Difference between revisions of "1951 AHSME Problems/Problem 21"
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<math>\textbf{(B)}\ x - z > y - z\implies x>y</math>, just add <math>z</math> to both sides | <math>\textbf{(B)}\ x - z > y - z\implies x>y</math>, just add <math>z</math> to both sides | ||
− | <math>\textbf{(C)}\ xz > yz\implies x>y\text{ | + | <math>\textbf{(C)}\ xz > yz\implies x>y\text{ if }x>0</math>, so that means that our desired answer is <math>\boxed{\textbf{(C)}\ xz > yz}</math>. |
As a check: | As a check: |
Latest revision as of 02:34, 28 June 2017
Problem
Given: and . The inequality which is not always correct is:
Solution
, just subtract from both sides
, just add to both sides
, so that means that our desired answer is .
As a check:
, we can divide safely and without worry because .
, similar reasoning as above but instead, multiply .
See Also
1951 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.