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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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 and y are positive integers and x^2 + y^2 = 100 [#permalink]

Show Tags

18 Aug 2012, 15:22

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

53% (01:30) correct
47% (01:08) wrong based on 15 sessions

HideShow timer Statistics

If x and y are positive integers and \(x^2 + y^2 = 100\), then the greatest possible value of x is between (A) 4 and 5 (B) 6 and 7 (C) 7 and 8 (D) 9 and 10 (E) 10 and 11

I don't agree with the OA. According to the question, x is an integer, therefore the greatest value of x could be 8 (Choice C). However, the OE is this: To maximize x, minimize y. Since both variables are positive integers, the smallest y could be is 1. Thus: \(x^2 + y^2 = 100\) \(x^2 + 1^2 = 100\) \(x^2 = 99\) Since 100 is \(10^2\), 99 must be the square of a little less than 10. The correct choice is (D).

Re: If x and y are positive integers and x^2 + y^2 = 100 [#permalink]

Show Tags

18 Aug 2012, 15:37

metallicafan wrote:

If x and y are positive integers and \(x^2 + y^2 = 100\), then the greatest possible value of x is between (A) 4 and 5 (B) 6 and 7 (C) 7 and 8 (D) 9 and 10 (E) 10 and 11

I don't agree with the OA. According to the question, x is an integer, therefore the greatest value of x could be 8 (Choice C). However, the OE is this: To maximize x, minimize y. Since both variables are positive integers, the smallest y could be is 1. Thus: \(x^2 + y^2 = 100\) \(x^2 + 1^2 = 100\) \(x^2 = 99\) Since 100 is \(10^2\), 99 must be the square of a little less than 10. The correct choice is (D).

Both x and y can take integer values between 1 and 9, so not really sure as to the phrasing of the question, especially the word between.
_________________

If x is an integer, then without even reading the rest of the question none of the answer choices could possibly be right ('between' means 'strictly between' unless you add the word 'inclusive').

I don't know if there's a typo in the original question - I guess so, considering how the OE reads - but the question makes no sense as written. I suppose it makes sense if you take out the word 'integers' and just require x and y to be positive.

edit: or perhaps the question means to say "If \(x^2\) and \(y^2\) are positive integers..." Then the solution is right.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

gmatclubot

Re: If x and y are positive integers and x^2 + y^2 = 100
[#permalink]
19 Aug 2012, 01:54

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...