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

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

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New post 09 May 2012, 16:25
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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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New post 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.

Answer: A.

Hope it's clear.
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Re: If Y divisible by 28?  [#permalink]

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New post 09 May 2012, 17:52
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Re: If Y divisible by 28?  [#permalink]

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New post 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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New post Updated on: 03 Jan 2013, 15:10
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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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New post 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.
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Re: For positive integers x and y,x^2 = 350y. Is y divisible by  [#permalink]

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New post 24 Nov 2012, 22:26
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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.

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Re: If Y divisible by 28?  [#permalink]

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New post 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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New post 03 Jan 2013, 15:09
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sachin,

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

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

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