Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
The question is asking whether x is an integer. Glancing at the statements, we can see that statement (2) only involves y, so it cannot be sufficient. (All we are told in the stem is that xy is not equal to 0, another way of saying that neither x nor y is equal to 0. That’s not a lot of information.) So we can rule out B and D without even analyzing (2) closely.
Statement (1) tells us that xy is an integer. This does not guarantee that x is an integer. Of course, it could be. If y = 1, for instance, then xy = x, so if xy is an integer, then x is as well. However, if y = -2, then x could be ½, which is not an integer. ½ raised to the -2 power is 4. So we can rule out A.
Now, put the two pieces of information together. We are told in (2) that y is a prime number with y unique factors. But every prime number has just 2 unique positive factors (1 and itself), so y must be 2. Combining this fact with the other statement, we know that x2 is an integer. Does this tell us whether x is an integer? Of course, x could be an integer (22= 4), but the question is really whether x has to be an integer. The answer is no. After all, x2 could equal 3. Then x would be equal to the square root of 3. Knowing that the square of x is an integer does not guarantee that x itself is an integer.
The correct answer is E.
