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The squares of two consecutive positive integers differ by 5

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by Max@Math Revolution » Sun Feb 17, 2019 11:32 pm
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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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by Brent@GMATPrepNow » Mon Feb 18, 2019 5:48 am
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)² - x² = 55
Expand: x² + 2x + 1 - x² = 55
Simplify: 2x + 1 = 55
So: 2x = 54
Solve: x = 54/2 = 27

Answer: A

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Wed Feb 20, 2019 5:19 pm
=>

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
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