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# If x and y are positive integers and (x-y)^2+y^2=25, which of the foll

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If x and y are positive integers and (x-y)^2+y^2=25, which of the foll  [#permalink]

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05 Mar 2019, 01:15
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Difficulty:

25% (medium)

Question Stats:

78% (01:46) correct 22% (02:57) wrong based on 36 sessions

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[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 $$x$$?

$$A. 6$$
$$B. 7$$
$$C. 8$$
$$D. 9$$
$$E. 10$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 12 Apr 2011 Posts: 149 Location: United Arab Emirates Concentration: Strategy, Marketing Schools: CBS '21, Yale '21, INSEAD GMAT 1: 670 Q50 V31 GMAT 2: 720 Q50 V37 WE: Marketing (Telecommunications) Re: If x and y are positive integers and (x-y)^2+y^2=25, which of the foll [#permalink] ### Show Tags 05 Mar 2019, 01:39 MathRevolution 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 $$x$$? $$A. 6$$ $$B. 7$$ $$C. 8$$ $$D. 9$$ $$E. 10$$ From the question we know: $$(x-y)^2$$ and $$y^2$$ will be positive. Also, we can treat these two to be a part of Pythagorean triplets. Hence we can conclude: $$4^2+3^2=5^2$$ => $$(x-y)^2=4^2$$ & $$(y)^2=3^2$$ => y=3 and x=7 Hence B is the correct answer. _________________ Hit Kudos if you like what you see! Senior Manager Joined: 04 Aug 2010 Posts: 474 Schools: Dartmouth College Re: If x and y are positive integers and (x-y)^2+y^2=25, which of the foll [#permalink] ### Show Tags 05 Mar 2019, 04:36 MathRevolution 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)² = (7-3)² = 16 and y² = 9, with the result that (x-y)² + y² = 25. _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8003 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are positive integers and (x-y)^2+y^2=25, which of the foll [#permalink] ### Show Tags 07 Mar 2019, 01:15 => 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 $$1$$. Therefore, B is the answer. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If x and y are positive integers and (x-y)^2+y^2=25, which of the foll   [#permalink] 07 Mar 2019, 01:15
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