2025 CAT IIM Exam Slot 2: Quantitative Ability

This page organizes my video explanations to all of the 22 quantitative ability questions that are part of the 2025 CAT exam Slot 2. The entire exam in pdf format can be downloaded from this link: 2025 CAT Quant Slot 2: Quantitative Ability.

Question 1: If $9^{x^2+2x-3} – 4\left(3^{x^2+2x-2}\right) + 27 = 0$, then the product of all possible values of $x$ is

$30$

$20$

$15$

Question 2: The average number of copies of a book sold per day by a shopkeeper is $60$ in the initial seven days and $63$ in the initial eight days, after the book launch. On the ninth day, she sells $11$ copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes $66$. The number of copies sold on the first day of the book launch is

Question 3: The set of all real values of $x$ for which $(x^2 – |x+9| + x )> 0$, is

$(-\infty,-3)\cup(3,\infty)$

$(-\infty,-9)\cup(3,\infty)$

$(-9,-3)\cup(3,\infty)$

$(-\infty,-9)\cup(9,\infty)$

Question 4: An item with a cost price of Rs $1650$ is sold at a certain discount on a fixed marked price to earn a profit of $20\%$ on the cost price. If the discount was doubled, the profit would have been Rs $110$. The rate of discount, in percentage, at which the profit percentage would be equal to the rate of discount, is nearest to

$16$

$18$

$14$

$12$

Question 5: If $m$ and $n$ are integers such that $(m+2n)(2m+n)=27$, then the maximum possible value of $2m-3n$ is

Question 6: The sum of digits of the number $(625)^{65}\times(128)^{36}$ is

Question 7: The equations $3x^2 – 5x + p = 0$ and $2x^2 – 2x + q = 0$ have one common root. The sum of the other roots of these two equations is

$\dfrac{8}{3} – p + \dfrac{3}{2}q$

$\dfrac{2}{3} – p + \dfrac{3}{2}q$

$\dfrac{8}{3} + p + \dfrac{1}{3}q$

$\dfrac{2}{3} – 2p + \dfrac{2}{3}q$

Question 8: If $\log_{64} x^2 + \log_{8} \sqrt{y} + 3\log_{512}(\sqrt{y}\,z) = 4$, where $x$, $y$, and $z$ are positive real numbers, then the minimum possible value of $(x + y + z)$ is

$48$

$36$

$24$

$96$

Question 9: Rita and Sneha can row a boat at $5$ km/h and $6$ km/h in still water, respectively. In a river flowing with a constant velocity, Sneha takes $48$ minutes more to row $14$ km upstream than to row the same distance downstream. If Rita starts from a certain location in the river and returns downstream to the same location, taking a total of $100$ minutes, then the total distance, in km, Rita will cover is

Question 10: Suppose $a$, $b$, and $c$ are three distinct natural numbers such that $3ac = 8(a+b)$. Then, the smallest possible value of $3a + 2b + c$ is

Question 11: Let $f(x)=\dfrac{x}{(2x-1)}$ and $g(x)=\dfrac{x}{(x-1)}$. Then, the domain of the function $h(x)=f(g(x)) + g(f(x))$ is all real numbers except

$-1,\ \dfrac{1}{2},\ \text{and } 1$

$\dfrac{1}{2},\ 1,\ \text{and } \dfrac{3}{2}$

$-\dfrac{1}{2},\ \dfrac{1}{2},\ \text{and } 1$

$\dfrac{1}{2}\ \text{and } 1$

Question 12: A loan of Rs $1000$ is fully repaid by two installments of Rs $530$ and Rs $594$, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is

$10$

$11$

Question 13: Two tangents drawn from a point $P$ touch a circle with center $O$ at points $Q$ and $R$. Points $A$ and $B$ lie on $PQ$ and $PR$, respectively, such that $AB$ is also a tangent to the same circle. If $\angle AOB = 50^\circ$, then $\angle APB$, in degrees, equals

Question 14: The number of divisors of $\left(2^{6} \times 3^{5} \times 5^{3} \times 7^{2}\right)$ which are of the form $(3r+1)$, where $r$ is a non-negative integer, is

$56$

$24$

$36$

$42$

Question 15: Let $ABCDEF$ be a regular hexagon and $P$ and $Q$ be the midpoints of $AB$ and $CD$, respectively. Then, the ratio of the areas of trapezium $PBCQ$ and hexagon $ABCDEF$ is

$6:19$

$5:24$

$6:25$

$7:24$

Question 16: If $a, b, c,$ and $d$ are integers such that their sum is $46$, then the minimum possible value of $(a-b)^2 + (a-c)^2 + (a-d)^2$ is

Question 17: The ratio of expenditures of Lakshmi and Meenakshi is $2:3$, and the ratio of income of Lakshmi to expenditure of Meenakshi is $6:7$. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is $4:9$, then the ratio of their incomes is

$3:5$

$5:6$

$2:1$

$7:8$

Question 18: Let $a_n$ be the $n^{\text{th}}$ term of a decreasing infinite geometric progression. If $a_1 + a_2 + a_3 = 52$ and $a_1a_2 + a_2a_3 + a_3a_1 = 624$, then the sum of this geometric progression is

$57$

$54$

$60$

$63$

Question 19: A mixture of coffee and cocoa, $16\%$ of which is coffee, costs Rs $240$ per kg. Another mixture of coffee and cocoa, of which $36\%$ is coffee, costs Rs $320$ per kg. If a new mixture of coffee and cocoa costs Rs $376$ per kg, then the quantity, in kg, of coffee in $10$ kg of this new mixture is

$2.5$

Question 20: In a $\triangle ABC$, points $D$ and $E$ are on the sides $BC$ and $AC$, respectively. $BE$ and $AD$ intersect at point $T$ such that $AD:AT = 4:3$, and $BE:BT = 5:4$. Point $F$ lies on $AC$ such that $DF$ is parallel to $BE$. Then, $BD:CD$ is

$15 : 4$

$11 : 4$

$7 : 4$

$9 : 4$

Question 21: Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after $20$ days. If the job got completed in $60$ days, the number of days needed by Chandan to complete the job alone is

Question 22: A certain amount of money was divided among Pinu, Meena, Rinu, and Seema. Pinu received $20\%$ of the total amount and Meena received $40\%$ of the remaining amount. If Seema received $20\%$ less than Pinu, the ratio of the amounts received by Pinu and Rinu is

$2:1$

$1:2$

$5:8$

$8:5$

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