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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # if y is the smallest +ve integer such that 3150*y is the squ  Question banks Downloads My Bookmarks Reviews Important topics
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TAGS: Moderator  Joined: 07 Jan 2018
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if y is the smallest +ve integer such that 3150*y is the squ [#permalink]
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Question Stats: 68% (00:56) correct 31% (01:26) wrong based on 45 sessions
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
[Reveal] Spoiler: OA GRE Instructor Joined: 10 Apr 2015
Posts: 3909
Followers: 164

Kudos [?]: 4777  , given: 70

Re: if y is the smallest +ve integer such that 3150*y is the squ [#permalink]
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Expert's post
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.

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  Manager  Joined: 06 Jun 2018
Posts: 94
Followers: 2

Kudos [?]: 80  , given: 0

Re: if y is the smallest +ve integer such that 3150*y is the squ [#permalink]
1
KUDOS
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

3150y = perfect square.

3150 = 2*5*5*3*3*7

In order to make it perfect square y has to be 14 as we only a 2 and a 7. To get a prime square each prime factor must have even exponents.

So y is 14.

3150*14 = 2*5*5*3*3*7*7*2.

It looks like: $$2^25^23^27^2$$ Manager Joined: 19 Mar 2018
Posts: 64
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Re: if y is the smallest +ve integer such that 3150*y is the squ [#permalink]
1
KUDOS
Prime factorize --> 3150*y = N square
So N has perfect square, so its a power of 2
3150 = 5^2 x 2 x 3^2 x 7 x Y
so to make it perfect square, it must be = 2 x 7 = 14
Ans is E Manager  Joined: 19 Nov 2018
Posts: 102
Followers: 0

Kudos [?]: 108  , given: 53

Re: if y is the smallest +ve integer such that 3150*y is the squ [#permalink]
1
KUDOS
Here's how I thought of it. Basically, we can take everything out of the square root we can, and then y can be whatever factors we need to take out any remaining prime factors.
Attachments daum_equation_1568750352592.png [ 95.86 KiB | Viewed 794 times ] Re: if y is the smallest +ve integer such that 3150*y is the squ   [#permalink] 17 Sep 2019, 11:55
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