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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If x and y are positive integers and (x-y)^2+y^2=25, which o tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## If x and y are positive integers and (x-y)^2+y^2=25, which o ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] If x and y are positive integers and (x-y)^2+y^2=25, which of the following could be the value of x? A. 6 B. 7 C. 8 D. 9 E. 10 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[GMAT math practice question]

If x and y are positive integers and (x-y)^2+y^2=25, which of the following could be the value of x?

A. 6
B. 7
C. 8
D. 9
E. 10
Identify two perfect squares that sum to 25:
1, 4, 9, 16...
The two values in blue sum to 25.
If y=3 and x=7, then (x-y)Â² = (7-3)Â² = 16 and yÂ² = 9, with the result that (x-y)Â² + yÂ² = 25.

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The possible values of the pair (x-y,y), with x and y positive, are (0,5), (3,4), (-3,4), (4,3) and (-4,3).
So, (x,y) = (5,5), (7,4), (1,4), (7,3) or (-1,3).
Thus, x could be 5, 7 or 1.

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Only $149 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 Max@Math Revolution wrote: [GMAT math practice question] If x and y are positive integers and (x-y)^2+y^2=25, which of the following could be the value of x? A. 6 B. 7 C. 8 D. 9 E. 10 We need the sum of two perfect squares to equal 25. So the two numbers could be 9 and 16, since 3^2 + 4^2 = 5^2, or 9 + 16 = 25. Thus, if y = 3, then x = 7, so that (7 - 3)^2 + 3^2 = 25. Or, if y = 4, then x = 7, so that (7 - 4)^2 + 4^2 = 25. In either case, we see that x is 7. (Note: We see that 0^2 + 5^2 = 25. That is, if y = 0, then x = 5, so that (5 - 0)^2 + 0^2 = 25; however this is not possible because y is given to be a positive integer. On the other hand if y = 5, then x = 5, so that (5 - 5)^2 + 5^2 = 5. We see that x could be 5 also; however, 5 is not one of the answer choices.) Answer: B _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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