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# If x and y are negative integers, which of the following must be true?

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3302
Location: India
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If x and y are negative integers, which of the following must be true?  [#permalink]

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Updated on: 31 Oct 2018, 21:23
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35% (medium)

Question Stats:

68% (00:42) correct 32% (00:40) wrong based on 28 sessions

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If x and y are negative integers, which of the following must be true?

I. $$x - y > 0$$
II. $$\frac{x}{y} > y$$
III. $$x^2 > y$$

A. I only
B. II only
C. III only
D. I and III
E. II and III

_________________

You've got what it takes, but it will take everything you've got

Originally posted by pushpitkc on 31 Oct 2018, 17:12.
Last edited by Bunuel on 31 Oct 2018, 21:23, edited 2 times in total.
Edited the question and the tags.
Intern
Joined: 27 Sep 2017
Posts: 3
Re: If x and y are negative integers, which of the following must be true?  [#permalink]

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31 Oct 2018, 21:36
pushpitkc wrote:
If x and y are negative integers, which of the following must be true?

I. $$x - y > 0$$
II. $$\frac{x}{y} > y$$
III. $$x^2 > y$$

A. I only
B. II only
C. III only
D. I and III
E. II and III

ANS SHOULD BE E
Manager
Joined: 24 Dec 2017
Posts: 145
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: If x and y are negative integers, which of the following must be true?  [#permalink]

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31 Oct 2018, 22:29
X and Y are -ve integers

(I) x - y>0
Case 1: x=-2 and y =-3
-2+3 = 1>0 (YES)
Case 2: x=-3 and y=-2
-3+2 = -1>0 (NO)

Hence A & D can be ruled out

(II) x/y >y
Case 1: x= -2 and y=-3
-2/-3 > -3
0.66 > -3 (YES)

LHS will be always positive since numerator and denominator are -ve and RHS is always -ve
Hence it must be true

(III) x^2>y
Case 1: x = -2 and y=-3
=>(-2)^2>-3
=>4>-3

This case is always true because a -ve integer will turn +ve once squared and RHS will be always -ve
Hence it must be true

Answer IMO is E
Director
Joined: 31 Oct 2013
Posts: 777
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If x and y are negative integers, which of the following must be true?  [#permalink]

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10 Nov 2018, 01:30
pushpitkc wrote:
If x and y are negative integers, which of the following must be true?

I. $$x - y > 0$$
II. $$\frac{x}{y} > y$$
III. $$x^2 > y$$

A. I only
B. II only
C. III only
D. I and III
E. II and III

both x and y are negative.

I. x - y>0. could be when negative y is greater than negative x. Here we have to be careful about sign.

II. all time true. whenever we divide a negative number by another it yields positive one. thus the result will be greater than negative y.

III.$$x^2$$= positive. True.
Re: If x and y are negative integers, which of the following must be true? &nbs [#permalink] 10 Nov 2018, 01:30
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# If x and y are negative integers, which of the following must be true?

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