The CAT QA section requires speed and accuracy, along with a thorough understanding of the Integers. This article provides a set of MCQs on Integers to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
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CAT MCQs on Integers
1. Let \(n\) and \(m\) be two positive integers such that there are exactly \(41\) integers greater than \(8^m\) and less than \(8^n\) , which can be expressed as powers of \(2\) . Then, the smallest possible value of \(n +m\) is
A
44
B
16
C
42
D
14
2. If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is
A
56
B
59
C
49
D
46
3. Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is
A
6
B
5
C
7
D
4
4. In how many ways can a pair of integers \((x , a)\) be chosen such that \(x^2-2|x|+|a-2|=0\) ?
A
4
B
5
C
6
D
7
5. The number of integers that satisfy the equality \((x^2-5x+7)^{x+1} = 1\) is
A
2
B
3
C
5
D
4
6. For any positive integer n, let f(n) = n(n + 1) if n is even, and f(n) = n + 3 if n is odd. If m is a positive integer such that 8f(m + 1) - f(m) = 2, then m equals
A
13
B
12
C
11
D
10
7. Consider a function ƒ satisfying ƒ(x + y) = ƒ(x)ƒ(y) where x,y are positive integers , and ƒ(1) = 2 . If ƒ(a+1) + ƒ(a+2) + ... + ƒ(a+n) = 16(2n - 1) then a is equal to
A
4
B
1
C
3
D
2
8. What is the largest positive integer n such that \(\frac{n^2+7n+12}{n^2-n-12}\) is also a positive integer?
A
8
B
12
C
16
D
6
9. The sum of the squares of three consecutive integers is 194. Find the integers.
A
7, 8, 9
B
6, 7, 8
C
5, 6, 7
D
8, 9, 10
10. (BE)2 = MPB, where B, E, M and P are distinct integers. Then M =
A
2
B
3
C
9
D
None of these
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