Question

If $21x4$ is divisible by 6, where $x$ is a single digit, then what might be the value(s) of $x$?

• A.
  2
• B.
  All of these
• C.
  5
• D.
  8

Answer 1

The correct option is B

All of these
Given that the number $21x4$ is divisible by 6. So it has to be divisible by factors of 6, that is, 2 and 3.
Now the unit digit in $21x4$ is 4, so this number is always divisible by 2.
This number $21x4$ will be divisible by 3 if the sum of the digits in this number, that is, $2+1+x+4=7+x$ is a multiple of 3.
Let's check for the given options.

(a) When $x=2,7+x=9$ (multiple of 3)
(b) When $x=5,7+x=12$ (multiple of 3)
(c) When $x=8,7+x=15$ (multiple of 3)

So, for each of the given value of $x$, the given number $21x4$ will be divisible by 6.
So, option (d) is correct.