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: If q is a positive integer, is p*q/q^(1/2) an integer?
[#permalink]

Show Tags

16 Nov 2014, 22:20

1) q=p^2 take the square root on both sides p=(sqroot)q

so p*(q/(sqroot)q) = (sqroot)q * q/(sqroot)q = q and from definition we know that q is a positive integer. sufficient

2)p is an integer let p=2 and q=3 then the equation becomes 2 * 3 / (sqroot)3 which is not an integer let p=2 and q=4 then the equations becomes 2 * 4 / (sqroot)4 = 4 which is an integer insufficient

Re: If q is a positive integer, is p*q/q^(1/2) an integer?
[#permalink]

Show Tags

17 Nov 2014, 01:39

If \(q\) is a positive integer, is \(p\frac{q}{\sqrt{q}}\) an integer?

(1) \(q = p^2\). Take the square root from botth sides: \(p=\sqrt{q}\). Substitute \(p\): \(p\frac{q}{\sqrt{q}}=\sqrt{q}*\frac{q}{\sqrt{q}} = q = \text{integer}\). Sufficient.

(2) \(p\) is a positive integer. So, we have that \(p\frac{q}{\sqrt{q}}=\text{integer}*\sqrt{q}\). This product may or may not be an integer depending on \(q\). Not sufficient.

WE: General Management (Non-Profit and Government)

Re: If q is a positive integer, is p*q/q^(1/2) an integer?
[#permalink]

Show Tags

17 Nov 2014, 04:25

Expression given pq/q^1/2

this can be further simplified as (pq/q^1/2)*(q^1/2)/q^1/2

this will reduced to pq^1/2

1)q=p^2 since q is positive integer the main expression will be =p^2. is an integer. Sufficient 2)p is positive integer. this does not provide any solution. Insufficient

Re: If q is a positive integer, is p*q/q^(1/2) an integer?
[#permalink]

Show Tags

17 Nov 2014, 11:29

statement 1: sufficient If q=p^2 and q is a positive integer, then p must also be an integer. After plugging in p^2 for Q in the question , then after reducing you see that it is equal to p^2.

statement 2: insufficient If q=9 and p=2 then plug into the equation to get 6 as your answer. However, if you plug in q=6 and p=2, the equation does not equal an integer. not enough info.