[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
The squares of two consecutive positive integers differ by 5
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- Max@Math Revolution
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Let x = the smaller integerMax@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
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
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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.
Therefore, the answer is A.
Answer: A
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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