Difference between revisions of "2014 AMC 10A Problems/Problem 7"
(→Solution) |
|||
Line 17: | Line 17: | ||
==Solution== | ==Solution== | ||
+ | Clearly, <math>\text{(I)}</math> must be true (do you see why?) | ||
+ | |||
+ | Consider <math>x=-2013, a=1, y=-2013, b=1</math>. Clearly, we have <math>x<a</math> and <math>y<b</math>. Note that <math>\text{(II), (III), }</math> and <math>\text{(IV)}</math> are false, so our answer is <math>\boxed{\textbf{(B) 1}}</math> | ||
==See Also== | ==See Also== |
Revision as of 17:42, 7 February 2014
Problem
Nonzero real numbers , , , and satisfy and . How many of the following inequalities must be true?
$\textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}}\ 3\qquad\textbf{(E)}\ 4$ (Error compiling LaTeX. Unknown error_msg)
Solution
Clearly, must be true (do you see why?)
Consider . Clearly, we have and . Note that and are false, so our answer is
See Also
2014 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.