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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 ## The squares of two consecutive positive integers differ by 5 tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## The squares of two consecutive positive integers differ by 5 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 _________________ 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]

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)Â˛ - xÂ˛ = 55
Expand: xÂ˛ + 2x + 1 - xÂ˛ = 55
Simplify: 2x + 1 = 55
So: 2x = 54
Solve: x = 54/2 = 27

Cheers,
Brent

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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.

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