self, in this case, that the Occident defined itself through essentialist, ethnocentric, and racist representations of the Orient. Said’s work became a model for demonstrating cultural forms of imperialism in travel texts, showing how the political, economic, or administrative fact of dominance relies on legitimating discourses such as those articulated through travel writing$\dots$</p>
<p>Feminist geographers’ studies of travel writing challenge the masculinist history of geography by who and what are relevant subjects of geographic study and, indeed, what counts as geographic knowledge itself. Such questions are worked through ideological constructs that posit men as explorers and women as travelers – or, conversely, men as travelers and women as tied to the home. Studies of Victorian women who were professional travel writers, tourists, wives of colonial administrators, and other (mostly) elite women who wrote narratives about their experiences abroad during the $19 \text{th}$ century have been particularly revealing. From a “liberal” feminist perspective, travel presented one means toward female liberation for middle – and upper–class Victorian women. Many studies from the $1970 \text{s}$ onward demonstrated the ways in which women’s gendered identities were negotiated differently “at home” than they were “away,” thereby showing women’s self–development through travel. The more recent poststructural turn in studies of Victorian travel writing has focused attention on women’s diverse and fragmented identities as they narrated their travel experiences, emphasizing women’s sense of themselves as women in new locations, but only as they worked through their ties to nation, class, whiteness, and colonial and imperial power structures.</p>
<p>American travel literature of the $1920\text{s}:$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>developed the male protagonists’ desire for independence.</li>
<li>presented travellers’ discovery of their identity as different from others.</li>
<li>celebrated the freedom that travel gives.</li>
<li>showed participation in local traditions.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8166/cat2020-3-12Fri, 17 Sep 2021 13:45:03 +0000CAT2020-3: 13
https://aptitude.gateoverflow.in/8165/cat2020-3-13
<p>Mode of transportation affects the travel experience and thus can produce new types of travel writing and perhaps even new “identities.” Modes of transportation determine the types and duration of social encounters; affect the organization and passage of space and time; $\dots$ and also affect perception and knowledge – how and what the traveler comes to know and write about. The completion of the first $\text{U.S.}$ transcontinental highway during the $1920 \text{s} \dots$ for example, inaugurated a new genre of travel literature about the United States – the automotive or road narrative. Such narratives highlight the experiences of mostly male protagonists “discovering themselves” on their journeys, emphasizing the independence of road travel and the value of rural folk traditions.</p>
<p>Travel writing’s relationship to empire building – as a type of “colonialist discourse” – has drawn the most attention from academicians. Close connections have been observed between European (and American) political, economic, and administrative goals for the colonies and their manifestations in the cultural practice of writing travel books. Travel writers’ descriptions of foreign places have been analysed as attempts to validate, promote, or challenge the ideologies and practices of colonial or imperial domination and expansion. Mary Louise Pratt’s study of the genres and conventions of $18 \text{th} – $ and $19 \text{th} – \text{century} $ exploration narratives about South America and Africa (e.g., the “monarch of all I survey” trope) offered ways of thinking about travel writing as embedded within relations of power between metropole and periphery, as did Edward Said’s theories of representation and cultural imperialism. Particularly Said’s book, Orientalism, helped scholars understand ways in which representations of people in travel texts were intimately bound up with notions of self, in this case, that the Occident defined itself through essentialist, ethnocentric, and racist representations of the Orient. Said’s work became a model for demonstrating cultural forms of imperialism in travel texts, showing how the political, economic, or administrative fact of dominance relies on legitimating discourses such as those articulated through travel writing$\dots$</p>
<p>Feminist geographers’ studies of travel writing challenge the masculinist history of geography by who and what are relevant subjects of geographic study and, indeed, what counts as geographic knowledge itself. Such questions are worked through ideological constructs that posit men as explorers and women as travelers – or, conversely, men as travelers and women as tied to the home. Studies of Victorian women who were professional travel writers, tourists, wives of colonial administrators, and other (mostly) elite women who wrote narratives about their experiences abroad during the $19 \text{th}$ century have been particularly revealing. From a “liberal” feminist perspective, travel presented one means toward female liberation for middle – and upper–class Victorian women. Many studies from the $1970 \text{s}$ onward demonstrated the ways in which women’s gendered identities were negotiated differently “at home” than they were “away,” thereby showing women’s self–development through travel. The more recent poststructural turn in studies of Victorian travel writing has focused attention on women’s diverse and fragmented identities as they narrated their travel experiences, emphasizing women’s sense of themselves as women in new locations, but only as they worked through their ties to nation, class, whiteness, and colonial and imperial power structures.</p>
