1967 AHSME Problems/Problem 7

Problem

If $\frac{a}{b}<-\frac{c}{d}$ where $a$ , $b$ , $c$ , and $d$ are real numbers and $bd \not= 0$ , then:

$\text{(A)}\ a \; \text{must be negative} \qquad \text{(B)}\ a \; \text{must be positive} \qquad$ $\text{(C)}\ a \; \text{must not be zero} \qquad \text{(D)}\ a \; \text{can be negative or zero, but not positive } \\ \text{(E)}\ a \; \text{can be positive, negative, or zero}$

Solution

Notice that $b$ and $d$ are irrelevant to the problem. Also notice that the negative sign is irrelevant since $c$ can be any real number. So the question is equivalent to asking what values $a$ can take on given the inequality $a<c$ . The answer, is of course, that $a$ could be anything, or $\boxed{\textbf{(E) } \ a \; \text{can be positive, negative, or zero}}$

~ proloto

1967 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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1967 AHSME Problems/Problem 7

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