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:

Seems like a straight forward problem, however the answer choices are a little confusing .

both D& E seem to be contendors for the right answer though the OA is D

D-> Because the sum of two perfect square needn't necessarily be a perfect square e.g 4+9=13, not a perfect square, however 9 & 16 = 25 which is a perfect square) E-> Because a perfect square to the power 5 (an ODD number) cannot be a perfect square right ?

Re: If X & Y are perfect squares, then which one of the [#permalink]
05 Jun 2012, 02:57

x = a^2 y = b^2

a) (a^2)^2, ok b) a^2 * b^2 = (ab)^2, ok c) 4*a^2 = 2^2*a^2 = (2a)^2, ok d) a^2 + b^2, clearly not ok for all a/b, e.g a = 8, b = 2, 64 + 4 = 68 which is not a perfect square. e) (a^2)^5 = (a^5)^2, ok _________________

Re: If x and y are perfect squares, then which one of the [#permalink]
22 Apr 2013, 23:31

sdas wrote:

Option B is not clear to me.... X=a^2 Y=b^2

Therefore X*Y = (ab)^2 But, if x=4 and y=9 , then xy=25 However, if x= 4 and y = 25, then xy = 100 which is not perfect square

So, how can we rule out B?

Please explain

If x=4 and y=9 xy =36 which is a perfect square. and xy=100 is a perfect square. its the square of 10. for that matter , product of any two perfect squares is a perfect square. as you pointed out (ab)^2. so square root of the product is ab an integer.

Seems like a straight forward problem, however the answer choices are a little confusing .

both D& E seem to be contendors for the right answer though the OA is D

D-> Because the sum of two perfect square needn't necessarily be a perfect square e.g 4+9=13, not a perfect square, however 9 & 16 = 25 which is a perfect square) E-> Because a perfect square to the power 5 (an ODD number) cannot be a perfect square right ?

Please explain.

Thanks, Shreya

If x=y=1^2=1, then each option but D is a perfect square, therefore D is NOT necessarily a perfect square.

Answer: D.

P.S. Notice that x+y could be a perfect square for example if x=3^2=9 and y=4^2=16 --> x+y=25=5^2. _________________