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

### 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

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

# 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

Math Expert
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

28 Aug 2017, 03:25
1
1
11
00:00

Difficulty:

95% (hard)

Question Stats:

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

### HideShow timer Statistics

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) $$x^2=1$$

_________________
Math Expert
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

28 Aug 2017, 03:25
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) $$x^2=1$$

Previous version had a typo in it. Had to re-post. Sorry about it.
_________________
Senior Manager
Joined: 29 Jun 2017
Posts: 448
GPA: 4
WE: Engineering (Transportation)
Re: If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x?  [#permalink]

### Show Tags

28 Aug 2017, 03:37
Ans is D, both are sufficient to give x=1
see the attached pic.
Attachments

IMG_2438.JPG [ 1.71 MiB | Viewed 1256 times ]

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

### Show Tags

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
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

24 Dec 2018, 02:14
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) $$x^2=1$$

_________________
Math Expert
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

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
_________________
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