<p>From the passage, we can infer that feminist scholars’ understanding of the experiences of Victorian women travellers is influenced by all of the following $\text{EXCEPT}$ scholars’:</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>perspective that they bring to their research.</li>
<li>knowledge of class tensions in Victorian society.</li>
<li>awareness of gender issues in Victorian society.</li>
<li>awareness of the ways in which identity is formed.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8165/cat2020-3-13Fri, 17 Sep 2021 13:45:03 +0000CAT2020-3: 14
https://aptitude.gateoverflow.in/8164/cat2020-3-14
<p>Mode of transportation affects the travel experience and thus can produce new types of travel writing and perhaps even new “identities.” Modes of transportation determine the types and duration of social encounters; affect the organization and passage of space and time; $\dots$ and also affect perception and knowledge – how and what the traveler comes to know and write about. The completion of the first $\text{U.S.}$ transcontinental highway during the $1920 \text{s} \dots$ for example, inaugurated a new genre of travel literature about the United States – the automotive or road narrative. Such narratives highlight the experiences of mostly male protagonists “discovering themselves” on their journeys, emphasizing the independence of road travel and the value of rural folk traditions.</p>
<p>Travel writing’s relationship to empire building – as a type of “colonialist discourse” – has drawn the most attention from academicians. Close connections have been observed between European (and American) political, economic, and administrative goals for the colonies and their manifestations in the cultural practice of writing travel books. Travel writers’ descriptions of foreign places have been analysed as attempts to validate, promote, or challenge the ideologies and practices of colonial or imperial domination and expansion. Mary Louise Pratt’s study of the genres and conventions of $18 \text{th} – $ and $19 \text{th} – \text{century} $ exploration narratives about South America and Africa (e.g., the “monarch of all I survey” trope) offered ways of thinking about travel writing as embedded within relations of power between metropole and periphery, as did Edward Said’s theories of representation and cultural imperialism. Particularly Said’s book, Orientalism, helped scholars understand ways in which representations of people in travel texts were intimately bound up with notions of self, in this case, that the Occident defined itself through essentialist, ethnocentric, and racist representations of the Orient. Said’s work became a model for demonstrating cultural forms of imperialism in travel texts, showing how the political, economic, or administrative fact of dominance relies on legitimating discourses such as those articulated through travel writing. . . . </p>
<p>Feminist geographers’ studies of travel writing challenge the masculinist history of geography by who and what are relevant subjects of geographic study and, indeed, what counts as geographic knowledge itself. Such questions are worked through ideological constructs that posit men as explorers and women as travelers – or, conversely, men as travelers and women as tied to the home. Studies of Victorian women who were professional travel writers, tourists, wives of colonial administrators, and other (mostly) elite women who wrote narratives about their experiences abroad during the $19 \text{th}$ century have been particularly revealing. From a “liberal” feminist perspective, travel presented one means toward female liberation for middle – and upper–class Victorian women. Many studies from the $1970 \text{s}$ onward demonstrated the ways in which women’s gendered identities were negotiated differently “at home” than they were “away,” thereby showing women’s self–development through travel. The more recent poststructural turn in studies of Victorian travel writing has focused attention on women’s diverse and fragmented identities as they narrated their travel experiences, emphasizing women’s sense of themselves as women in new locations, but only as they worked through their ties to nation, class, whiteness, and colonial and imperial power structures.</p>
<p>From the passage, we can infer that travel writing is most similar to:</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>feminist writing.</li>
<li>historical fiction.</li>
<li>political journalism.</li>
<li>autobiographical writing.</li>
</ol>Othershttps://aptitude.gateoverflow.in/8164/cat2020-3-14Fri, 17 Sep 2021 13:45:03 +0000