Hi All,
We’re told that Y is the SMALLEST positive integer such that 3150(Y) is the SQUARE of an INTEGER. We’re asked for the value of Y. This question is based on a specific Number Property rule involving squares, so while you could potentially ‘brute force’ your way to the correct answer by TESTing THE ANSWERS (since one of those answers, when multiplied by 3150, WILL create a Perfect Square), you can use Prime Factorization to get to the correct answer quicker.
By definition, a ‘perfect square’ has an EVEN number of every one of its PRIME FACTORS. For example:
9 is a perfect square because 9 = (3)(3) → it has two 3s.
16 is a perfect square because 16 = (4)(4) = (2)(2)(2)(2) → it has four 2s
36 is a perfect square because 36 = (6)(6) = (2)(3)(2)(3) → it has two 2s and two 3s.
Etc.
We’re told that 3150(Y) is a perfect square, so we have to first break 3150 down into its prime factors, then figure out what Y has to equal so that there will be an EVEN number of each of those prime factors.
3150 = (315)(10) = (63)(5)(2)(5) = (7)(9)(5)(2)(5) = (7)(3)(3)(5)(2)(5)
Notice that there are two 3s and two 5s… but only one 2 and one 7. This means that for Y to be as small as possible, it has to include one 2 and one 7 in its prime factorization. Thus, Y = (2)(7)
Final Answer:
GMAT Assassins aren’t born, they’re made,
Rich
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