If x

Question

If x < y, which of the following must be true? (A) x < y^2 (B) x^2 < y (C) x^2 < y^2 (D) (x – y)^2 > 0 (E) x^3 > y

BrentGMATPrepNow · Accepted Answer

If x < y, then we can also conclude that x ≠ y. 
If x ≠ y, then we can be certain that x - y ≠ 0
If x - y ≠ 0, then we can be certain that (x – y)^2 > 0

Answer: D

ASIDE: Another approach would be to take values that satisfy the inequality x < y, and plug them into each answer choice until we eventually eliminate all answer choices other than D. 
I'll leave that to you...

GMATinsight · Answer

x - y < 0

Squaring both sides

(x - y)^2 > 0

Answer: Option D

Kinshook · Answer

Asked: If x < y, which of the following must be true? (A) x < y^2 (B) x^2 < y (C) x^2 < y^2 (D) (x – y)^2 > 0 must be true since x-y eq 0 (E) x^3 > y IMO D

Farina · Answer

If we plug in values say x = -3 and y = -2 we dont get the correct answer D, instead A is correct in this case?
Can you please explain this.

ARIEN3228 · Answer

x = -3 and y = -2 
i.e (-3+2)^2 > 0

Tip: If x is not equal to y, the square of sum or difference of x and y is always greater than 0. Option D is always correct.

wizakoraksha · Answer

Here, the given statement = x < y. We can also re-write the statement as x-y < 0.

If you square the statement on both sides, the greater than / lesser than sign also changes sides.

Here squaring both sides we get (x-y)^2 > 0.

When looking at the answer options here, D is exactly in line with the answer we have derive because, x < y and x-y isn't 0.

Hence the correct answer is D.

K S Raksha
GMAT Tutor at Wizako GMAT Classes & Online Courses

sathriyan · Answer

How can we square both sides the highlighted portion, Since we don't have any information about the sign of the X-Y?

abhitg0612 · Answer

Option D is right -

X < Y 
X - Y < 0 
** Square of any value is > 0

Option A is not correct for few cases where X & Y lie between 0 & 1, X = 0.3, Y = 0.4 & Y^2 = 0.16

pratiksha1998 · Answer

Can someone explain how A must not be true?

Isa1989 · Answer

Hi.
Since x<y, we know that x-y is negative.

Isa1989 · Answer

If x=1/4 and y=1/2 then y^2=1/4 and x would be equal to y^2 and not less than it.This eliminates option A since a MUST BE true option would be true for all cases.

Hope this helps.

nishantrana6 · Answer

can someone explain how option C is not true. 
X < Y, 
squaring both sides gives us X^2 < Y^2,

sanyasanha · Answer

Experts, please help with option C. I am not able to rule it out.

Bunuel   chetan2u

Bunuel · Answer

Consider negative x (and y between x and -x). For example: 
If x = -2 and y = -1, then (x^2 = 4) > (y^2 = 1);
If x = -2 and y = 1, then (x^2 = 4) > (y^2 = 1);
...

So, C (x^2 < y^2) is not always true.

chetan2u · Answer

Whenever x < y but |x|>|y|, you will get x^2>y^2 . One such scenario will be when both are negative integers. (-5)^2>(-1)^2 , while -5<-1.

luisdicampo · Answer

Deconstructing the Question

We are given:

\(x < y\)

We need to find which statement must always be true.

Strategy: test counterexamples. If a statement fails even once, it is not always true.

Step-by-step

A: \(x < y^2\)

Take \(x=0,\ y=0.5\)

\(0 < 0.5\) is true, but \(0 < 0.25\) is false.

So A is not always true.

B: \(x^2 < y\)

Take \(x=-2,\ y=1\)

\(-2 < 1\) is true, but \(4 < 1\) is false.

So B is not always true.

C: \(x^2 < y^2\)

Take \(x=-3,\ y=2\)

\(-3 < 2\) is true, but \(9 < 4\) is false.

So C is not always true.

D: \((x - y)^2 > 0\)

Since \(x < y\), we know \(x \ne y\), so \(x - y \ne 0\).

The square of a nonzero number is always positive.

So this must be true.

E: \(x^3 > y\)

Take \(x=1,\ y=2\)

\(1 < 2\) is true, but \(1^3 > 2\) is false.

So E is not always true.

Answer D

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

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