If \frac{p^3}{q} 0, then which of the following must be less than 1?

If \frac{p^3}{q} < 0 and \frac{q}{r} > 0, then whi... | Free GMAT Practice Question | GMAT Panda

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GMAT Quant — Quant (Inequalities)

If \frac{p ^{3}}{q} < 0 and \frac{q}{r} > 0, then which of the following must be less than 1?

Explanation	Calculations	Help
$Statement I gives that p^{3} / q < 0, so p and q have opposite signs$	$p^{3} / q < 0 ⟹ p and q have opposite signs$	Theory & Tactics Method Card INEQ2-A Click to view full details
$Statement II gives that q / r > 0, so q and r have the same sign$	$q / r > 0 ⟹ q and r have the same sign$	Theory & Tactics Method Card INEQ2-C Click to view full details
$Since p and q have opposite signs and q and r have the same sign, p and r must have opposite signs$	$p and r have opposite signs$
$The product of two numbers with opposite signs is negative, so p r < 0$	$p \times r < 0$	Theory & Tactics Method Card PN2-C Click to view full details
$Any negative number is less than 1, so p r < 1$	$p r < 1$

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A

GMAT Quant — Quant (Inequalities)

If \frac{p ^{3}}{q} < 0 and \frac{q}{r} > 0, then which of the following must be less than 1?

Explanation	Calculations	Help
$Statement I gives that p^{3} / q < 0, so p and q have opposite signs$	$p^{3} / q < 0 ⟹ p and q have opposite signs$	Theory & Tactics Method Card INEQ2-A Click to view full details
$Statement II gives that q / r > 0, so q and r have the same sign$	$q / r > 0 ⟹ q and r have the same sign$	Theory & Tactics Method Card INEQ2-C Click to view full details
$Since p and q have opposite signs and q and r have the same sign, p and r must have opposite signs$	$p and r have opposite signs$
$The product of two numbers with opposite signs is negative, so p r < 0$	$p \times r < 0$	Theory & Tactics Method Card PN2-C Click to view full details
$Any negative number is less than 1, so p r < 1$	$p r < 1$

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A