#### Question

If 21*y*5 is a multiple of 9, where *y* is a digit, what is the value of *y*?

#### Solution

If a number is a multiple of 9, then the sum of its digits will be divisible by 9.

Sum of digits of 21*y*5 = 2 + 1 + *y* + 5 = 8 + *y*

Hence, 8 + *y* should be a multiple of 9.

This is possible when 8 + *y* is any one of these numbers 0, 9, 18, 27, and so on …

However, since *y* is a single digit number, this sum can be 9 only. Therefore, *y* should be 1 only.

Is there an error in this question or solution?

Solution If 21y5 is a Multiple of 9, Where Y is a Digit, What is the Value of Y? Concept: Tests of Divisibility - Divisibility by 9 and 3.