The squares of two consecutive positive integers differ by 5

[Max@Math Revolution]

[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

[Brent@GMATPrepNow]

[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

[Max@Math Revolution]

=>

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