2025 CAT IIM Exam Slot 3: 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 3. The entire exam in pdf format can be downloaded from this link: 2025 CAT Quant Slot 3: Quantitative Ability.

Question 1: If $\left(x^2 + \dfrac{1}{x^2}\right) = 25$ and $x > 0$, then the value of $\left(x^7 + \dfrac{1}{x^7}\right)$ is

$44853\sqrt{3}$

$44856\sqrt{3}$

$44859\sqrt{3}$

$44850\sqrt{3}$

Question 2: The monthly sales of a product from January to April were $120$, $135$, $150$ and $165$ units, respectively. The cost price of the product was Rs. $240$ per unit, and a fixed marked price was used for the product in all the four months. Discounts of $20\%$, $10\%$ and $5\%$ were given on the marked price per unit in January, February and March, respectively, while no discounts were given in April. If the total profit from January to April was Rs. $138825$, then the marked price per unit, in rupees, was

$520$

$525$

$510$

$515$

Question 3: Teams $A$, $B$, and $C$ consist of five, eight, and ten members, respectively, such that every member within a team is equally productive. Working separately, teams $A$, $B$, and $C$ can complete a certain job in $40$ hours, $50$ hours, and $4$ hours, respectively. Two members from team $A$, three members from team $B$, and one member from team $C$ together start the job, and the member from team $C$ leaves after $23$ hours. The number of additional member(s) from team $B$ that would be required to replace the member from team $C$, to finish the job in the next one hour, is

Question 4: In a school with $1500$ students, each student chooses any one of the streams out of science, arts, and commerce, by paying a fee of Rs $1100$, Rs $1000$, and Rs $800$, respectively. The total fee paid by all the students is Rs $15{,}50{,}000$. If the number of science students is not more than the number of arts students, then the maximum possible number of science students in the school is

Question 5: In an arithmetic progression, if the sum of fourth, seventh and tenth terms is $99$, and the sum of the first fourteen terms is $497$, then the sum of the first five terms is

Question 6: Ankita walks from $A$ to $C$ through $B$, and runs back through the same route at a speed that is $40\%$ more than her walking speed. She takes exactly $3$ hours $30$ minutes to walk from $B$ to $C$ as well as to run from $B$ to $A$. The total time, in minutes, she would take to walk from $A$ to $B$ and run from $B$ to $C$, is

Question 7: For a $4$-digit number (greater than $1000$), the sum of the digits in the thousands, hundreds, and tens places is $15$. The sum of the digits in the hundreds, tens, and units places is $16$. Also, the digit in the tens place is $6$ more than the digit in the units place. The difference between the largest and smallest possible value of the number is

$811$

$3289$

$735$

$4078$

Question 8: Rahul starts on his journey at $5$ pm at a constant speed so that he reaches his destination at $11$ pm the same day. However, on his way, he stops for $20$ minutes, and after that, increases his speed by $3$ km per hour to reach on time. If he had stopped for $10$ minutes more, he would have had to increase his speed by $5$ km per hour to reach on time. His initial speed, in km per hour, was

$12$

$15$

$18$

$20$

Question 9: The rate of water flow through three pipes $A$, $B$, and $C$ are in the ratio $4 : 9 : 36$. An empty tank can be filled up completely by pipe $A$ in $15$ hours. If all the three pipes are used simultaneously to fill up this empty tank, the time, in minutes, required to fill up the entire tank completely is nearest to

$73$

$78$

$76$

$71$

Question 10: If $f(x) = (x^2 + 3x)(x^2 + 3x + 2)$, then the sum of all real roots of the equation $\sqrt{f(x) + 1} = 9701$ is

$-6$

$-3$

Question 11: For real values of $x$, the range of the function $f(x) = \displaystyle \frac{2x – 3}{2x^2 + 4x – 6}$ is

$(-\infty, \dfrac{1}{8}] \cup [1, \infty)$

$(-\infty, \dfrac{1}{4}] \cup [1, \infty)$

$(-\infty, \dfrac{1}{8}] \cup [\dfrac{1}{2}, \infty)$

$(-\infty, \dfrac{1}{4}] \cup [\dfrac{1}{2}, \infty)$

Question 12: The sum of all the digits of the number $\left(10^{50} + 10^{25} – 123\right)$ is

$212$

$221$

$324$

$255$

Question 13: A triangle $ABC$ is formed with $AB = AC = 50$ cm and $BC = 80$ cm. Then, the sum of the lengths, in cm, of all three altitudes of triangle $ABC$ is

Question 14: In a class of $150$ students, $75$ students chose physics, $111$ students chose mathematics, and $40$ students chose chemistry. All students chose at least one of the three subjects and at least one student chose all three subjects. The number of students who chose both physics and chemistry is equal to the number of students who chose both chemistry and mathematics, and this is half the number of students who chose both physics and mathematics. The maximum possible number of students who chose physics but not mathematics is

$30$

$35$

$40$

$55$

Question 15: The sum of all possible real values of $x$ for which $\log_{x-3}(x^2 – 9) = \log_{x-3}(x + 1) + 2$ is

$-3$

$\sqrt{33}$

$\dfrac{3 + \sqrt{33}}{2}$

Question 16: The average salary of $5$ managers and $25$ engineers in a company is $60000$ rupees. If each of the managers received a $20\%$ salary increase while the salary of the engineers remained unchanged, the average salary of all $30$ employees would have increased by $5\%$. The average salary, in rupees, of the engineers is

$45000$

$50000$

$54000$

$40000$

Question 17: $ABCD$ is a trapezium in which $AB$ is parallel to $DC$, $AD$ is perpendicular to $AB$, and $AB = 3DC$. If a circle inscribed in the trapezium touching all the sides has a radius of $3$ cm, then the area, in sq. cm, of the trapezium is

$48$

$30\sqrt{3}$

$36\sqrt{2}$

$54$

Question 18: If $12^{12x} \times 4^{24x+12} \times 5^{2y} = 8^{4z} \times 20^{12x} \times 243^{3x-6}$, where $x$, $y$ and $z$ are natural numbers, then $x+y+z$ equals

Question 19: In $\triangle ABC$, $AB = AC = 12$ cm and $D$ is a point on side $BC$ such that $AD = 8$ cm. If $AD$ is extended to a point $E$ such that $\angle ACB = \angle AEB$, then the length, in cm, of $AE$ is

$20$

$16$

$18$

$14$

Question 20: Vessels $A$ and $B$ contain $60$ litres of alcohol and $60$ litres of water, respectively. A certain volume is taken out from $A$ and poured into $B$. After stirring, the same volume is taken out from $B$ and poured into $A$. If the resultant ratio of alcohol and water in $A$ is $15:4$, then the volume, in litres, initially taken out from $A$ is

Question 21: The ratio of the number of coins in boxes $A$ and $B$ was $17:7$. After $108$ coins were shifted from box $A$ to box $B$, this ratio became $37:20$. The number of coins that needs to be shifted further from $A$ to $B$, to make this ratio $1:1$, is

Question 22: Let $p$, $q$ and $r$ be three natural numbers such that their sum is $900$, and $r$ is a perfect square whose value lies between $150$ and $500$. If $p$ is not less than $0.3q$ and not more than $0.7q$, then the sum of the maximum and minimum possible values of $p$ is

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