Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: For positive integers x and y, x^2 = 350y. Is y divisible [#permalink]
10 May 2012, 00:48

4

This post received KUDOS

Expert's post

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.

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.

Re: For positive integers x and y,x^2 = 350y. Is y divisible by [#permalink]
24 Nov 2012, 21:26

1

This post received KUDOS

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.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Re: For positive integers x and y, x^2 = 350y. Is y divisible [#permalink]
20 Feb 2014, 07:00

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________