CAT Quantitative Ability & Data Interpretation PYQ | Prasnya

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In a battle, the commander-in-chief arranges his soldiers in a formation of three concentric circles. The radii of the circles are in an arithmetic progression: the smallest radius is 70m (meters) and the largest is 140m. If each soldier is to be separated from the adjacent soldiers standing on the same circle by 1m, how many soldiers are required to complete the formation? (Consider

\pi = \frac{22}{7}

04 January 2026

In a business school, only three specializations are offered: marketing, finance and operations. A student can opt for either one, or two, or no specializations. In the current batch of 120 students, 60 are specializing in marketing, 50 are specializing in finance and 30 are specializing in operations. During the placement process, all students specializing either in marketing or in finance are shortlisted for consulting job interviews. If 45 students are not shortlisted for consulting job interviews, what is the MINIMUM possible number of students specializing in both marketing and finance?

04 January 2026

An archer, from the point A, is aiming at a target, placed on the top of a 56 feet tall tree. The base of the tree is at the point C. From the archer’s position, the angle of elevation to the target is 45

^\circ

from his eye level. The archer, facing the tree, moves backwards on the straight line joining the points A and C, to a new position at the point B. From the point B, the angle of elevation from his eye level to the target becomes 30

^\circ

. How far did the archer move from A to B (in feet) if his eye level is at a height of 6 feet from the ground?

04 January 2026

Two buses travel between Jamshedpur and Kolkata in the opposite directions, on the same road. On that road, the maximum allowed speeds are different (but constant) for the opposite directions. Usually, both buses travel at the respective maximum allowed speeds to their respective destinations: the bus from Jamshedpur to Kolkata takes 4 hours, while the bus from Kolkata to Jamshedpur takes 3 hours. One day, the two buses start at the same time. However, one hour after starting, the bus from Jamshedpur to Kolkata reduces its speed to half of its maximum allowed speed due to congestion on the road. If both buses do not stop anywhere in between, how many hours after starting do they meet?

04 January 2026

Consider a seven-digit number 735x6y4, divisible by 44, where the two digits x and y are unknown. Consider the following two additional pieces of information: I. x and y are even numbers II. x and y are equal To determine the values of x and y UNIQUELY, which of the above pieces of information is/are MINIMALLY SUFFICIENT?

04 January 2026

The swimming pool in an exclusive club is a circular strip. A water flow is artificially maintained in the strip, along a clockwise direction, at a constant speed of 3km/h (kilometers/hour). One morning, Ayub and Rana start swimming at the same time from two diametrically opposite points on the strip. Ayub swims in a counterclockwise direction, while Rana swims in a clockwise direction. They swim at constant, but different, speeds. When they meet for the first time, Ayub has covered 60m (meters). They meet again after Rana has covered 180m from the first meeting point. If Rana swims at the speed of 3 km/h in still water, how long does Ayub take to complete one round of the circular strip, if he swims in the clockwise direction?

04 January 2026

125 is multiplied by either 10 or 15. The resultant number is again multiplied by either 10 or 15. This process continues. Which of the following CANNOT be a resultant number at any point in time?

04 January 2026

Three categories of candidates appear for an admission test: diligent (10%), lazy (30%) and confused (60%). A diligent candidate is 10 times more likely to clear the admission test compared to a lazy candidate. If 40% of the candidates clearing the admission test are confused, what is the MAXIMUM possible value of the probability of a confused candidate clearing the test? A B C 2/3 D 6/7 E 37/100

04 January 2026

In a multiple-choice examination, there are 20 questions. Each correct answer is worth 4 marks, while 2 marks are to be deducted for every wrong answer. Further, 1 mark is to be deducted for every unattempted question. One student receives a total of 46 marks in the examination. However, before releasing the marks, the professor realizes that she has, by mistake, deducted 2 marks for every unattempted question and 1 mark for every wrong answer. After correction, how many marks will the student get?

04 January 2026

f: \mathbb{R}^{2} \to \mathbb{R}

be a real-valued function defined as

f(0, y) = y + 1

f(x + 1, y) = f\!\left(x, f(x, y)\right) + x.

What is the value of

f(2, 2)

04 January 2026

a_1<a_2<\cdots<a_n

be the list of all prime numbers less than

25

\text{Define } X_i = \frac{b_i}{a_i},

b_i

is the sum of all

a_k

k

1

n, \; k\neq i

B

be the set of all integer-valued

X_i

. What is the smallest element of

B

04 January 2026

Consider two circles, each having radius of 5cm (centimeters), touching each other at a point P. A direct tangent QR is drawn touching one circle at a point Q and the other circle at a point R. Inside the region PQR inscribed by the two circles and the tangent, a square ABCD is inscribed with its base AB on the tangent and the other side touching the two circles at points D and C, respectively. Find the area of the square ABCD.

