Bunuel wrote:
Official Solution:
(1) \(A\) is divisible by 9. In order an integer to be divisible by 9, the sum of its digit must be divisible by 9. Hence \(1+5+4+3+@+2=15+@\) must be divisible by 9, and since \(@\) is a digit then it can only equal to 3. Sufficient.
(2) \(A\) is divisible by 4. In order an integer to be divisible by 4, its last two digits must be divisible by 4. Hence \(@2\) must be divisible by 4, which is possible if \(@=1\), \(@=3\), \(@=5\), \(@=7\), or \(@=9\). Not sufficient.
Answer: A
I really didn't get this. So if A = 1543@2 and the sum of the digit is 15, then
can be 0, or 3 (adding to 18), or 6 (adding to 21) or 9 (adding to 24). All these numbers make it divisible by 3 and hence insufficient.
As for statement 2, again the last 2 digits can be either 3 or 9 as 32 and 92 are divisible by 4. Again insufficient.
So shouldn't the answer be E?
Please explain where am I going wrong?