GMAT Practice Question Source:
Difficulty: Sub-600 Level
GMAT Study Guide Module:
GMAT Timing Tips:
- Prime factors of a perfect square, perfect cube, etc.: First, we need to know that all prime factors of a perfect square have exponents that are even. If we find that any of the prime factors of 3,150 do not have even exponents, y will need to contain each of those prime factors, so that the prime factorization of 3,150*y will have an even exponent for each of those prime factors.
- Prime factorization: In order to determine the prime factors of y, we need to do the prime factorization of 3,150, so let’s try to do it as efficiently as possible. Because factors of 10 and 5 are easy to see, I recommend starting by factoring 3,150 into 315*10, then 63*5*2*5. We can also recognize that 63 = 9*7 = 32*7. This means that the prime factorization of 3,150 is 2 * 32 * 52 * 7. Since there are odd powers of 2 and 7, y must contain factors of 2 and 7, and the smallest possible value of y is 2*7 = 14.
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