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# If y is the smallest positive integer such that 3,150

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If y is the smallest positive integer such that 3,150 [#permalink]

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12 Jun 2008, 05:00
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76% (01:02) correct 24% (01:27) wrong based on 998 sessions

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If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

A. 2
B. 5
C. 6
D. 7
E. 14
[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Jun 2013, 04:33, edited 3 times in total.

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Re: PS - S26 q30 [#permalink]

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13 Jun 2008, 04:35
IMO E should be the answer for this

i just tried plugging in the numbers and found out that

14*3150 = 44, 100, which is a square of 210

HTH
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Re: If y is the smallest positive integer such that 3,150 [#permalink]

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28 Jan 2012, 17:42
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answer E. factor out the number and find any prime numbers that are not paired. 7 & 2.
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Re: If y is the smallest positive integer such that 3,150 [#permalink]

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28 Jan 2012, 18:00
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mrwaxy wrote:
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be
A. 2
B. 5
C. 6
D. 7
E. 14

Detailed explanation would be appreciated.

$$3,150=2*3^2*5^2*7$$, now $$3,150*y$$ to be a perfect square $$y$$ must complete the odd powers of 2 and 7 to even number (perfect square has even powers of its primes), so the least value of $$y$$ is 2*7=14. In this case $$3,150y=(2*3^2*5^2*7)*(2*7)=(2*3*5*7)^2=perfect \ square$$.

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Hope it helps.
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Re: If y is the smallest positive integer such that 3,150 [#permalink]

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30 Jan 2012, 09:46
factorise 3150, to find out the missing doubles... 3150 = 5x5x3x3x2x7... so 2x7=14... when multiplied to 3150, will make it a perfect square... answere is E

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Re: If y is the smallest positive integer such that 3,150 [#permalink]

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12 Jun 2013, 05:25
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Re: If y is the smallest positive integer such that 3,150 [#permalink]

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13 Jun 2013, 02:07
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mrwaxy wrote:
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

A. 2
B. 5
C. 6
D. 7
E. 14

In such questions we need to break the number into the smallest possible prime factors. So the smallest prime factors of 3150 are:
315*10=63*5*2*5=7*9*5*2*5=7*3*3*5*2*5. In order to get a square of an integer we have to have at least two identical primes. In our case we have 3*3 and 5*5 corresponding to this condition but not 2*7 so our smallest number should be 14.

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Re: if y is the smallest positive interger such that 3150 multip [#permalink]

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29 Aug 2013, 01:35
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kumar83 wrote:
if y is the smallest positive interger such that 3150 multiplied by y is the square of an interger, that Y must be

A) 2
B) 5
C) 6
D) 7
E) 14

Kindly Explain.

3150 =$$2*3^2*5^2*7$$
For it to be perfect square all the prime number should be least raised to the power 2
in 3150 ...only 2 and 7 needs to be multiplied so that all prime will be raised power 2
hence least value of $$4y = 2*7 = 14$$

hence E
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Re: If y is the smallest positive integer such that 3,150 [#permalink]

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22 Jul 2014, 04:18
Hello,

can anyone help me with this type of question? I don't get it why the remaining numbers, 7 and 2, are the smallest positive integer y. Which chapter in the MGMAT books should i restudy to deal with this kind of problem? I don't understand the explanation in the OG which says: "To be a perfect square, 3,150y must have an even number of each of its prime factors."

Any help is appreciated!

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Re: If y is the smallest positive integer such that 3,150 [#permalink]

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22 Jul 2014, 04:31
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If y is the smallest positive integer such that 3,150 multiplied by y [#permalink]

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03 Apr 2015, 09:57
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

a) 2

b) 5

c) 6

d) 7

e) 14

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Re: If y is the smallest positive integer such that 3,150 [#permalink]

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03 Apr 2015, 10:00
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Awli wrote:
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

a) 2

b) 5

c) 6

d) 7

e) 14

Merging topics. Please search before posting. Thank you.
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Re: If y is the smallest positive integer such that 3,150 [#permalink]

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01 Aug 2016, 02:08
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Re: If y is the smallest positive integer such that 3,150 [#permalink]

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16 Oct 2016, 23:54
3150 = 5*5*3*3*2*7

To be a perfect square y needs to be 2*7=14

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Re: If y is the smallest positive integer such that 3,150 [#permalink]

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24 Aug 2017, 12:03
Expert's post
Top Contributor
mrwaxy wrote:
If y is the smallest positive integer such that 3,150 multiplied by 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.

[Reveal] Spoiler:
E

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Re: If y is the smallest positive integer such that 3,150   [#permalink] 24 Aug 2017, 12:03
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