2025 CAT IIM Exam Slot 1: 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 1. The entire exam in pdf format can be downloaded from this link: 2025 CAT Quant Slot 1: Quantitative Ability.

Question 1: A value of $c$ for which the minimum value of $f(x)=x^{2}-4cx+8c$ is greater than the maximum value of $g(x)=-x^{2}+3cx-2c$ is:

$\dfrac{1}{2}$

$-\dfrac{1}{2}$

$-2$

Question 2: Shruti travels a distance of $224$ km in four parts for a total travel time of $3$ hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of $960$ meters per minute for $30$ minutes to cover the first part, then the distance, in meters, she travels in the fourth part is:

$76800$

$112000$

$96000$

$86400$

Question 3: In a $3$-digit number $N$, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of $N$ is:

Question 4: Let $3 \le x \le 6$ and $[x^{2}] = [x]^{2}$, where $[x]$ is the greatest integer not exceeding $x$. If set $S$ represents all feasible values of $x$, then a possible subset of $S$ is:

$(3,\sqrt{10}) \cup [5,\sqrt{26}) \cup \{6\}$

$[3,\sqrt{10}] \cup [5,\sqrt{26}]$

$[3,\sqrt{10}] \cup [4,\sqrt{17}] \cup \{6\}$

$(4,\sqrt{18}) \cup [5,\sqrt{27}) \cup \{6\}$

Question 5: Stocks $A$, $B$, and $C$ are priced at ₹$120$, ₹$90$, and ₹$150$ per share, respectively. A trader holds a portfolio consisting of $10$ shares of stock $A$, and $20$ shares of stocks $B$ and $C$ put together. If the total value of her portfolio is ₹$3300$, then the number of shares of stock $B$ that she holds is:

Question 6: For any natural number $k$, let $a_k = 3^{k}$. The smallest natural number $m$ for which $\{(a_1)^1 \times (a_2)^2 \times \cdots \times (a_{20})^{20}\} < \{a_{21} \times a_{22} \times \cdots \times a_{20+m}\}$ is:

$58$

$59$

$56$

$57$

Question 7: The number of distinct integers $n$ for which $\log_{\left(\tfrac14\right)}(n^{2}-7n+11) > 0$ is:

$\text{infinite}$

Question 8: The number of distinct pairs of integers $(x,y)$ satisfying $x > y \ge 3$ and $x + y < 14$ is:

Question 9: At a certain simple rate of interest, a given sum amounts to ₹$13920$ in $3$ years, and to ₹$18960$ in $6$ years and $6$ months. If the same given sum had been invested for $2$ years at the same rate as before but with interest compounded every $6$ months, then the total interest earned, in rupees, would have been nearest to:

$3221$

$3180$

$3150$

$3096$

Question 10: A container holds $200$ litres of a solution of acid and water, having $30\%$ acid by volume. Atul replaces $20\%$ of this solution with water, then replaces $10\%$ of the resulting solution with acid, and finally replaces $15\%$ of the solution thus obtained with water. The percentage of acid by volume in the final solution obtained after these three replacements is nearest to:

$23$

$25$

$29$

$27$

Question 11: In a class, there were more than $10$ boys and a certain number of girls. After $40\%$ of the girls and $60\%$ of the boys left the class, the remaining number of girls was $8$ more than the remaining number of boys. Then, the minimum possible number of students initially in the class was:

Question 12: A cafeteria offers $5$ types of sandwiches. For each type, a customer can choose one of $4$ breads and opt for either a small or large sized sandwich. Optionally, the customer may also add up to $2$ out of $6$ available sauces. The number of different ways in which an order can be placed for a sandwich is:

$880$

$840$

$800$

$600$

Question 13: In the set of consecutive odd numbers $\{1,3,5,\ldots,57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals:

$41$

$39$

$43$

$37$

Question 14: Arun, Varun, and Tarun, if working alone, can complete a task in $24$, $21$, and $15$ days, respectively. They charge ₹$2160$, ₹$2400$, and ₹$2160$ per day, respectively, even if they are employed for a partial day. If the task needs to be completed in $10$ days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is:

$38400$

$38880$

$34400$

$47040$

Question 15: Kamala divided her investment of ₹$100000$ between stocks, bonds, and gold. Her investment in bonds was $25\%$ of her investment in gold. With annual returns of $10\%$, $6\%$, and $8\%$ on stocks, bonds, and gold, respectively, she gained a total amount of ₹$8200$ in one year. The amount, in rupees, that she gained from the bonds was:

Question 16: If $a – 6b + 6c = 4$ and $6a + 3b – 3c = 50$, where $a$, $b$, and $c$ are real numbers, the value of $2a + 3b – 3c$ is:

$20$

$14$

$18$

$15$

Question 17: The $(x,y)$ coordinates of vertices $P$, $Q$, and $R$ of a parallelogram $PQRS$ are $(-3,-2)$, $(1,-5)$, and $(9,1)$, respectively. If the diagonal $SQ$ intersects the $x$-axis at $(a,0)$, then the value of $a$ is:

$\dfrac{27}{7}$

$\dfrac{10}{3}$

$\dfrac{13}{4}$

$\dfrac{29}{9}$

Question 18: In a circle with center $C$ and radius $6\sqrt{2}$ cm, $PQ$ and $SR$ are two parallel chords separated by one of the diameters. If $\angle PQC = 45^\circ$, and the ratio of the perpendicular distances of $PQ$ and $SR$ from $C$ is $3:2$, then the area, in square centimeters, of the quadrilateral $PQRS$ is:

$4(3+\sqrt{14})$

$4(3\sqrt{2}+\sqrt{7})$

$20(3+\sqrt{14})$

$20(3\sqrt{2}+\sqrt{7})$

Question 19: The ratio of the number of students in the morning shift and afternoon shift of a school was $13:9$. After $21$ students moved from the morning shift to the afternoon shift, this ratio became $19:14$. Next, some new students joined the morning and afternoon shifts in the ratio $3:8$, and then the ratio of the number of students in the morning shift and the afternoon shift became $5:4$. The number of new students who joined is:

$110$

$88$

$121$

$99$

Question 20: If the length of a side of a rhombus is $36$ cm and the area of the rhombus is $396$ sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is:

Question 21: The number of non-negative integer values of $k$ for which the quadratic equation $x^2 – 5x + k = 0$ has only integer roots, is:

Question 22: A shopkeeper offers a discount of $22\%$ on the marked price of each chair, and gives $13$ chairs to a customer for the discounted price of $12$ chairs to earn a profit of $26\%$ on the transaction. If the cost price of each chair is ₹$100$, then the marked price, in rupees, of each chair is:

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