2007 AMC 8 Problems/Problem 19
Contents
[hide]Problem
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?
Solution
Let the smaller of the two numbers be x Then, the problem states that (x+1)+x<100. (x+1)^2-x^2=x^2+2x+1-x^2=2x+1 2x+1 is obviously odd, so only answer choices C and E need to be considered.
2x+1=131 refutes the fact that 2x+1<100 so the answer is C
Video Solution by WhyMath
~savannahsolver
See Also
2007 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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