Question

A prime number x greater than 100 leaves a remainder y on division by 26. How many values can y take?

• A. 8
• B. 9
• C. 7
• D. 6

Answer 1

The correct option is B

9

The number can be written in the form x = 26n + y , where n is a natural number .

If y = 1 , x can be 53 ( n =2 )

y = 2

x = 2(23n + 1) , which is not a prime number.

y = 3 , x can be 29 ( n=1 )

If y = 4

x = 2(23n+2) which is not a prime number.

So y = 1, 3,5,7,9,11,17,21,23 satisfies the condition.