Difference between revisions of "2014 AMC 10A Problems/Problem 7"
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==Solution== | ==Solution== | ||
| + | Clearly, <math>\text{(I)}</math> must be true (do you see why?) | ||
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| + | 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 18:42, 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 | ||
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