DS problem

[amb2512]

Need Help with this one:

If a and b are the digits of the two-digit number X, what is the remainder when X is divided by 9?

(1) a + b = 11

(2) X + 7 is divisible by 9



There is no useful rephrasing that can be done for this question. However, we can keep in mind that for a number to be divisible by 9, the sum of its digits must be divisible by 9.

This is the explanation given in the CAT.
(1) SUFFICIENT: The sum of the digits a and b here is not divisible by 9, so X is not divisible by 9. It turns out, however, that the sum of the digits here can also be used to find the remainder. Since the sum of the digits here has a remainder of 2 when divided by 9, the number itself has a remainder of 2 when divided by 9.

We can use a few values for a and b to show that this is the case:

When a = 5 and b = 6, 56 divided by 9 has a remainder of 56 - 54 = 2
When a = 7 and b = 4, 74 divided by 9 has a remainder of 74 - 72 = 2

(2) SUFFICIENT: If X + 7 is divisible by 9, X - 2 would also be divisible by 9 (X - 2 + 9 = X + 7). If X - 2 is divisible by 9, then X itself has a remainder of 2 when divided by 9.

Again we could use numbers to prove this:
If X + 7 = 27, then X = 20, which has a remainder of 2 when divided by 9
If X + 7 = 18, then X = 11, which has a remainder of 2 when divided by 9

The correct answer is D.


My question is y cant we take a negative value of x for the seond statement
for ex.
if x=-16 then x+7=-9 which is divisible by 9
but the remainder in this case will be -7
so statement 2 by itself should not be sufficient.

[Ben Ku]

A Data Sufficiency question should be posted in one of the Math folders, not in this General Verbal folder.