2023 CAT Exam Slot 2: Quantitative Ability

This page organizes my video explanations to all of the 22 quantitative ability questions that are part of the 2023 CAT exam Slot 2. The entire exam in pdf format can be downloaded from this link: 2023 CAT Quant Slot 2: Quantitative Ability.

Question 1: Let $a, b, m$ and $n$ be natural numbers such that $a > 1$ and $b>1$. If $a^m b^n = 144^{145}$, then the largest possible value of $n-m$ is

$\quad 579$

$\quad 580$

$\quad 289$

$\quad 290$

Video Explanation

Question 2: For any natural numbers $m, n,$ and $k$ such that $k$ divides both $m+2n$ and $3m+4n$, $k$ must be a common divisor of

$\quad$ $2m$ and $n$

$\quad$ $2m$ and $3n$

$\quad$ $m$ and $n$

$\quad$ $m$ and $2n$

Video Explanation

Question 3: The sum of all possible values of $x$ satisfying the equation $2^{4x^2} – 2^{2x^2+x+16} + 2^{2x+30} = 0$, is

$\quad 3$

$\quad \displaystyle \frac{5}{2}$

$\quad \displaystyle \frac{1}{2}$

$\quad \displaystyle \frac{3}{2}$

Video Explanation

Question 4: Any non-zero real numbers $x, y$ such that $y \neq 3$ and $\displaystyle \frac{x}{y} \lt \frac{x+3}{y-3}$, will satisfy the condition

$\quad \displaystyle \frac{x}{y} \lt \frac{y}{x}$

$\quad$If $y>10$, then $-x>y$

$\quad$If $x \lt 0$, then $-x \lt y$

$\quad$If $y \lt 0$, then $-x \lt y$

Video Explanation

Question 5: The number of positive integers less than $50$, having exactly two distinct factors other than 1 and itself, is

Video Explanation

Question 6: For some positive real number $x$, if $\log_{\sqrt{3}} {(x)} + \displaystyle \frac{\log_{x} (25)}{\log_{x} {(0.008)}} = \frac{16}{3}$, then the value of $\log_{3} {(3x^2)}$ is

Video Explanation

Question 7: Let $k$ be the largest integer such that the equation $(x-1)^2+2kx+11=0$ has no real roots. If $y$ is a positive real number, then the least possible value of $\displaystyle \frac{k}{4y} + 9y$ is

Video Explanation

Question 8: In a company, $20\%$ of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees is

$\quad 5:4$

$\quad 4:5$

$\quad 6:5$

$\quad 5:6$

Video Explanation

Question 9: Pipes $A$ and $C$ are fill pipes while Pipe $B$ is a drain pipe of a tank. Pipe $B$ empties the full tank in one hour less than the time taken by Pipe $A$ to fill the empty tank. When pipes $A$, $B$ and $C$ are turned on together, the empty tank is filled in two hours. If pipes $B$ and $C$ are turned on together when the tank is empty and Pipe $B$ is turned off after one hour, then Pipe $C$ takes another one hour and $15$ minutes to fill the remaining tank. If Pipe $A$ can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe $C$ to fill the empty tank is

$\quad 120$

$\quad 60$

$\quad 90$

$\quad 75$

Video Explanation

Question 10: Anil borrows Rs $2$ lakhs at an interest rate of $8\%$ per annum, compounded half-yearly. He repays Rs $10320$ at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to

$\quad 40991$

$\quad 45311$

$\quad 33130$

$\quad 51311$

Video Explanation

Question 11: The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing $18$ units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be $288000$. Then, the price of the original precious stone is

$\quad 972000$

$\quad 1944000$

$\quad 1620000$

$\quad 1296000$

Video Explanation

Question 12: Minu purchases a pair of sunglasses at Rs.$1000$ and sells to Kanu at $20\%$ profit. Then, Kanu sells it back to Minu at $20\%$ loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs.$500$, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is

$\quad 26\%$

$\quad 52\%$

$\quad 35.42\%$

$\quad 31.25\%$

Video Explanation

Question 13: Ravi is driving at a speed of $40$ km/h on a road. Vijay is $54$ meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of $50$ km/h and is $225$ meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is

$\quad 64.4$

$\quad 67.2$

$\quad 61.6$

$\quad 58.8$

Video Explanation

Question 14: Jayant bought a certain number of white shirts at the rate of Rs $1000$ per piece and a certain number of blue shirts at the rate of Rs $1125$ per piece. For each shirt, he then set a fixed market price which was $25\%$ higher than the average cost of all the shirts. He sold all the shirts at a discount of $10\%$ and made a total profit of Rs $51000$. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is

Video Explanation

Question 15: A container has $40$ liters of milk. Then, $4$ liters are removed from the container and replaced with $4$ liters of water. This process of replacing $4$ liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is

Video Explanation

Question 16: If a certain amount of money is divided equally among $n$ persons, each one receives Rs $352$. However, if two persons receive Rs $506$ each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs $330$. Then, the maximum possible value of $n$ is

Video Explanation

Question 17: A triangle is drawn with its vertices on the circle $C$ such that one of its sides is a diameter of $C$ and the other two sides have their lengths in the ratio of $a:b$. If the radius of the circle is $r$, then the area of the triangle is

$\quad \displaystyle \frac{4abr^2}{a^2+b^2}$

$\quad \displaystyle \frac{2abr^2}{a^2+b^2}$

$\quad \displaystyle \frac{abr^2}{a^2+b^2}$

$\quad \displaystyle \frac{abr^2}{2(a^2+b^2)}$

Video Explanation

Question 18: In a rectangle $ABCD$, $AB = 9$ cm and $BC = 6$ cm. $P$ and $Q$ are two points on $BC$ such that the areas of the figures $ABP$, $APQ$, and $AQCD$ are in geometric progression. If the area of the figure $AQCD$ is four times the area of triangle $ABP$, then $BP : PQ : QC$ is

$\quad 1:2:4$

$\quad 1:2:1$

$\quad 2:4:1$

$\quad 1:1:2$

Video Explanation

Question 19: The area of the quadrilateral bounded by the $Y-$axis, the line $x=5$, and the lines $|x-y|-|x-5|=2$, is

Video Explanation

Question 20: If $p^2+q^2-29=2pq-20=52-2pq$, then the difference between the maximum and minimum possible value of $(p^3-q^3)$ is

$\quad 486$

$\quad 378$

$\quad 189$

$\quad 243$

Video Explanation

Question 21: Let both the series $a_1, a_2, a_3, \ldots$ and $b_1, b_2, b_3, \ldots$ be in arithmetic progression such that the common differences of both the series are prime numbers. If $a_5 = b_9$, $a_{19}=b_{19}$ and $b_2=0$, then $a_{11}$ equals

$\quad 83$

$\quad 86$

$\quad 79$

$\quad 84$

Video Explanation

Question 22: Let $a_n$ and $b_n$ be two sequences such that $a_n=13+6(n-1)$ and $b_n = 15+7(n-1)$ for all natural numbers $n$. Then, the largest three digit integer that is common to both these sequences, is

Video Explanation