1956 AHSME Problems/Problem 44

Problem 44

If $x < a < 0$ means that $x$ and $a$ are numbers such that $x$ is less than $a$ and $a$ is less than zero, then:

$\textbf{(A)}\ x^2 < ax < 0 \qquad \textbf{(B)}\ x^2 > ax > a^2 \qquad \textbf{(C)}\ x^2 < a^2 < 0 \\ \textbf{(D)}\ x^2 > ax\text{ but }ax < 0 \qquad \textbf{(E)}\ x^2 > a^2\text{ but }a^2 < 0$

Solution

Note that since $x$ and $a$ are negative, $x^2, a^2,$ and $ax$ are all positive. Hence the only correct answer is $\fbox{B}$ .

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1956 AHSME Problems/Problem 44

Problem 44

Solution