Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 17 Jul 2019, 14:14

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.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56277
If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x?  [#permalink]

Show Tags

New post 28 Aug 2017, 03:25
1
1
11
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

34% (02:37) correct 66% (02:19) wrong based on 142 sessions

HideShow timer Statistics


Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56277
If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x?  [#permalink]

Show Tags

New post 28 Aug 2017, 03:25
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 448
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x?  [#permalink]

Show Tags

New post 28 Aug 2017, 03:37
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 1256 times ]


_________________
Give Kudos for correct answer and/or if you like the solution.
Current Student
User avatar
P
Joined: 18 Aug 2016
Posts: 617
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Reviews Badge
Re: If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x?  [#permalink]

Show Tags

New post 28 Aug 2017, 03:43
1
Bunuel wrote:

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) \(x^2=1\)


(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
_________________
We must try to achieve the best within us


Thanks
Luckisnoexcuse
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56277
Re: If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x?  [#permalink]

Show Tags

New post 24 Dec 2018, 02:14
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
Re: If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x?  [#permalink]

Show Tags

New post 24 Dec 2018, 07:29
Bunuel wrote:

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) \(x^2=1\)



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

(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
_________________
GMAT Club Bot
Re: If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x?   [#permalink] 24 Dec 2018, 07:29
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





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