Last visit was: 18 May 2026, 13:23 It is currently 18 May 2026, 13:23
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)|   Algebra|   Exponents|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 May 2026
Posts: 110,678
Own Kudos:
815,592
 [33]
Given Kudos: 106,295
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,678
Kudos: 815,592
 [33]
If xy 0 and x^(y + 1) = 2x^y - 1, what is the value of x? 28 Aug 2017, 03:25
1
Kudos
Add Kudos
31
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:

38% (02:28) correct 62% (02:20) wrong based on 469 sessions

History

Date
Time
Result
Not Attempted Yet
If \(xy ≠ 0\) and \(x^{(y + 1)} = 2x^y - 1\), what is the value of x?

(1) \(x^y = x\)

(2) \(x^2=1\)


M36-25

Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 May 2026
Posts: 110,678
Own Kudos:
815,592
 [3]
Given Kudos: 106,295
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,678
Kudos: 815,592
 [3]
If xy 0 and x^(y + 1) = 2x^y - 1, what is the value of x? 11 Oct 2021, 04:48
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

Fresh GMAT Club Tests' Challenge Question:



If \(xy ≠ 0\) and \(x^{(y + 1)} = 2x^y - 1\), what is the value of x?

(1) \(x^y = x\)

(2) \(x^2=1\)


M36-25
Show more

Official Solution:


If \(xy ≠ 0\) and \(x^{(y + 1)} = 2x^y - 1\), what is the value of \(x\)?

(1) \(x^y = x\)

Substitute \(x^y = x\) in the equation given in the stem \(x^{y}*x = 2x^y - 1\):

\(x*x = 2x - 1\);

\(x^2 - 2x + 1= 0\)

\((x - 1)^2 = 0\)

\(x = 1\). Sufficient.

(2) \(x^2=1\)

\(x=1\) or \(x=-1\)

Check whether these values satisfy the equation given in the stem \(x^{(y + 1)} = 2x^y - 1\):

If \(x = 1\), then \(x^{(y + 1)} = 1^{y+1}=1\) and \(2x^y - 1=2*1^y - 1 = 2-1=1\). LHS = RHS. So, \(x\) can be 1.

If \(x = -1\), then we'd have: \((-1)^{y+1}=2*(-1)^y - 1\):

\((-1)^y*(-1)=2*(-1)^y - 1\);

\((-1)^y= \frac{1}{3}\). This is not possible because -1 in any power is ether 1 or -1. So, \(x\) cannot be -1.

Thus, \(x = 1\). Sufficient.


Answer: D
General Discussion
User avatar
sahilvijay
User avatar
Joined: 29 Jun 2017
Last visit: 16 Apr 2021
Posts: 289
Own Kudos:
932
 [3]
Given Kudos: 76
GPA: 4
WE:Engineering (Transportation)
Products:
My Reviews
Posts: 289
Kudos: 932
 [3]
If xy 0 and x^(y + 1) = 2x^y - 1, what is the value of x? 28 Aug 2017, 03:37
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Ans is D, both are sufficient to give x=1
see the attached pic.
Attachments

IMG_2438.JPG
IMG_2438.JPG [ 1.71 MiB | Viewed 7053 times ]

User avatar
Luckisnoexcuse
User avatar
Current Student
Joined: 18 Aug 2016
Last visit: 31 Mar 2026
Posts: 513
Own Kudos:
686
 [3]
Given Kudos: 198
Concentration: Strategy, Technology
Schools: Kenan-Flagler '20 (M)
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Products:
My Reviews
Schools: Kenan-Flagler '20 (M)
GMAT 2: 740 Q51 V38
Posts: 513
Kudos: 686
 [3]
If xy 0 and x^(y + 1) = 2x^y - 1, what is the value of x? 28 Aug 2017, 03:43
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel

Fresh GMAT Club Tests' Challenge Question:



If \(xy ≠ 0\) and \(x^{(y + 1)} = 2x^y - 1\), what is the value of x?

