1996 AIME Problems/Problem 2
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Problem
For each real number , let denote the greatest integer that does not exceed x. For how many positive integers is it true that and that is a positive even integer?
Solution
For integers , we want , or . Thus, must satisfy these inequalities (since ):
There are for the first inequality, for the second, for the third, and for the fourth, so the answer is .
See also
1996 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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