Hi All,

We're told that in the multiplication table above, each letter represents an INTEGER. We're asked for the value of C. While this question might look 'complex', it's actually based on some really low-level Arithmetic (specifically multiplication) and can be solved with a little note-taking and logic.

To start, it's important to define what the information in the table really means. Since it's a MULTIPLICATION TABLE, we can deduce the following:
(A)(A) = D
(A)(B) = E
(A)(C) = F
(B)(B) = G
Etc.

1) C = F

Fact 1 tells us that C and F are the SAME integer. Since (A)(C) = F there are two possibilities to consider:
1) A = 1 and C and F are ANY integer.
2) C and F are both 0 and A is ANY integer
Unfortunately, we don't have enough information to figure out any of the values, so C could be ANY integer.
Fact 1 is INSUFFICIENT

2) H is NOT equal to 0.

Fact 2 tells us that H cannot equal 0. Since (B)(C) = H, this means that neither B nor C can equal 0 either. Unfortunately, we still don't have enough information to figure the value of C (we just know that it can't be 0).
Fact 2 is INSUFFICIENT

Combined, we know
Neither B, C nor H can equal 0
A = 1
Based on the deductions that we made in Fact 1, we know that C can be any integer - and with Fact 2, we know that C can't be 0. There's still an infinite number of possible values for C though.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich