amorphous wrote:

if y is the smallest +ve 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

src: orbit test prep

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)

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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