GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 11 Aug 2022, 03:14
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
If x < y, which of the following must be true?
12 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 86563
CAT Tests Top Member of the Month
If x < y, which of the following must be true? [#permalink] New post  10 Mar 2020, 03:24
11
Bookmarks
Expert Reply
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

69% (01:32) correct 31% (01:15) wrong based on 447 sessions

Hide Show timer Statistics

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
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Expert Reply
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 6760
Location: Canada
Top Member of the Month
Re: If x < y, which of the following must be true? [#permalink] New post  19 Jan 2022, 09:44
1
Kudos
Expert Reply
Top Contributor
Bunuel wrote:
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


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...
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more
Signature Read More
General Discussion
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5873
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE:Education (Education)
Reviews Badge
Re: If x < y, which of the following must be true? [#permalink] New post  10 Mar 2020, 03:43
2
Kudos
Expert Reply
Bunuel wrote:
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


x - y < 0

Squaring both sides

(x - y)^2 > 0

Answer: Option D
_________________
GMATinsight
Great Results (Q≥50 and V≥40) l Honest and Effective Admission Support l 100% Satisfaction !!!
One-on-One GMAT Skype classes l On-demand Quant Courses and Pricing l Admissions Consulting
Call/mail: +91-9999687183 l info@gmatinsight.com (for FREE Demo class/consultation)
SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l GMAT730+ESCP
FREE Resources: 22 FULL LENGTH TESTS l OG QUANT 50 Qn+VIDEO Sol. l NEW:QUANT REVISION Topicwise Quiz
Signature Read More
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 4738
Location: India
Schools: HBS '22, CBS '22, Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Reviews Badge Forum Quiz Mode
Re: If x < y, which of the following must be true? [#permalink] New post  10 Mar 2020, 03:49
Bunuel wrote:
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


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 \(x-y \neq 0 \)
(E) x^3 > y

IMO D
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Signature Read More
User avatar
B
Farina
Manager
Manager
Joined: 21 Aug 2019
Posts: 116
Re: If x < y, which of the following must be true? [#permalink] New post  15 Mar 2020, 05:46
1
Kudos
Kinshook wrote:
Bunuel wrote:
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


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 \(x-y \neq 0 \)
(E) x^3 > y

IMO D


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.
_________________
I don't believe in giving up!
Signature Read More
User avatar
P
ARIEN3228
Manager
Manager
Joined: 18 Jan 2018
Posts: 160
Location: India
Concentration: Operations, International Business
Schools: Ivey '22, ISB'22, CBS '22
GPA: 3.27
WE:Operations (Other)
Re: If x < y, which of the following must be true? [#permalink] New post  15 Mar 2020, 23:01
2
Kudos
Farina wrote:
Kinshook wrote:
Bunuel wrote:
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


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 \(x-y \neq 0 \)
(E) x^3 > y

IMO D


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.



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.
_________________
Believe!!
Signature Read More
User avatar
B
wizakoraksha
Intern
Intern
Joined: 16 Dec 2016
Posts: 7
GMAT 1: 710 Q49 V38
Reviews Badge
Re: If x < y, which of the following must be true? [#permalink] New post  16 Mar 2020, 02:58
2
Kudos
1
Bookmarks
Expert Reply
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
avatar
B
sathriyan
Intern
Intern
Joined: 22 Feb 2019
Status:Stay Hungry, Stay Foolish
Posts: 12
Re: If x < y, which of the following must be true? [#permalink] New post  03 Apr 2020, 05:31
wizakoraksha wrote:
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


How can we square both sides the highlighted portion, Since we don't have any information about the sign of the X-Y?
avatar
B
abhitg0612
Intern
Intern
Joined: 31 Mar 2020
Posts: 2
Re: If x < y, which of the following must be true? [#permalink] New post  06 Apr 2020, 06:01
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
avatar
B
pratiksha1998
Manager
Manager
Joined: 11 Aug 2021
Posts: 51
Location: India
Concentration: General Management, Strategy
Schools: Emory Goizueta
GMAT 1: 600 Q47 V27
Re: If x < y, which of the following must be true? [#permalink] New post  18 Sep 2021, 04:29
Can someone explain how A must not be true?
avatar
B
Isa1989
Intern
Intern
Joined: 14 Aug 2021
Posts: 14
Re: If x < y, which of the following must be true? [#permalink] New post  21 Sep 2021, 06:28
sathriyan wrote:
wizakoraksha wrote:
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


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


Hi.
Since x<y, we know that x-y is negative.
avatar
B
Isa1989
Intern
Intern
Joined: 14 Aug 2021
Posts: 14
Re: If x < y, which of the following must be true? [#permalink] New post  21 Sep 2021, 06:32
1
Kudos
pratiksha1998 wrote:
Can someone explain how A must not be true?


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.
GMAT Club Bot
gmatclubot
Re: If x < y, which of the following must be true? [#permalink]
21 Sep 2021, 06:32
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
10477 posts
Bunuel
Math Expert
86564 posts
generis
Senior SC Moderator
5453 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3025 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions