Difference between revisions of "2010 AMC 12A Problems/Problem 4"
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<math>\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}</math> | <math>\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}</math> | ||
− | + | == Solution == | |
+ | <math>x</math> is negative, so we can just place a negative value into each expression and find the one that is positive. Suppose we use <math>-1</math>. | ||
+ | |||
+ | <math>\textbf{(A)} \Rightarrow \frac{-1}{|-1|} = -1</math> | ||
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+ | <math>\textbf{(B)} \Rightarrow -(-1)^2 = -1</math> | ||
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+ | <math>\textbf{(C)} \Rightarrow -2^{(-1)} = -\frac{1}{2}</math> | ||
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+ | <math>\textbf{(D)} \Rightarrow -(-1)^{(-1)} = 1</math> | ||
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+ | <math>\textbf{(E)} \Rightarrow \sqrt[3]{-1} = -1</math> | ||
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+ | |||
+ | Obviously only <math>\boxed{\textbf{(D)}}</math> is positive. |
Revision as of 16:30, 10 February 2010
Problem 4
If , then which of the following must be positive?
Solution
is negative, so we can just place a negative value into each expression and find the one that is positive. Suppose we use .
Obviously only is positive.