If \frac{a^{5}}{b} 0, then which of the following must be less than 1?

If \frac{a^{5}}{b} < 0 and \frac{b}{c} > 0, then w... | Free GMAT Practice Question | GMAT Panda

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GMAT Quant — Quant (Inequalities)

If \frac{a ^{5}}{b} < 0 and \frac{b}{c} > 0, then which of the following must be less than 1?

Explanation	Calculations	Help
$We note that the inequality \frac{a ^{5}}{b} < 0 implies the sign of \frac{a ^{5}}{b} matches that of \frac{a}{b} because a^{4} is always positive. Using the xy < 0 implies one positive, one negative rule, we conclude that a and b have opposite signs.$	$a^{4} > 0$
$We note that \frac{a ^{5}}{b} < 0 implies \frac{a}{b} < 0 because a^{4} is always positive, so the sign of \frac{a ^{5}}{b} matches that of \frac{a}{b} .$	$\frac{a ^{5}}{b} < 0 ⟹ \frac{a}{b} < 0$	Theory & Tactics Method Card INEQ2-A Click to view full details
$From the fact that \frac{b}{c} > 0, by the x/y > 0 implies same sign rule we know that b and c have the same sign.$	$\frac{b}{c} > 0$	Theory & Tactics Method Card INEQ2-C Click to view full details
$From the fact that \frac{b}{c} > 0, we know that b and c have the same sign.$	$b and c have the same sign$

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B

GMAT Quant — Quant (Inequalities)

If \frac{a ^{5}}{b} < 0 and \frac{b}{c} > 0, then which of the following must be less than 1?

Explanation	Calculations	Help
$We note that the inequality \frac{a ^{5}}{b} < 0 implies the sign of \frac{a ^{5}}{b} matches that of \frac{a}{b} because a^{4} is always positive. Using the xy < 0 implies one positive, one negative rule, we conclude that a and b have opposite signs.$	$a^{4} > 0$
$We note that \frac{a ^{5}}{b} < 0 implies \frac{a}{b} < 0 because a^{4} is always positive, so the sign of \frac{a ^{5}}{b} matches that of \frac{a}{b} .$	$\frac{a ^{5}}{b} < 0 ⟹ \frac{a}{b} < 0$	Theory & Tactics Method Card INEQ2-A Click to view full details
$From the fact that \frac{b}{c} > 0, by the x/y > 0 implies same sign rule we know that b and c have the same sign.$	$\frac{b}{c} > 0$	Theory & Tactics Method Card INEQ2-C Click to view full details
$From the fact that \frac{b}{c} > 0, we know that b and c have the same sign.$	$b and c have the same sign$

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B