04 January 2026

Rajan is a fruit seller. On any day, he sells only one kind of fruit. On the first day, he buys 9 kg of blueberries. On the second day, he buys 22 kg of kiwis. On the third day, he buys 50 kg of peaches. The per kg purchase price of each fruit is an integer. Further, on each of these three days, he spends the same amount to purchase fruits. On the fourth day, he buys mangoes at Rs. 35/kg and spends Rs. 15 less than any of the previous three days. If he then sells all the mangoes at Rs. 50/kg, what is his MINIMUM possible profit on the fourth day?

04 January 2026

How many solutions

(x, y, z)

of the equation

x + y^2 + z^3 = 50

exist, where x, y and z are positive integers?

04 January 2026

A triangular plot is such that two of its sides, of lengths 90m (meter) and 60m, are perpendicular to each other. There is a housing complex in a rectangular region within the plot. The area of the rectangular region is 4/9th of the area of the triangular plot. Additionally, two sides of the rectangular region lie on the two perpendicular sides of the triangle, and one vertex is on the hypotenuse. The members of the housing complex want to construct a wall along the perimeter of the rectangular region. If the cost of construction is Rs. 5000/m, what is the MINIMUM possible cost of building the wall?

04 January 2026

During Durga Puja, for the purpose of lighting, one puja pandal in Kolkata used many identical structures made of wooden sticks. The design of the structures was as follows: each structure was constructed with the help of six wooden sticks by combining an isosceles triangular structure, and a square structure, with the bases of both structures being the same. Let us take one such structure. Call the triangle PAB, with PA = PB, and the square ABCD, with AB being the same wooden stick as a common base for the triangle and the square. To make the structure strong, the two equal sides of the triangular structure were tied with the opposite side of square’s base, i.e., CD, at points E and F, in such a way that CE = EF = FD. The structure was hung from P. If AB = 0.5m (meter), the total length of wooden sticks required for twenty such structures is: A 70m B C D E x, y, z ( ) x + y + 2 z = 3 50 20 + 1 m ( 5 ) 10 + 4 m ( 10 ) 40 + 1 m ( 3 ) 40 m 3

04 January 2026

A park has two gates, Gate 1 and Gate 2. These two gates are connected via two alternate paths. If one takes the first path from Gate 1, they need to walk 80m (meters) towards east, then 80m towards south, and finally 20m towards west to arrive at Gate 2. The second path is a semi-circle connecting the two gates, where the diameter of the semi-circle is the straight-line distance between the two gates. A person walking at a constant speed of 5 kilometers/hour enters the park through Gate 1, walks along the first path to reach Gate 2 and then takes the second path to come back to Gate 1. Which of the following is the CLOSEST to the time the person takes, from entering the park to coming back to Gate 1, if she never stops in between?

04 January 2026

Ronny uses a 5-digit key for a combination lock, where 5 digits need to be entered in a fixed sequence. While he remembers that the 5 digits are 9, 8, 7, 5 and 4, he has forgotten the sequence he uses. He also remembers that the sum of the first three digits is a multiple of 3, and so is the sum of the last three digits. Further, the sum of the last four digits is a multiple of 4. Which of the following is DEFINITELY FALSE?

04 January 2026

There are three rectangular tanks in a building. The length, width and height of the first tank are m meters each, and the length, width and height of the second tank are n meters each. However, the length, width and height of the third tank are m meters, n meters and 1 meter, respectively.Initially, the first tank is full of water, while the second and the third are empty. When the second and the third tanks are completely filled with water transferred from the first tank, 85,000 liters of water is still left in the first tank. If both m and n are positive integers, what is the value of m? (1 meter =1000 liters)

04 January 2026

What is the interest owed by Chhuttan to Brijbhushan at the end of the year?

04 January 2026

What is the MAXIMUM possible value of the total loan Brijbhushan has given to these five farmers?

04 January 2026

If the width of the Aditya’s plot is 25 meters, what is the MINIMUM possible length of Binod’s plot?

04 January 2026

Based on the given information and the sunburst chart, the MOST LIKELY values of u, v and w, respectively, are:

04 January 2026

Based on the given information and the sunburst chart, which of the following has the HIGHEST number of employees?

04 January 2026

Based on the given information and the sunburst chart, which of the following statements CANNOT BE TRUE?

04 January 2026

What BEST can be said about the value of x?

04 January 2026

What BEST can be said about the value of y?

04 January 2026

What BEST can be said about the profit generated by Upanshu at the end of his probation period?

04 January 2026