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if y is the smallest +ve integer such that 3150*y is the squ

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if y is the smallest +ve integer such that 3150*y is the squ [#permalink] New post 04 Sep 2018, 22:14
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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
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Re: if y is the smallest +ve integer such that 3150*y is the squ [#permalink] New post 05 Sep 2018, 07:15
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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)
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: if y is the smallest +ve integer such that 3150*y is the squ [#permalink] New post 07 Sep 2018, 20:11
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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: \(2^25^23^27^2\)


The best answer is E.
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Re: if y is the smallest +ve integer such that 3150*y is the squ [#permalink] New post 13 Sep 2018, 12:36
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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
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Re: if y is the smallest +ve integer such that 3150*y is the squ [#permalink] New post 17 Sep 2019, 11:55
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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.
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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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