(1) \(x^y = x\)

(2) \(x^2=1\)
Show more

(1) (x^y) * x = 2x^y - 1
x^2 -2x +1 = 0
(x-1)^2 = 0
x=1
Sufficient

(2)
x=+1 or -1
if x =1 then x^{(y + 1)} = 2x^y - 1 holds for all cases of y (odd,even)
if x= -1 then x^{(y + 1)} = 2x^y - 1 does not hold
hence x can only be 1
sufficient
D
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 May 2026
Posts: 110,678
Own Kudos:
815,592
Given Kudos: 106,295
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,678
Kudos: 815,592
If xy 0 and x^(y + 1) = 2x^y - 1, what is the value of x? 24 Dec 2018, 02:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

Fresh GMAT Club Tests' Challenge Question:



If \(xy ≠ 0\) and \(x^{(y + 1)} = 2x^y - 1\), what is the value of x?

(1) \(x^y = x\)

(2) \(x^2=1\)
Show more

Par of GMAT CLUB'S New Year's Quantitative Challenge Set

User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 18 May 2026
Posts: 11,239
Own Kudos:
45,205
 [1]
Given Kudos: 337
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,239
Kudos: 45,205
 [1]
If xy 0 and x^(y + 1) = 2x^y - 1, what is the value of x? 24 Dec 2018, 07:29
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

Fresh GMAT Club Tests' Challenge Question:



If \(xy ≠ 0\) and \(x^{(y + 1)} = 2x^y - 1\), what is the value of x?

(1) \(x^y = x\)

(2) \(x^2=1\)
Show more


\(x^{(y + 1)} = 2x^y - 1.............x*x^y=2x^y-1....\)

(1) \(x^y = x\)
Substitute this in equation above...
\(x*x=2x-1\)......
\(x^2-2x+1=0\).....
\((x-1)^2=0\)
Therefore, x=1...
Sufficient

(2) \(x^2=1\)
so x=1 or -1..
Now \(x*x^y=2x^y-1.............(2-x)x^y=1\)..
Substitute x as 1..
\((2-x)x^y=1\)......
\((2-1)1^y=1\).. Possible, so X can be 1
Substitute x as -1
\((2-x)x^y=1\)......
\((2-(-1))*(-1)^y=1\).......
\(3*(-1)^y=1\).. not possible
So X is 1
Sufficient

D
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,679
Own Kudos:
1,473
Given Kudos: 607
Location: United States
Posts: 1,679
Kudos: 1,473
If xy 0 and x^(y + 1) = 2x^y - 1, what is the value of x? 22 Oct 2019, 08:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

If \(xy ≠ 0\) and \(x^{(y + 1)} = 2x^y - 1\), what is the value of x?

(1) \(x^y = x\)

(2) \(x^2=1\)
Show more

\(xy ≠ 0…(x,y)≠0\)
\(x^{(y + 1)} = 2x^y - 1…(x^y)(x)=2(x^y)-1…x^y(x-2)=-1\)

(1) \(x^y = x\) sufic.
\(x^y(x-2)=-1…x(x-2)=-1…x^2-2x+1=0…(x-1)^2=0…x=1\)

(2) \(x^2=1\) sufic.
\(x^2=1…|x|=(1,-1)\)
\(x=-1:x^y(x-2)=-1…[-1]([-1]-2)=-1…-1(-3)≠-1\)
\(x=1:x^y(x-2)=-1…[1]([1]-2)=-1…(-1)=-1\)

Answer (D)
User avatar
analytica233
User avatar
Joined: 04 Aug 2019
Last visit: 15 Nov 2022
Posts: 62
Own Kudos:
90
Given Kudos: 745
Location: Viet Nam
Concentration: Organizational Behavior, Strategy
Schools: Desautels '23
GMAT 1: 740 Q49 V42
WE:Research (Other)
Products:
My Reviews
Schools: Desautels '23
GMAT 1: 740 Q49 V42
Posts: 62
Kudos: 90
If xy 0 and x^(y + 1) = 2x^y - 1, what is the value of x? 22 Jul 2020, 04:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

Fresh GMAT Club Tests' Challenge Question:



If \(xy ≠ 0\) and \(x^{(y + 1)} = 2x^y - 1\), what is the value of x?

(1) \(x^y = x\)

(2) \(x^2=1\)
Show more

My solution is presented in the image attached.
Attachments

108174253_579052036306770_8866468411894112518_n.jpg
108174253_579052036306770_8866468411894112518_n.jpg [ 251.05 KiB | Viewed 4969 times ]

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,097
Own Kudos:
1,125
Posts: 39,097
Kudos: 1,125
If xy 0 and x^(y + 1) = 2x^y - 1, what is the value of x? 14 Jun 2025, 11:42
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
110678 posts
kingbucky
498 posts
Gmat860sanskar
264 posts