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

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Math Expert
Joined: 02 Sep 2009
Posts: 47110
If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x? [#permalink]

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28 Aug 2017, 03:25
1
2
00:00

Difficulty:

95% (hard)

Question Stats:

35% (02:02) correct 65% (01:34) wrong based on 62 sessions

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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) $$x^2=1$$

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Math Expert
Joined: 02 Sep 2009
Posts: 47110
If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x? [#permalink]

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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) $$x^2=1$$

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Senior Manager
Joined: 29 Jun 2017
Posts: 497
GPA: 4
WE: Engineering (Transportation)
Re: If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x? [#permalink]

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28 Aug 2017, 03:37
Ans is D, both are sufficient to give x=1
see the attached pic.
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Joined: 18 Aug 2016
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Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
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Re: If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x? [#permalink]

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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
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Re: If xy ≠ 0 and x^(y + 1) = 2x^y - 1, what is the value of x?   [#permalink] 28 Aug 2017, 03:43
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