2010 AMC 12A Problems/Problem 4: Difference between revisions
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== Problem | == Problem == | ||
If <math>x<0</math>, then which of the following must be positive? | If <math>x<0</math>, then which of the following must be positive? | ||
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Obviously only <math>\boxed{\textbf{(D)}}</math> is positive. | Obviously only <math>\boxed{\textbf{(D)}}</math> is positive. | ||
== See also == | |||
{{AMC12 box|year=2010|num-b=3|num-a=5|ab=A}} | |||
[[Category:Introductory Algebra Problems]] | |||
Revision as of 21:58, 25 February 2010
Problem
If 
, then which of the following must be positive?
![$\textbf{(A)}\ \frac{x}{\left|x\right|} \qquad \textbf{(B)}\ -x^2 \qquad \textbf{(C)}\ -2^x \qquad \textbf{(D)}\ -x^{-1} \qquad \textbf{(E)}\ \sqrt[3]{x}$](http://latex.artofproblemsolving.com/8/a/6/8a6b210377d3c8faaed5b00e17cbd935d20a0295.png)
Solution
is negative, so we can just place a negative value into each expression and find the one that is positive. Suppose we use 
.
![$\textbf{(E)} \Rightarrow \sqrt[3]{-1} = -1$](http://latex.artofproblemsolving.com/5/d/a/5da4b91ca769554cfbff384adaa5aa432a2ef63a.png)
Obviously only 
is positive.
See also
| 2010 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 3 |
Followed by Problem 5 |
| 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 12 Problems and Solutions | |
