Is 9,5a8 divisible by 6, where a is some number from the set {0, 1, 2,

Step 1: Analyse Question Stem

The digit ‘a’ could take any value from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
We have to find out if the number 95a8 is divisible by 6.

A number is divisible by 6 if it is divisible by both 2 and 3.
For a number to be divisible by 2, the units digit of the number should be even; for a number to be divisible by 3, the sum of its digits should be divisible by 3.

The units digit of the given number is 8, therefore, it is definitely divisible by 2; therefore, if we have to find if the number is divisible by 6, we have to check if the sum of the digits is divisible by 3.

The sum of the digits of the given number = 9 + 5 + 8 + a = 22 + a. For this to be divisible by 3, a should be 2 or 5 or 8.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: a is even

If a = 2, then the number is divisible by 3 and hence by 6.
If a = 4, the number is not divisible by 3 and hence not divisible by 6.

The data in statement 1 is insufficient to find out if the number is divisible by 6.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2: a is prime

If a = 2, then the number is divisible by 3 and hence by 6.
If a = 3, the number is not divisible by 3 and hence not divisible by 6.

The data in statement 2 is insufficient to find out if the number is divisible by 6.
Statement 2 alone is insufficient. Answer option B can be eliminated.

Step 3: Analyse Statements by combining

From statement 1: a is even
From statement 2: a is prime

Combining both, we can say that a is an even prime i.e. a = 2.

When a = 2, the number is divisible by 3 and hence by 6.

The combination of statements is sufficient to say that the number 95a8 is divisible by 6.
Statements 1 and 2 together are sufficient. Answer option E can be eliminated.

The correct answer option is C.