If which x

Question

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

A. y + 1 < x
B. y - 1 < x
C. xy^2 < x
D. xy < y^2
E. xy < x^2

KSBGC · Answer

Plugging in numbers is the best one for this question.

Note: both x and y are negative. Between x and y, x is lower than y 
 
Let assume the value of x and y .

x = -2 x= -0.5
y = -1 y = -0.25

Option E is always true .

E) xy < x^2 
 
 = (-1)(-2) < (-2)^2

=2 < 4

Plugging In Fraction :

(-0.5)(-0.25) <  (0.5)^2

0.125 < 0.25......true.

Thus E is the best answer.

chetan2u · Answer

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

A. y + 1 < x
Let x=-2 and y=-1........-1+1<-2...0<-2....NO

B. y - 1 < x
Let x=-2 and y=-1......-1-1<-2......-2<-2.....NO

C. xy^2 < x
\(x-xy^2>0......x(1-y^2)>0.......x<0, so:(1-y^2)<0......y^2>1\)...Not necessary, y can be -1/2

D. xy < y^2
\(y^2-xy>0.......y(y-x)>0......y<0, so:(y-x)<0......y<x\)....NO

E. xy < x^2
\(x^2-xy>0.....x(x-y)>0......X<0,so:(x-y)<0.....X<y\)...yes always

E

PKN · Answer

Bunuel  Sir,

Kindly provide OE.

I am getting the answer as E but the OE provided is D.

Thanking you.

Bunuel · Answer

The OA is E. Edited. Thank you.

Kem12 · Answer

Hi thanks for the explanation but I'm still trying to understand how you simplified option E... Isn't the answer supposed to be x>0 (x-y) >0. Why the sign change?

Posted from my mobile device

chetan2u · Answer

Hi.. We have X(x-y)>0.... There are two cases.. 1) both X and x-y are positive since +*+=+>0 2) both X and x-y are negative since -*-=+>0 And it is given X<0, so case 1 is out.. In case II X<0, and therefore x-y<0...X

ScottTargetTestPrep · Answer

We can see that both x and y are negative, and y is greater than x. So A is not true. B is not true, either, since we don’t know how much y is greater than x. If we divide both sides by x in the inequality in C (and switch the inequality sign since x is negative), we have:

y^2 > 1

However, since we don’t know the value of y, we can’t determine whether its square is in fact greater than 1. So C might not be true. If we divide both sides by y in the inequality in D (and switch the inequality sign since y is negative), we have:

x > y

This is not true since we know y > x. So the correct answer must be E. However, let’s verify it by dividing both sides of the inequality by x:

y > x

This is true since we know y is indeed greater than x.

Answer: E

KarishmaB · Answer

Responding to a pm:

When you divide both sides by a variable, you lose out on a solution. So you should not divide both sides by a variable.

Also, here when you divide both sides by y which is negative, the sign of the inequality will flip. You will get 
 xy < y^2  becomes
 x > y

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 which x < y < 0, of the following inequalities 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