If x

Question

If x < y < 0, which of the following must be true? I. |x| > |y| II. x/y > 1 III. x^y < 0 A. I only B. II only C. III only D. I and II only E. I and III only M37-04

Bunuel · Accepted Answer

Official Solution: If x < y < 0 , which of the following must be true? I. \ |x| > |y| II. \ \frac{x}{y} > 1 III. \ x^y < 0 A. I only B. II only C. III only D. I and II only E. I and III only I. \ |x| > |y| . x < y < 0 means that x is further from 0 than y , so |x| > |y| . I must be true. II. \ \frac{x}{y} > 1 . Divide x < y < 0 by y and flip the signs (because y is negative): \frac{x}{y} > 1 > 0 . II must be true. III. \ x^y < 0 . This one is clearly wrong when y is even, so II is not always true. Answer: D

Ana4001 · Answer

Answer is A only

As x and y are negative with Mode of X always greater than Mode of Y

Second and third condition are may be true or may not bw

Posted from my mobile device

KarishmaB · Answer

x and y are both negative numbers. Imagine the number line: y is to the left of 0 and x is to the left of y. e.g. x = -2 and y = -1 or x = -1/2 and y = -1/3 and so on. The absolute value of x will be greater than absolute value of y to make x "more negative". Since x and y are both negative, x/y is positive. Since absolute value of x is greater than absolute value of y, x/y > 1 So both I and II will hold. III may not hold if y is even. e.g. x = -3, y = -2 so x^y = (-3)^(-2) = 1/9 (not negative) Answer (D) You can prove I and II algebraically too. x and y are negative. x < y Multiply both sides by -1 to get -x > -y Since x and y are negative, |x| = -x and |y| = -y So |x| > |y| x < y Divide both sides by y (which is negative) to get x/y > 1 (the inequality sign flips)

KanishkM · Answer

Given x |y|, will always be true, just plug in these values -2 < -1 < 0 or - 0.50 < - 0.25 < 0 II. x/y > 1, in this case, y will always be less than x, -4/-2 > 1, -0.1/ - 0.05 > 1, -6/-5 > 1 At this stage, we can just mark D and go ahead. Still, III. x^y < 0, if y is an even power, the relationship will become +ive which wont be < 0 if y is an odd power, the relationship will become -ive which is < 0 Answer D

Archit3110 · Answer

from given relation we can say that whether x & y are fractions or integers they would both be -ve values since <0 is mentioned

test the relations with x = -2 and y = -3 and fractions y= -1/3 and x = -1/2

upon reviewing the options we can conclude that options 1 & 2 would stand correct
IMO D

dimri10 · Answer

X<y<0 holds for 3 possibilities:
Negative integer v NI. -5 v -2
Fraction v F. -3/4 v -1/8
NI v F -3 v -1/2
In all 3 the Value of X is greater than y.
In all 3 X/y is greater than 1

Posted from my mobile device

Doer01 · Answer

Hi, x |y|? |-2| > |-1| ?? yes. All we care about is the absolute value of both the components; i.e without their signs. and 2>1. So I is true. II.x/y>1?? -2/-1>1?? yes. III. x^y>1?? (-2)^-1 >1?? NO So only i & II must be true. D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x < y < 0, which of the following must be true?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions