A number when divided by 18 leaves a remainder 7. The same number when divided…

Let the number be N. Since N leaves remainder 7 when divided by 18, write N = 18k + 7 for some integer k. Now divide this expression by 12: N mod 12 = (18k + 7) mod 12. Since 18 mod 12 = 6, this becomes (6k + 7) mod 12. If k is even, 6k is divisible by 12, so the remainder is 7. If k is odd, 6k leaves remainder 6 when divided by 12, so the remainder is 6 + 7 = 13, which gives remainder 1. Therefore n can only be 7 or 1, so n can take exactly 2 values. Hence Option A is correct.