Difference between revisions of "2017 AMC 10B Problems/Problem 3"
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==Problem== | ==Problem== | ||
− | Real numbers <math>x</math>, <math>y</math>, and <math>z</math> | + | Real numbers <math>x</math>, <math>y</math>, and <math>z</math> satisfy the inequalities |
<math>0<x<1</math>, <math>-1<y<0</math>, and <math>1<z<2</math>. | <math>0<x<1</math>, <math>-1<y<0</math>, and <math>1<z<2</math>. | ||
Which of the following numbers is necessarily positive? | Which of the following numbers is necessarily positive? |
Revision as of 12:53, 16 February 2017
Problem
Real numbers , , and satisfy 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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