2007 AMC 8 Problem 19
Attempt Problem 19 of the 2007 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
Pick two consecutive positive integers whose sum is less than Square both of those integers and then find the difference of the squares. Which of the following could be the difference?
Answer: C
Small hint:
Let the consecutive integers be and .
Big hint:
The difference of their squares simplifies to the sum of the two integers.
Solution:
Let the consecutive positive integers be and . Their sum is , which is less than .
The difference of their squares is
So the difference must be an odd number less than . Among the choices, is the only possibility, and it occurs for and .
Thus, C is the correct answer.
Problem 19 in other years
- 1985 AMC 8
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