Question

Find the possible values of a if the number 23x6 is divisible by 6.

• A. 2
• B. 1
• C. 3
• D. 7

Answer 1

Answer: (B), (D)

The correct options are
B

1

D

7

If a number is divisible by 6, it must be divisible by 2 and 3 both.

For divisibility by 3

2 + 3 + x + 6 = (11 + x) should be a multiple of 3.
The closest number more than 11 which is a multiple of 3 = 12 , so a = 1
The next in line would be 15, hence x = 4
The next in line would be 18, hence x = 7
The next would be 21, hence x = 10. However x is a single digit, hence it cannot be 10.

x = 1, 4, 7

For divisibility by 2, the number should be an even number, which means it should end with 0, 2 ,4, 6 or 8.

The given number ends with 6, hence it is divisible by 2.

So from the available options, x = 1 or 7 to make the number 23x6 divisible by 6.