That should be D. I'm not sure where this question is from, but it's unusual to see irrelevant information in a real GMAT question; here, for example, it doesn't matter that the number has two digits.silvia928 wrote:What is the remainder when the two-digit, positive integer x is divided by 3?
(1) the sum of the digits of x is 5
(2) the remainder when x is divided by 9 is 5
Ans....
....
(A)
On to the question:
1) Hopefully everyone here will know how to test whether a (positive) whole number is divisible by 3 (or 9): add the digits, and if the sum is divisible by 3 (or, respectively, 9), so is the original number. Less well known, but sometimes useful: you can use that test to find the remainder when you divide by 3 (or 9). Let's look at a different number:
3,472
If I add the digits, I get 16. The remainder is 1 when I divide 16 by 3, and that guarantees that the remainder will be 1 when I divide 3,472 by 3. The remainder will be 7 when I divide 3,472 by 9, because that's the remainder when I divide 16 by 9. One word of caution- these tests only work when you are dividing by 3 or 9, so only apply them in these cases.
In any event, if you know the above, you know immediately that Statment 1) is enough.
2) This tells us that x is five larger than a multiple of 9. But every multiple of 9 is certainly a multiple of 3, so x is five more than a multiple of 3. But the remainder can't be 5; it must be 0, 1 or 2 when we divide by 3. You can just subtract 3 from 5, in fact, and here's why:
x = 3q + 5 = 3q + 3 + 2 = 3(q+1) + 2
So x is 2 larger than a multiple of 3; the remainder is 2 when you divide x by 3. So the statement is sufficient.
