2017 AMC 10B Problems/Problem 3
Problem
Real numbers , , and satify the inequalities , , and . Which of the following numbers is necessarily positive?
Solution
Notice that must be positive because . Therefore the answer is .
The other choices:
As grows closer to , decreases and thus becomes less than .
can be as small as possible (), so grows close to as approaches .
For all , , and thus it is always negative.
The same logic as above, but when this time.
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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