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

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Kudos [?]: 132742 [1], given: 12360

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

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Difficulty:

  95% (hard)

Question Stats:

38% (02:15) correct 62% (01:31) wrong based on 50 sessions

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Kudos [?]: 132742 [1], given: 12360

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42257

Kudos [?]: 132742 [0], given: 12360

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

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New post 28 Aug 2017, 03:25

Kudos [?]: 132742 [0], given: 12360

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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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New post 28 Aug 2017, 03:37
Ans is D, both are sufficient to give x=1
see the attached pic.
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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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New post 28 Aug 2017, 03:43
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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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Kudos [?]: 161 [0], given: 134

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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