Bunuel wrote:
The number N is 6H12, the hundred's digit being represented by H. What is the value of H?
(1) N is divisible by 4.
(2) N is divisible by 9.
(1) For a number to be divisible by 4, its last two digits must be divisible by 4. So in case of 6H12, since last two digits are divisible by 4 (12 is a multiple of 4), 6H12 WILL be divisible by 4, irrespective of the value of H (meaning H can take any value from 0 to 9 doesnt matter). So Insufficient.
(2) For a number to be divisible by 9, its sum of digits must be divisible by 9. So 6+H+1+2 = 9+H must be divisible by 9. We can see that H can thus take two values: '0' and '9' for which the sum of digits will become 9 and 18 respectively, divisible by 9 in either case. So two values of H are possible. Not Sufficient.
Combining the two statements, still H can take two values of 0 and 9, so Insufficient.
Hence
E answer