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

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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

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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

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

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