amorphous wrote:
if y is the smallest positive integer such that 3150*y is the square of an integer then y must be
A) 2
B) 5
C) 6
D) 7
E) 14
Key concept:
The prime factorization of a perfect square (the square of an integer) will have an EVEN number of each prime. For example, 36 = (2)(2)(3)(3)
And 400 = (2)(2)(2)(2)(5)(5)
Likewise, 3150y must have an EVEN number of each prime in its prime factorization.
So, 3150y = (2)(3)(3)(5)(5)(7)y
We have an EVEN number of 3's and 7's, but we have a single 2 and a single 7.
If y =
(2)(7), then we get a perfect square.
That is: 3150y = (
2)(2)(3)(3)(5)(5)(
7)(7)
So, if y =
14, then 3150y is a perfect square.
Answer: E
Cheers,
Brent
ASIDE: This is actually an official GMAT question (see
https://gmatclub.com/forum/if-y-is-the- ... 10513.html)