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# If xy ≠ 0 and x ≠ y, what is the value of K?

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Math Expert
Joined: 02 Sep 2009
Posts: 55173
If xy ≠ 0 and x ≠ y, what is the value of K?  [#permalink]

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12 Apr 2018, 21:44
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Difficulty:

55% (hard)

Question Stats:

57% (01:30) correct 43% (01:55) wrong based on 58 sessions

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If xy ≠ 0 and x ≠ y, what is the value of K?

(1) $$Kx + x - Ky - y = 0$$

(2) $$(\frac{x}{y})^k = \frac{y}{x}$$

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Re: If xy ≠ 0 and x ≠ y, what is the value of K?  [#permalink]

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12 Apr 2018, 21:50
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Bunuel wrote:
If xy ≠ 0 and x ≠ y, what is the value of K?

(1) $$Kx + x - Ky - y = 0$$

(2) $$(\frac{x}{y})^k = \frac{y}{x}$$

Question: K = ?

Statement 1: $$Kx + x - Ky - y = 0$$

i.e. K (x-y) +(x-y) = 0
i.e. (K+1)(x-y) = 0

i.e. Either K = -1 or x=y but sine given that x ≠ y therefore K = 1

SUFFICIENT

Statement 2: $$(\frac{x}{y})^k = \frac{y}{x}$$

i.e. (x/y)^K = (x/y)^(-1)

i.e. K = -1

SUFFICIENT

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Re: If xy ≠ 0 and x ≠ y, what is the value of K?   [#permalink] 12 Apr 2018, 21:50
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