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# If x and y are integers, which of the following CANNOT be the value of

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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25 Jan 2018, 04:08
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Difficulty:

55% (hard)

Question Stats:

57% (01:45) correct 43% (02:17) wrong based on 101 sessions

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[GMAT math practice question]

If $$x$$ and $$y$$ are integers, which of the following CANNOT be the value of $$x^2+y^2$$?

$$A. 121$$
$$B. 122$$
$$C. 123$$
$$D. 125$$
$$E. 130$$

_________________
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" Senior Manager Joined: 17 Oct 2016 Posts: 314 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: If x and y are integers, which of the following CANNOT be the value of [#permalink] ### Show Tags 25 Jan 2018, 04:14 MathRevolution wrote: [GMAT math practice question] If $$x$$ and $$y$$ are integers, which of the following CANNOT be the value of $$x^2+y^2$$? $$A. 121$$ $$B. 122$$ $$C. 123$$ $$D. 125$$ $$E. 130$$ How can option A.121 fit the question criteria? IMO both A and C are answers Posted from my mobile device _________________ Help with kudos if u found the post useful. Thanks Intern Joined: 20 Oct 2017 Posts: 31 Location: India Concentration: Organizational Behavior, Sustainability WE: Other (Education) If x and y are integers, which of the following CANNOT be the value of [#permalink] ### Show Tags 25 Jan 2018, 04:26 1 Sasindran wrote: MathRevolution wrote: [GMAT math practice question] If $$x$$ and $$y$$ are integers, which of the following CANNOT be the value of $$x^2+y^2$$? $$A. 121$$ $$B. 122$$ $$C. 123$$ $$D. 125$$ $$E. 130$$ How can option A.121 fit the question criteria? IMO both A and C are answers Posted from my mobile device Assume x = 0 and y = 11; then x^2 + y ^2 = 0 + 121 = 121 i.e. Option A Hence only Option C remains as an answer. _________________ Giving Kudos is the best way to say 'Thank You' Senior Manager Joined: 17 Oct 2016 Posts: 314 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: If x and y are integers, which of the following CANNOT be the value of [#permalink] ### Show Tags 25 Jan 2018, 04:29 Jiggy11 wrote: Sasindran wrote: MathRevolution wrote: [GMAT math practice question] If $$x$$ and $$y$$ are integers, which of the following CANNOT be the value of $$x^2+y^2$$? $$A. 121$$ $$B. 122$$ $$C. 123$$ $$D. 125$$ $$E. 130$$ How can option A.121 fit the question criteria? IMO both A and C are answers Posted from my mobile device Assume x = 0 and y = 11; then x^2 + y ^2 = 0 + 121 = 121 i.e. Option A Hence only Option C remains as an answer. Got it. Thanks. Kudos to you Posted from my mobile device _________________ Help with kudos if u found the post useful. Thanks Intern Joined: 20 Oct 2017 Posts: 31 Location: India Concentration: Organizational Behavior, Sustainability WE: Other (Education) Re: If x and y are integers, which of the following CANNOT be the value of [#permalink] ### Show Tags 25 Jan 2018, 04:34 Sasindran wrote: Got it. Thanks. Kudos to you Posted from my mobile device Thank you so much!!! _________________ Giving Kudos is the best way to say 'Thank You' Math Expert Joined: 02 Aug 2009 Posts: 7952 Re: If x and y are integers, which of the following CANNOT be the value of [#permalink] ### Show Tags 25 Jan 2018, 06:47 MathRevolution wrote: [GMAT math practice question] If $$x$$ and $$y$$ are integers, which of the following CANNOT be the value of $$x^2+y^2$$? $$A. 121$$ $$B. 122$$ $$C. 123$$ $$D. 125$$ $$E. 130$$ the one point you require to know is that 11^2=121.. $$A. 121... 0^2+11^2$$ $$B. 122... 1^2+11^2$$ $$C. 123... ??? you require to check if 10^2, 9^2 or 8^2 can be added to any other square to get 123 .. NO$$ $$D. 125.. 2^2+11^2$$ $$E. 130... 3^2+11^2$$ C _________________ CEO Joined: 12 Sep 2015 Posts: 3990 Location: Canada Re: If x and y are integers, which of the following CANNOT be the value of [#permalink] ### Show Tags 25 Jan 2018, 10:32 1 Top Contributor MathRevolution wrote: [GMAT math practice question] If $$x$$ and $$y$$ are integers, which of the following CANNOT be the value of $$x^2+y^2$$? $$A. 121$$ $$B. 122$$ $$C. 123$$ $$D. 125$$ $$E. 130$$ Let's do this systematically: 0² = 0 1² = 1 2² = 4 3² = 9 4² = 16 5² = 25 6² = 36 7² = 49 8² = 64 9² = 81 10² = 100 11² = 121 A. 121 = 0² + 11² ELIMINATE A B. 122 = 1² + 11² ELIMINATE B C. 123 = can't eliminate D. 125 = 10² + 5² ELIMINATE D E. 130 = 9² + 7² ELIMINATE E Answer: C Cheers, Brent _________________ Test confidently with gmatprepnow.com Director Joined: 31 Jul 2017 Posts: 512 Location: Malaysia Schools: INSEAD Jan '19 GMAT 1: 700 Q50 V33 GPA: 3.95 WE: Consulting (Energy and Utilities) Re: If x and y are integers, which of the following CANNOT be the value of [#permalink] ### Show Tags 26 Jan 2018, 22:43 MathRevolution wrote: [GMAT math practice question] If $$x$$ and $$y$$ are integers, which of the following CANNOT be the value of $$x^2+y^2$$? $$A. 121$$ $$B. 122$$ $$C. 123$$ $$D. 125$$ $$E. 130$$ This can be easily solved by taking one of the Integer as 11. Hence, C. _________________ If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8001 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are integers, which of the following CANNOT be the value of [#permalink] ### Show Tags 28 Jan 2018, 18:45 => Squares of even integers, $$(2k)^2 = 4k^2$$ have the remainder $$0$$, when they are divided by $$4$$. Squares of odd integers, $$(2k+1)^2 = 4k^2 + 4k + 1$$ have the remainder $$1$$, when they are divided by $$4$$. Hence, squares of integers can have remainders of $$0$$ or $$1$$ only, when they are divided by $$4$$. So, the sum of two squares of integers cannot have the remainder of $$3$$ when it is divided by $$4$$. Thus, $$123$$ cannot be the value of $$x^2+y^2$$. Therefore, the answer is C. Answer: C _________________ 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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Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817
Re: If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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29 Jan 2018, 10:34
MathRevolution wrote:
[GMAT math practice question]

If $$x$$ and $$y$$ are integers, which of the following CANNOT be the value of $$x^2+y^2$$?

$$A. 121$$
$$B. 122$$
$$C. 123$$
$$D. 125$$
$$E. 130$$

A) 121

121 = 0^2 + 11^2

B) 122

122 = 1^1 + 11^2

C) 123

There are no two perfect squares that sum to 123.

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Re: If x and y are integers, which of the following CANNOT be the value of   [#permalink] 29 Jan 2018, 10:34
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