Yesterday, Integrated Learning posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:
To be a perfect square, you must be able to take the square root of Q. Practically, that means both x and y need to be even numbers.
Statement 1: We learn that Q has at least 4 3’s and 2 7’s in its prime factors, but we don’t know there aren’t more than that. Q could have 5 3’s, which case y would be 5 and you would not be able to square root Q.
Statement 2: Since 243 is 35 and 343 is 73, Q has less than 5 3’s, and less than 3 7’s in its prime factors. But again, y could be any number less than 5 and x any number less than 3, even or odd.
Together – Q has exactly 4 3’s and 2 7’s in its prime factors and is therefore a square of an integer.
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