Last visit was: 23 Apr 2026, 05:23 It is currently 23 Apr 2026, 05:23
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
805+ (Hard)|   Absolute Values|   Algebra|   Exponents|      
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,449
 [34]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,449
 [34]
If x, y and z are three different non-negative integers, which of the 17 Jun 2019, 09:25
2
Kudos
Add Kudos
32
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

31% (02:26) correct 69% (02:18) wrong based on 391 sessions

History

Date
Time
Result
Not Attempted Yet
If x, y and z are three different non-negative integers, which of the following COULD be true?

i) \(|x-y|=|x+y|=|y-z|\)

ii) \(x^y = y^z\)

iii) \(x^3 + y^3 = z^3\)

A) i only
B) ii only
C) iii only
D) i and ii
E) i and iii
ShowHide Answer
Official Answer
D
Every tricky question should trigger a follow up quiz. Build that habit with GMAT Club Forum Quiz →.
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 23 Apr 2026
Posts: 8,628
Own Kudos:
5,190
 [3]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Club Tests Forum Quiz
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,628
Kudos: 5,190
 [3]
If x, y and z are three different non-negative integers, which of the Updated on: 17 Jun 2019, 12:11
Originally posted by Archit3110 on 17 Jun 2019, 09:42.
Last edited by Archit3110 on 17 Jun 2019, 12:11, edited 2 times in total.
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
given that x, y and z are three different non-negative integers so they can be any integer value =>0
i x=0,y=1,z=2
we get 1=1=1
and
\(x^y = y^z\)
we can take x=1,y=2 and z=0
sufficient
IMO D

GMATPrepNow
If x, y and z are three different non-negative integers, which of the following COULD be true?

i) \(|x-y|=|x+y|=|y-z|\)

ii) \(x^y = y^z\)

iii) \(x^3 + y^3 = z^3\)

A) i only
B) ii only
C) iii only
D) i and ii
E) i and iii
Show more
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,449
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,449
If x, y and z are three different non-negative integers, which of the 17 Jun 2019, 11:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Archit3110
given that x, y and z are three different non-negative integers so they can be any integer value =>0
IMO A is sufficient only at x=0,y=1,x=2
we get 1=1=1
IMO A
Show more
Sorry, but the answer isn't A.
Keep trying!!
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 12 Mar 2026
Posts: 1,841
Own Kudos:
8,509
 [4]
Given Kudos: 707
Location: India
Posts: 1,841
Kudos: 8,509
 [4]
If x, y and z are three different non-negative integers, which of the Updated on: 17 Jun 2019, 12:25
Originally posted by nick1816 on 17 Jun 2019, 12:05.
Last edited by nick1816 on 17 Jun 2019, 12:25, edited 2 times in total.
1
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
i) If x>y
x-y=x+y
y=0
|x|=|x|=|-z|
As z can't be negative, it must be equal to x
Not possible under given constraints

If x<y
y-x=x+y
x=0
Hence
|-y|=|y|=|y-z|
|y|=|y-z|
There are 2 cases again
If y>z
y=y-z
z=0(not possible)

If z>y
y=z-y
z=2y(possible)


ii)\(x^y=y^z\)
Put x=1, y=2 and z=0
\((1)^2=2^0\)
1=1
Can be true

iii)
\(x^3+y^3=z^3\)
Fermat's last theorem, there are no three positive integer x,y and z satisfies \(x^n+y^n=z^n\) for n>2
If any of the number is equal to 0, then the absolute value of other 2 numbers is equal which is against out constraints.
Not Possible!!

GMATPrepNow
If x, y and z are three different non-negative integers, which of the following COULD be true?

i) \(|x-y|=|x+y|=|y-z|\)

ii) \(x^y = y^z\)

iii) \(x^3 + y^3 = z^3\)

A) i only
B) ii only
C) iii only
D) i and ii
E) i and iii
Show more
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,449
 [2]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,449
 [2]
If x, y and z are three different non-negative integers, which of the 17 Jun 2019, 12:17
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATPrepNow
If x, y and z are three different non-negative integers, which of the following COULD be true?

i) \(|x-y|=|x+y|=|y-z|\)

ii) \(x^y = y^z\)

iii) \(x^3 + y^3 = z^3\)

A) i only
B) ii only
C) iii only
D) i and ii
E) i and iii
Show more

I created this question to illustrate the importance of checking the answer choices each time you analyze one of the statements. Here’s why:

Once we know that statement i COULD be true (it's true when x = 0, y = 1 and z = 2), we should check the answer choices….
ELIMINATE answer choices B and C, since they incorrectly state that statement i CANNOT be true.

Once we know that statement ii COULD be true (it's true when x = 8, y = 2 and z = 6), check the remaining answer choices….
ELIMINATE answer choices A and E, since they incorrectly state that statement ii CANNOT be true.

So, by the process of elimination, we know that the correct answer is D
Best of all, we’re able to determine the correct answer WITHOUT analyzing statement iii, which is great since statement iii is VERY TRICKY.

By the way, if you had a hard time determining whether statement iii could be true, you’re not alone!
Statement iii is something mathematicians have struggled with since 1637, when a French mathematician named Pierre de Fermat (shown here)…

…suggested that the equation \(a^3 + b^3 = c^3\) cannot have a solution in which the values of a, b and c are POSITIVE integers.
In fact, Pierre de Fermat went even further to say that the equation \(a^n + b^n = c^n\) cannot have a solution in which the values of a, b and c are POSITIVE integers, for n > 2.

Unfortunately Fermat never proved his theorem. In fact, the theorem (famously known as Fermat’s Last Theorem) was found after his death. Fermat had written the theorem in the margin of one of his textbooks. In addition to the theorem, Fermat wrote that he had a marvelous proof for it, but that it was too long to fit in the margin of the book.

Since then, pretty much every mathematician has tried to prove (or disprove) Fermat’s Last Theorem, but it took until 1994 (357 years later!!!) when it was successfully proved by a mathematician named Andrew Wiles.

Cheers,
Brent
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,958
Own Kudos:
1,117
Posts: 38,958
Kudos: 1,117
If x, y and z are three different non-negative integers, which of the 07 Feb 2025, 22:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
109777 posts
Krunaal
Tuck School Moderator
853 posts