Download : 104 Number Theory Problems PDF

Few problems:

1.If both 11^{2} and 3^{3} are factors of the number a * 4^{3} * 6^{2} * 13^{11}, what is the smallest possible value of ‘a’?

- 121
- 3267
- 363
- 33
- 37

**Correct Answer**: Choice (3). The smallest possible value of ‘a’ is 363.

2.Find the largest five digit number that is divisible by 7, 10, 15, 21 and 28.

- 99,840
- 99,900
- 99,960
- 99,990
- 99,970

**Correct Answer**: Choice (3). 99960

3.Anita had to multiply two positive integers. Instead of taking 35 as one of the multipliers, she incorrectly took 53. As a result, the product went up by 540. What is the new product?

- 1050
- 540
- 1440
- 1520
- 1590

Correct Answer – **1590**. Choice (5)

4.Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?

- (x – z)
^{2}y is even - (x – z) y
^{2}is odd - (x – z) y is odd
- (x – y)
^{2}z is even - (x + y)
^{3}z is even

Correct Answer – **(x – z) ^{2} y is even**. Choice (1)

5.When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?

- 10
- 7
- 19
- 192
- None of these

Correct Answer – **7**. Choice (2)