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# For positive integers x and y, x^2 = 350y. Is y divisible

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Intern
Joined: 03 Apr 2012
Posts: 26
For positive integers x and y, x^2 = 350y. Is y divisible [#permalink]

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09 May 2012, 16:25
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Difficulty:

95% (hard)

Question Stats:

42% (01:59) correct 58% (01:46) wrong based on 190 sessions

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For positive integers x and y, x^2 = 350y. Is y divisible by 28?

(1) x is divisible by 4

(2) x^2 is divisible by 28
Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 605
Re: If Y divisible by 28? [#permalink]

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09 May 2012, 17:52
5
Explanation attached.
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Intern
Joined: 03 Apr 2012
Posts: 26
Re: If Y divisible by 28? [#permalink]

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09 May 2012, 18:02
1
dabral wrote:
Explanation attached.

awesome, thanks a lot. prime factorization tricks are killing me. so many ways to do the same problem. its amazing.
Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 605
Re: If Y divisible by 28? [#permalink]

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Updated on: 03 Jan 2013, 15:10
2
Here are some additional problems that are conceptually related:

1) Official Guide 12th Edition Problem Solving 142: need-help-thanks-91668.html

2) GMATPrep: if-n-and-y-are-positive-integers-and-450y-n-92562.html

3) Really old Official GMAT question: the-product-of-the-first-twelve-positive-integers-is-44758.html

4) Old official GMAT Question: http://www.urch.com/forums/gmat-math/26 ... teger.html

5) http://www.gmatquantum.com/blog/gmat-question20.html

6) http://www.gmatquantum.com/blog/gmat-question-7.html

I wrote the last two problems.
Dabral

Originally posted by dabral on 09 May 2012, 19:06.
Last edited by dabral on 03 Jan 2013, 15:10, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 46297
Re: For positive integers x and y, x^2 = 350y. Is y divisible [#permalink]

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10 May 2012, 01:48
5
2
For positive integers x and y, x^2 = 350y. Is y divisible by 28?

Given: $$x^2=2*5^2*7*y$$. Notice that since $$2*5^2*7*y$$ equals to some perfect square (x^2) then $$y$$ must complete the odd powers of other multiples to even numbers (remember perfect square has even powers of its primes), so the least value of $$y$$ is $$2*7=14$$ (y is a multiple of 14). So, we need one more 2 for $$y$$ in order it to be divisible by 28.

(1) x is divisible by 4 --> $$x^2$$ is divisible by 4^2=16=2^4, since 350 has only one 2 then $$y$$ must have the remaining 2^3, so we have that $$y$$ is divisible by 2^3*7=2*28. Sufficient.

(2) x^2 is divisible by 28 --> since the least value of $$y$$ is $$2*7=14$$ then $$x^2=2*5^2*7*14=28*(5^2*7)$$, so we already knew that $$x^2$$ is divisible by 28. Not sufficient.

Hope it's clear.
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Intern
Joined: 03 Apr 2012
Posts: 26
Re: If Y divisible by 28? [#permalink]

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11 May 2012, 13:35
dabral wrote:
Here are some additional problems that are conceptually related:

1) Official Guide 12th Edition Problem Solving 142: need-help-thanks-91668.html

2) GMATPrep: if-n-and-y-are-positive-integers-and-450y-n-92562.html

3) Really old Official GMAT question: the-product-of-the-first-twelve-positive-integers-is-44758.html

4) Old official GMAT Question: http://www.urch.com/forums/gmat-math/26 ... teger.html

5) http://www.gmatquantum.com/blog/gmat-da ... ion20.html

6) http://www.gmatquantum.com/blog/gmat-question-7.html

I wrote the last two problems.
Dabral

awesome, thanks a lot Dabral.
i am struggling with the concepts on prime factorizaiton as to when to apply to what kind of problem.
appreciate your time and help..

and to Bunuel too for providing an alternate sway to solve this problem.
VP
Joined: 02 Jul 2012
Posts: 1194
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: For positive integers x and y,x^2 = 350y. Is y divisible by [#permalink]

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24 Nov 2012, 22:26
1
Sachin9 wrote:
For positive integers x and y, x^2 = 350y. Is y divisible by 28?
(1) x is divisible by 4
(2) x^2 is divisible by 28

Somebody please explain me why 2 is not sufficient.

From the statement we get that at least $$y = 2^a*7^b*z$$

where a,b are positive odd integers and z is a perfect square

1)x is divisible by 4. So x had at least two 2s and so $$x^2$$ has at least four 2s. So y has at least three 2s. We know y also has a 7. So y is divisible by 28. Sufficient.

2)$$x^2$$ is divisible by 28. This would be true even if y has only one 2. i.e, y = 2*7 = 14. In this case, x^2 is divisible by 28 but y is not divisible by 28. From the previous statement we can get a situation where x and y are both divisible by 28. Insufficient.

Answer is hence A.

Kudos Please... If my post helped.
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Status: Gonna rock this time!!!
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GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
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Re: If Y divisible by 28? [#permalink]

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03 Jan 2013, 06:36
dabral wrote:
Here are some additional problems that are conceptually related:

1) Official Guide 12th Edition Problem Solving 142: need-help-thanks-91668.html

2) GMATPrep: if-n-and-y-are-positive-integers-and-450y-n-92562.html

3) Really old Official GMAT question: the-product-of-the-first-twelve-positive-integers-is-44758.html

4) Old official GMAT Question: http://www.urch.com/forums/gmat-math/26 ... teger.html

5) http://www.gmatquantum.com/blog/gmat-da ... ion20.html

6) http://www.gmatquantum.com/blog/gmat-question-7.html

I wrote the last two problems.
Dabral

Thanks a ton for these questions.. learnt a lot.. but unable to check the 5th link above..
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Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 605
Re: For positive integers x and y, x^2 = 350y. Is y divisible [#permalink]

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03 Jan 2013, 15:09
1
sachin,

here is the url to the 5th question:
http://www.gmatquantum.com/blog/gmat-question20.html

dabral
Manager
Joined: 13 Oct 2012
Posts: 61
Concentration: General Management, Leadership
Schools: IE '15 (A)
GMAT 1: 760 Q49 V46
Re: For positive integers x and y, x^2 = 350y. Is y divisible [#permalink]

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03 Jan 2013, 15:15
Thanks a ton!! These are great questions
Senior Manager
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 483
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: For positive integers x and y, x^2 = 350y. Is y divisible [#permalink]

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03 Jan 2013, 21:05
dabral wrote:
sachin,

here is the url to the 5th question:
http://www.gmatquantum.com/blog/gmat-question20.html

dabral

There was a lot of learning in this question.. Thanks dabral!
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hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

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Joined: 09 Sep 2013
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Re: For positive integers x and y, x^2 = 350y. Is y divisible [#permalink]

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15 Jan 2018, 09:46
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Re: For positive integers x and y, x^2 = 350y. Is y divisible   [#permalink] 15 Jan 2018, 09:46
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# For positive integers x and y, x^2 = 350y. Is y divisible

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