XAT Basics of Numbers MCQs with Solutions: Practice XAT Previous Year Questions (PYQs)

Senior Content Strategist | MBA Professional | Updated 3+ months ago

Basics of Numbers is an important topic in the Quantitative Ability and Data Interpretation section in XAT exam. Practising this topic will increase your score overall and make your conceptual grip on XAT exam stronger.

This article gives you a full set of XAT Basics of Numbers MCQs with explanations and XAT previous year questions (PYQs) for effective practice. Practice of Quantitative Ability and Data Interpretation MCQs including Basics of Numbers questions regularly will improve accuracy, speed, and confidence in the XAT 2026 exam.

XAT Basics of Numbers MCQs with Solutions

1.
Solve for the number of integral values of \(x: \frac{(x^2-15x+47)(x-13)}{(x-8)}<0\).
- 5
- 6
- 7
- 8
- 3
View Solution
2.
Amit has forgotten his 4-digit locker key. He remembers that all the digits are positive integers and are different from each other. Moreover, the fourth digit is the smallest and the maximum value of the first digit is 3. Also, he recalls that if he divides the second digit by the third digit, he gets the first digit. How many different combinations does Amit have to try for unlocking the locker?
- 2
- 1
- 4
- 5
- 3
View Solution
3.
If ‘n’ and ‘a’ are positive integers such that nn = 3324 and n3 + 3n is an integral multiple of 3a, then find the largest possible value of a.
- 5
- 6
- 8
- 12
- 15
View Solution
4.
If l, m, and n are real numbers such that \(l + m = 10lm, m + n = 12mn\), and \(n + l = 4nl\), then find the value of \(\frac{180lmn}{lm+mn+nl}\).
- 18
- 20
- 24
- 32
- 36
View Solution
5.
Let x and y be two positive integers and p be a prime number. If x (x – p) – y (y + p) = 7p, what will be the minimum value of x – y?
- 1
- 3
- 5
- 7
- None of the above
View Solution
6.
Which of the following can be the perimeter of a triangle if one of its sides is 7776 units, the second side (say p) is a square of the perfect square of an integer number, and the third side (say q) is a power of 6. It is also known that q is six times of p.
- 16848 units
- 16832 units
- 16880 units
- 16874 units
- 16866 units
View Solution
7.
Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?
- 67
- 58
- 49
- 40
- None of the above
View Solution

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XAT Basics of Numbers MCQs with Solutions

1.Solve for the number of integral values of \(x: \frac{(x^2-15x+47)(x-13)}{(x-8)}<0\).

3.If ‘n’ and ‘a’ are positive integers such that nn = 3324 and n3 + 3n is an integral multiple of 3a, then find the largest possible value of a.

4.If l, m, and n are real numbers such that \(l + m = 10lm, m + n = 12mn\), and \(n + l = 4nl\), then find the value of \(\frac{180lmn}{lm+mn+nl}\).

5.Let x and y be two positive integers and p be a prime number. If x (x – p) – y (y + p) = 7p, what will be the minimum value of x – y?

6.Which of the following can be the perimeter of a triangle if one of its sides is 7776 units, the second side (say p) is a square of the perfect square of an integer number, and the third side (say q) is a power of 6. It is also known that q is six times of p.

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1.
Solve for the number of integral values of \(x: \frac{(x^2-15x+47)(x-13)}{(x-8)}<0\).

3.
If ‘n’ and ‘a’ are positive integers such that nn = 3324 and n3 + 3n is an integral multiple of 3a, then find the largest possible value of a.

4.
If l, m, and n are real numbers such that \(l + m = 10lm, m + n = 12mn\), and \(n + l = 4nl\), then find the value of \(\frac{180lmn}{lm+mn+nl}\).

5.
Let x and y be two positive integers and p be a prime number. If x (x – p) – y (y + p) = 7p, what will be the minimum value of x – y?

6.
Which of the following can be the perimeter of a triangle if one of its sides is 7776 units, the second side (say p) is a square of the perfect square of an integer number, and the third side (say q) is a power of 6. It is also known that q is six times of p.