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:

If x, y, and z are positive integers, where x > y and [#permalink]
15 Nov 2009, 21:47

1

This post received KUDOS

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

41% (03:21) correct
59% (02:32) wrong based on 101 sessions

If x, y, and z are positive integers, where x > y and z=x^(1/2), are x and y consecutive perfect squares? (A perfect square is defined as the square of an integer. For example, 36 is a perfect square since it equals 6 squared, while 38 is not a perfect square since it is not equal to the square of any integer.)

Re: Are x and y consecutive perfect squares [#permalink]
16 Nov 2009, 00:27

1

This post received KUDOS

ctrlaltdel wrote:

If x, y, and z are positive integers, where x > y and z=x^(1/2), are x and y consecutive perfect squares? (A perfect square is defined as the square of an integer. For example, 36 is a perfect square since it equals 6 squared, while 38 is not a perfect square since it is not equal to the square of any integer.)

(1) x + y = 8z +1 (2) x – y = 2z – 1

Happy Solving

B

1. x+ y = 8z+1 the values of x and y satisfying this equation is 25 and 16 which are consecutive perfect squares the values of x and y satisfying this equation is 64 and 1 which are NOT consecutive perfect squares Hence insuff

2. x -y = 2z-1 the values x and y satisfying this equation will be all consecutive perfect squares (be it [4,1] [9,4][2500,2401] non consecutive perfect squares will not satisfy the equation hence suff

Re: If x, y, and z are positive integers, where x > y and [#permalink]
26 Sep 2013, 03:00

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. _________________

Re: If x, y, and z are positive integers, where x > y and [#permalink]
11 Mar 2014, 17:31

IM BACK!

The difference of perfect squares can be expressed as an odd number. Or viceversa, an odd number can be expressed as the difference of two consecutive perfect squares

Namely,

(k+1)^2 - (k)^2 = 2k + 1

Hope this clarifies

gmatclubot

Re: If x, y, and z are positive integers, where x > y and
[#permalink]
11 Mar 2014, 17:31