Question

A number G236G0 can be divided by 36 if G is:

• A. 8
• B. 6
• C. 1
• D. More than one value is possible

Hint:

36 = 9 × 4; use the digit-sum rule for 9 on 11 + 2G to narrow G down to a single value.

Answer 1

The Correct Option is A

Rather than testing every digit blindly, it helps to first narrow down the candidates using the easier rule (divisibility by 4) before applying the digit-sum rule for 9.

1. Divisibility by 4 depends only on the last two digits, “G0”. Since any digit followed by 0 gives a multiple of 10, and every multiple of 20 is also a multiple of 4, in fact G0 is divisible by 4 for every digit G from 0 to 9 that is even; but since G0 must also just be a two-digit multiple of 4 in general, this check does not narrow things down much on its own, so the deciding test is really the digit-sum rule for 9.
2. Digit sum $= G+2+3+6+G+0 = 2G+11$.
3. Testing G from 0 to 9, only $G=8$ gives $2(8)+11=27$, a clean multiple of 9.

So the only value of G that works is 8.

The correct answer is option A.