Question

If 37y4 is exactly divisible by 9, then the smallest value of y is

• A. 2
• B. 3
• C. 1
• D. 4

Answer 1

The correct option is D

4

To make 37y4 exactly divisible by 9, the sum of its digits must be divisible by 9.
On adding the digits of 37y4, we get
= 3 + 7 + y + 4
= 14 + y
$\therefore$ 14 + y is divisible by 9.

Now, the smallest multiple of 9 which is greater than 14 is 18.
$\therefore$ 14 + y = 18
$\Rightarrow$ y = 4
$\therefore$ The smallest possible value of y is 4.