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# The squares of two consecutive positive integers differ by 55. What is

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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The squares of two consecutive positive integers differ by 55. What is  [#permalink]

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18 Feb 2019, 00:53
2
1
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Difficulty:

15% (low)

Question Stats:

83% (01:20) correct 17% (01:46) wrong based on 47 sessions

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[GMAT math practice question]

The squares of two consecutive positive integers differ by 55. What is the smaller of the two integers?

A. 27
B. 29
C. 30
D. 32
E. 35

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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" NUS School Moderator Joined: 18 Jul 2018 Posts: 1020 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: The squares of two consecutive positive integers differ by 55. What is [#permalink] ### Show Tags 18 Feb 2019, 01:00 1 1 Let the consecutive integers be a and a+1 $$(a+1)^2-a^2 = 55$$ $$a^2+2a+1-a^2 = 55$$ $$2a = 54$$ $$a = 27$$ The consecutive integers are 27 and 28, 27 being the smallest. A is the answer. _________________ Press +1 Kudos If my post helps! GMAT Club Legend Joined: 18 Aug 2017 Posts: 5020 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: The squares of two consecutive positive integers differ by 55. What is [#permalink] ### Show Tags 18 Feb 2019, 01:10 MathRevolution wrote: [GMAT math practice question] The squares of two consecutive positive integers differ by 55. What is the smaller of the two integers? A. 27 B. 29 C. 30 D. 32 E. 35 given square of two consecutive no is 55 lets solve considering answer options 27 (28^2-27^2) = 55 (28+27)*(28-27) = 55 55*1=55 LHS = RHS sufficient IMO A Director Joined: 09 Mar 2018 Posts: 994 Location: India Re: The squares of two consecutive positive integers differ by 55. What is [#permalink] ### Show Tags 18 Feb 2019, 01:19 MathRevolution wrote: [GMAT math practice question] The squares of two consecutive positive integers differ by 55. What is the smaller of the two integers? A. 27 B. 29 C. 30 D. 32 E. 35 Let smaller term = x Next consecutive term = x+1 So now as per given, "The squares of two consecutive positive integers differ by 55" $$[m](x-1)^2$$[/m] - $$x^2$$ = 55 just expand this to get x = 27 _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. VP Joined: 31 Oct 2013 Posts: 1465 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Re: The squares of two consecutive positive integers differ by 55. What is [#permalink] ### Show Tags 18 Feb 2019, 02:59 MathRevolution wrote: [GMAT math practice question] The squares of two consecutive positive integers differ by 55. What is the smaller of the two integers? A. 27 B. 29 C. 30 D. 32 E. 35 *** consecutive positive integers. x and x + 1 $$( x + 1)^2 - x^2 = 55$$ ( x + 1 + x) ( x + 1 - x) = 55 2x + 1 =55 x = 27. A is the correct answer. GMAT Club Legend Joined: 12 Sep 2015 Posts: 4009 Location: Canada Re: The squares of two consecutive positive integers differ by 55. What is [#permalink] ### Show Tags 18 Feb 2019, 07:21 Top Contributor MathRevolution wrote: [GMAT math practice question] The squares of two consecutive positive integers differ by 55. What is the smaller of the two integers? A. 27 B. 29 C. 30 D. 32 E. 35 Let x = the smaller integer So, x+1 = the larger integer (since the numbers are CONSECUTIVE) The squares of two consecutive positive integers differ by 55. We can write: (x + 1)² - x² = 55 Expand: x² + 2x + 1 - x² = 55 Simplify: 2x + 1 = 55 So: 2x = 54 Solve: x = 54/2 = 27 Answer: A Cheers, Brent _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The squares of two consecutive positive integers differ by 55. What is [#permalink] ### Show Tags 20 Feb 2019, 18:36 => Let the two consecutive positive integers be $$n$$ and $$n+1$$. Then $$(n+1)^2 – n^2 = 55$$, so $$2n+1 = 55.$$ It follows that $$2n = 54$$ and $$n = 27$$. Therefore, the answer is A. Answer: A _________________ 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: The squares of two consecutive positive integers differ by 55. What is   [#permalink] 20 Feb 2019, 18:36
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