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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