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

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Intern
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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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45% (02:24) correct 55% (02:13) wrong based on 166 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
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Re: For positive integers x and y, x^2 = 350y. Is y divisible  [#permalink]

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10 May 2012, 01:48
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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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Re: If Y divisible by 28?  [#permalink]

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09 May 2012, 17:52
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Explanation attached.
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Re: If Y divisible by 28?  [#permalink]

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

awesome, thanks a lot. prime factorization tricks are killing me. so many ways to do the same problem. its amazing.
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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.
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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.

and to Bunuel too for providing an alternate sway to solve this problem.
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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.

Kudos Please... If my post helped.
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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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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
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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
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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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Re: For positive integers x and y, x^2 = 350y. Is y divisible  [#permalink]

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09 Apr 2019, 13:23
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Re: For positive integers x and y, x^2 = 350y. Is y divisible   [#permalink] 09 Apr 2019, 13:23
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