CAT Practice Test 2026

About the CAT exam

The Common Admission Test (CAT) is a mba & business examination administered in India. It is designed to assess candidates' knowledge and proficiency across 3 key subject areas including Verbal Ability & Reading Comprehension, Data Interpretation & Logical Reasoning, Quantitative Aptitude. This exam is widely recognized as an essential benchmark for students and professionals.

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8 free CAT practice questions (2026)

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1. Two trains start at the same time from points A and B towards each other. After crossing each other, they take 4 hours and 9 hours respectively to reach B and A. If the speed of the first train is 60 km/h, what is the speed of the second train?

   • 40 km/h
   • 45 km/h
   • 90 km/h
   • 30 km/h
   Show answer & explanation

   Answer: A. 40 km/h

   Using the relation between speeds and times after crossing each other: S1 / S2 = sqrt(T2 / T1). Here, S1 = 60 km/h, T1 = 4 hours, and T2 = 9 hours. Thus, 60 / S2 = sqrt(9 / 4) = 3 / 2. Solving for S2 gives S2 = (60 * 2) / 3 = 40 km/h.

   Topic: Quantitative Aptitude · easy

2. Find the value of x that satisfies the equation: log_3(x) + log_9(x) + log_27(x) + log_81(x) = 25/4.

   • 9
   • 27
   • 81
   • 243
   Show answer & explanation

   Answer: B. 27

   Change all bases to 3: log_3(x) + (1/2)log_3(x) + (1/3)log_3(x) + (1/4)log_3(x) = 25/4. Factoring out log_3(x) gives log_3(x) * (1 + 1/2 + 1/3 + 1/4) = 25/4. The sum in parentheses is 25/12. So, log_3(x) * (25/12) = 25/4, which simplifies to log_3(x) = 3. Therefore, x = 3^3 = 27.

   Topic: Quantitative Aptitude · medium

3. What is the remainder when 7^103 is divided by 25?

   • 7
   • 18
   • 14
   • 21
   Show answer & explanation

   Answer: B. 18

   Using Euler's Totient function, phi(25) = 20. By Euler's Theorem, 7^20 = 1 (mod 25). Therefore, 7^103 = (7^20)^5 * 7^3 = 1^5 * 343 = 343 (mod 25). Since 343 = 25 * 13 + 18, the remainder is 18.

   Topic: Quantitative Aptitude · medium

4. In a triangle ABC, the lengths of sides AB, BC, and CA are 13, 14, and 15 respectively. A line parallel to BC cuts AB at D and AC at E such that the area of quadrilateral BDEC is equal to the area of triangle ADE. Find the length of DE.

   • 7 * sqrt(2)
   • 7
   • 14 * (sqrt(2) - 1)
   • 10
   Show answer & explanation

   Answer: A. 7 * sqrt(2)

   Since DE is parallel to BC, triangle ADE is similar to triangle ABC. Let the area of triangle ADE be A_1 and the area of quadrilateral BDEC be A_2. We are given A_1 = A_2. Thus, the area of triangle ABC = A_1 + A_2 = 2 * A_1. The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides: Area(ADE) / Area(ABC) = (DE / BC)^2 => 1/2 = (DE / 14)^2. Solving for DE gives DE = 14 / sqrt(2) = 7 * sqrt(2).

   Topic: Quantitative Aptitude · medium

5. A vessel contains 80 liters of pure milk. 8 liters of milk is replaced by 8 liters of water. This process is repeated two more times. What is the ratio of milk to water in the final mixture?

   • 729:271
   • 729:1000
   • 81:19
   • 243:91
   Show answer & explanation

   Answer: A. 729:271

   The formula for the remaining quantity of original liquid is Q = I * (1 - x/V)^n. Here, I = 80, x = 8, V = 80, and n = 3. Remaining Milk = 80 * (1 - 8/80)^3 = 80 * (9/10)^3 = 80 * (729/1000) = 58.32 liters. The quantity of water is 80 - 58.32 = 21.68 liters. The ratio of milk to water is 58.32 : 21.68 = 729 : 271.

   Topic: Quantitative Aptitude · easy

6. If the roots of the quadratic equation x^2 - px + q = 0 are two consecutive integers, then which of the following is true?

   • p^2 - 4q = 1
   • p^2 - 4q = 0
   • p^2 + 4q = 1
   • p^2 - 4q = -1
   Show answer & explanation

   Answer: A. p^2 - 4q = 1

   Let the roots be n and n+1. The sum of the roots is p = 2n + 1, and the product of the roots is q = n(n+1). Substituting these into the expression p^2 - 4q gives (2n+1)^2 - 4n(n+1) = 4n^2 + 4n + 1 - 4n^2 - 4n = 1.

   Topic: Quantitative Aptitude · easy

7. In how many ways can 5 distinct balls be distributed into 3 identical boxes such that no box remains empty?

   • 25
   • 150
   • 50
   • 125
   Show answer & explanation

   Answer: A. 25

   This is equivalent to partitioning a set of 5 elements into 3 non-empty subsets (Stirling numbers of the second kind, S(5,3)). The possible partition sizes are {3, 1, 1} and {2, 2, 1}. For {3, 1, 1}, the number of ways is 5C3 * 2C1 * 1C1 / 2! = 10. For {2, 2, 1}, the number of ways is 5C2 * 3C2 * 1C1 / 2! = 15. Total ways = 10 + 15 = 25.

   Topic: Quantitative Aptitude · medium

8. Three fair six-sided dice are rolled. What is the probability that the sum of the numbers shown is a prime number?

   • 73/216
   • 79/216
   • 67/216
   • 5/18
   Show answer & explanation

   Answer: A. 73/216

   The total outcomes are 6^3 = 216. The sum of 3 dice ranges from 3 to 18. The prime sums possible are 3, 5, 7, 11, 13, and 17. The number of ways to get these sums are: Sum 3 (1 way), Sum 5 (6 ways), Sum 7 (15 ways), Sum 11 (27 ways), Sum 13 (21 ways), and Sum 17 (3 ways). Summing these up gives 1 + 6 + 15 + 27 + 21 + 3 = 73 ways. Thus, the probability is 73/216.

   Topic: Quantitative Aptitude · hard

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CAT Exam Subjects

Available practice subjects: Verbal Ability & Reading Comprehension, Data Interpretation & Logical Reasoning, Quantitative Aptitude. Select a subject for focused preparation. Coverage is not a guarantee of the complete official syllabus.

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