2020 CAT IIM Exam Slot 3: Quantitative Ability

This page organizes my video explanations to all of the 26 quantitative ability questions that are part of the 2020 CAT exam Slot 3. The entire exam in pdf format can be downloaded from this link: 2020 CAT Quant Slot 3: Quantitative Ability.

Question 1: Let $m$ and $n$ be natural numbers such that $n$ is even and $0.2 < \dfrac{m}{20}, \dfrac{n}{m}, \dfrac{n}{11} < 0.5.$ Then $m-2n$ equals

Question 2: If $\log_a 30=A$, $\log_a\!\left(\dfrac{5}{3}\right)=-B$ and $\log_2 a=\dfrac{1}{3}$, then $\log_3 a$ equals

$\dfrac{A+B-3}{2}$

$\dfrac{A+B}{2}-3$

$\dfrac{2}{A+B-3}$

$\dfrac{2}{A+B}-3$

Question 3: A batsman played $n+2$ innings and got out on all occasions. His average in these $n+2$ innings was $29$; he scored $38$ and $15$ in the last two. In the first $n$ innings, his average was $30$ and the lowest score was $x$. The smallest possible value of $x$ is

Question 4: The points $(2,1)$ and $(-3,-4)$ are opposite vertices of a parallelogram. If the other two vertices lie on the line $x+9y+c=0$, then $c$ is

$12$

$13$

$14$

$15$

Question 5: In the final examination, Bishnu scored $52\%$ and Asha $64\%$. Bishnu’s marks are $23$ less and Asha’s $34$ more than Ramesh’s. The marks of Geeta, who scored $84\%$, is

$417$

$357$

$399$

$439$

Question 6: The vertices of a triangle are $(0,0)$, $(4,0)$, $(3,9)$. The area of the circle through these points is

$\dfrac{14\pi}{3}$

$\dfrac{123\pi}{7}$

$\dfrac{12\pi}{5}$

$\dfrac{205\pi}{9}$

Question 7: Let $k$ be a constant. The equations $kx+y=3$ and $4x+ky=4$ have a unique solution if and only if

$k\ne 2$

$|k|=2$

$|k|\ne 2$

$k=2$

Question 8: Let $m,n$ be positive integers. If $x^{2}+mx+2n=0$ and $x^{2}+2nx+m=0$ have real roots, then the smallest possible value of $m+n$ is

Question 9: A man buys $35$ kg sugar and marks for $20\%$ profit. He sells $5$ kg at this price, $15$ kg at $10\%$ discount; $3$ kg is wasted. He raises the marked price by $p\%$ on the remaining so overall profit is $15\%$. Then $p$ is nearest to

$22$

$25$

$35$

$31$

Question 10: In a trapezium $ABCD$, $AB\parallel DC$, $BC\perp DC$ and $\angle BAD=45^\circ$. If $DC=5$ cm and $BC=4$ cm, the area (in $\text{cm}^2$) is

Question 11: If $a,b,c\ne 0$ and $14^a=36^b=84^c$, then $6b\!\left(\dfrac{1}{c}-\dfrac{1}{a}\right)$ equals

Question 12: A person invested at $10\%$ p.a., compounded half-yearly. After $1.5$ years, amount became ₹$18522$. The invested amount (in ₹) was

Question 13: How many of the integers $1,2,\ldots,120$ are divisible by none of $2,5,7$?

$42$

$43$

$41$

$40$

Question 14: Let $N,x,y$ be positive integers with $N=x+y$, $2 \lt x \lt 10$, $14 \lt y \lt 23$. If $N>25$, how many distinct values are possible for $N$?

Question 15: Anil, Sunil, Ravi run on a $3$ km circular path at $15$, $10$, $8$ km/h. How much distance (km) will Ravi have run when Anil and Sunil meet again first at the start point?

$4.8$

$4.6$

$5.2$

$4.2$

Question 16: Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick’s age is $1$ year less than the average of all three, then Harry’s age (years) is

Question 17: A contractor must construct $6$ km in $200$ days with $140$ people. After $60$ days only $1.5$ km is done. How many additional people are needed to finish exactly on time?

Question 18: $\dfrac{2\cdot 4\cdot 8\cdot 16}{(\log_{2}4)^{2}(\log_{4}8)^{3}(\log_{8}16)^{4}}$ equals

Question 19: If $f(x+y)=f(x)f(y)$ and $f(5)=4$, then $f(10)-f(-10)$ equals

$15.9375$

$14.0625$

Question 20: How many pairs $(a,b)$ of positive integers are there such that $a\le b$ and $ab=4^{2017}$?

$2017$

$2019$

$2018$

$2020$

Question 21: A and B are stations $90$ km apart. Train from A leaves $9{:}00$ am at $40$ km/h. Train from B leaves $10{:}30$ am at $20$ km/h. They meet at

$11{:}20$ $\text{am}$

$10{:}45$ $\text{am}$

$11{:}45$ $\text{am}$

$11{:}00$ $\text{am}$

Question 22: The area enclosed by $x=2$, $y=|x-2|+4$, the axes equals

$12$

$10$

Question 23: If $x_1=-1$ and $x_m=x_{m+1}+(m+1)$ for all positive integers $m$, then $x_{100}$ equals

$-5150$

$-5051$

$-5050$

$-5151$

Question 24: Two alcohol solutions A and B are mixed $1:3$ by volume; the mixture is then doubled by adding A to get $72\%$ alcohol. If A has $60\%$ alcohol, then the percentage of alcohol in B is

$89\%$

$94\%$

$90\%$

$92\%$

Question 25: How many integers in $\{100,101,\ldots,999\}$ have at least one digit repeated?

Question 26: Vimla starts at $9$ am; usual speed $40$ km/h reaches on time; at $35$ km/h she is $6$ minutes late. One day she covers two-thirds of the distance in one-third of usual time, then stops $8$ minutes. The speed (km/h) for the rest to be exactly on time is

$28$

$26$

$29$

$27$

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