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Last Updated on May 17, 2023
GMAT OFFICIAL GUIDE PS
Solution:
This problem is testing us on the rule that when we express a perfect square by its unique prime factors, every prime factor’s exponent is an even number.
Let’s start by prime factorizing 3,150.
3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2
3,150 = 2^1 x 3^2 x 5^2 x 7^1
(Notice that the exponents of both 2 and 7 are not even numbers. This tells us that 3,150 itself is not a perfect square.)
We also are given that 3,150 multiplied by y is the square of an integer. We can write this as:
2^1 x 3^2 x 5^2 x 7^1 x y = square of an integer
According to our rule, we need all unique prime factors’ exponents to be even numbers. Thus, we need one more 2 and one more 7. Therefore, y = 7 x 2 = 14
Answer: E
