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

If \frac{x^3}{y} < 0, and \frac{y}{z} > 0, then wh... | Free GMAT Practice Question | GMAT Panda

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GMAT Quant — Quant (Inequalities)

If \frac{x ^{3}}{y} < 0, and \frac{y}{z} > 0, then which of the following must be less than 1?

Explanation	Calculations	Help
$From \frac{x ^{3}}{y} < 0, we know the numerator x^{3} and denominator y have opposite signs.$	$x < 0 and y > 0 or x > 0 and y < 0$	Theory & Tactics Method Card INEQ2-A Click to view full details
$From \frac{y}{z} > 0, we know y and z have the same sign.$	$y > 0 and z > 0 or y < 0 and z < 0$	Theory & Tactics Method Card INEQ2-C Click to view full details
$Combining the two results gives two possible sign assignments for (x, y, z) .$	$Case 1: x < 0, y > 0, z > 0 Case 2: x > 0, y < 0, z < 0$
$For option E, x y^{2} z^{3} is negative in both cases, and any negative number is less than 1.$	$Case 1: x < 0, y^{2} > 0, z^{3} > 0 ⟹ x y^{2} z^{3} < 0 < 1 Case 2: x > 0, y^{2} > 0, z^{3} < 0 ⟹ x y^{2} z^{3} < 0 < 1$

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E

GMAT Quant — Quant (Inequalities)

If \frac{x ^{3}}{y} < 0, and \frac{y}{z} > 0, then which of the following must be less than 1?

Explanation	Calculations	Help
$From \frac{x ^{3}}{y} < 0, we know the numerator x^{3} and denominator y have opposite signs.$	$x < 0 and y > 0 or x > 0 and y < 0$	Theory & Tactics Method Card INEQ2-A Click to view full details
$From \frac{y}{z} > 0, we know y and z have the same sign.$	$y > 0 and z > 0 or y < 0 and z < 0$	Theory & Tactics Method Card INEQ2-C Click to view full details
$Combining the two results gives two possible sign assignments for (x, y, z) .$	$Case 1: x < 0, y > 0, z > 0 Case 2: x > 0, y < 0, z < 0$
$For option E, x y^{2} z^{3} is negative in both cases, and any negative number is less than 1.$	$Case 1: x < 0, y^{2} > 0, z^{3} > 0 ⟹ x y^{2} z^{3} < 0 < 1 Case 2: x > 0, y^{2} > 0, z^{3} < 0 ⟹ x y^{2} z^{3} < 0 < 1$

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E