If \frac{x-y}{z} = 1 then what is the value of \frac{x}{x-y}

Question

If  \frac{x-y}{z} = 1  then what is the value of  \frac{x}{x-y} ?

(1)  \frac{x}{y} = \frac{2}{3} 
(2)  x-y = 6

yangsta8 · Answer

I think the Answer is A

Statement 1:
x/y = 2/3
x=2 y=3 (or any ratio where x/y = 2/3 such as 4/6)
Answer will always = -2
Sufficient

Statement 2:
x-y = 6. 
Let x = 9 and y = 3
x/(x-y) = 9/6 = 3/2
Let x = 7 and y = 1
x/(x-y) = 7/6
Not sufficient.

Economist · Answer

Agree with A.

z is of no use.

AKProdigy87 · Answer

Statement 1:  \frac{x}{y} = \frac{2}{3}

\frac{x}{x-y} = n

\frac{x-y}{x} = \frac{1}{n}

1-\frac{y}{x} = \frac{1}{n}

1-\frac{3}{2} = \frac{1}{n}

-\frac{1}{2} = \frac{1}{n}

n = -2

Therefore, sufficient.

Statement 2:  x-y = 6

Not sufficient as shown above.

Answer is  A .

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