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19 Jun 2023, 10:28
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B
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Difficulty:
45%
(medium)
Question Stats:
69% (01:48) correct
31%
(01:53)
wrong
based on 58
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If \(\frac{x - y}{x + y} - \frac{x + y}{x - y} = 0\), what is the value of x ?
(1) xy = 0
(2) y > 0
(1) xy = 0
(2) y > 0
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19 Jun 2023, 11:24
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Bunuel
Let's simplify the premise -
\(\frac{x - y}{x + y} - \frac{x + y}{x - y} = 0\)
\(\frac{(x - y)(x-y)}{(x + y)(x-y)} - \frac{(x + y)(x+y)}{(x - y)(x+y)} = 0\)
\(\frac{(x - y)^2}{x^2 - y^2} - \frac{(x + y)^2}{(x^2-y^2)} = 0\)
\(\frac{(x - y)^2 - (x+y)^2}{x^2 - y^2} = 0\)
\(\frac{-4xy}{x^2 - y^2} = 0\)
As the RHS of the equation = 0
-4xy should be equal to zero.
Inference:
1) Either x = 0 ;or y = 0 and x can take any value
2) Both x and y cannot be equal to 0 as the operation will result in the denominator = 0
Target Question: Is x = 0 ?
Statement 1
(1) xy = 0
We already know this from the premise, hence this statement provides us with no new information. The statement alone is not sufficient to answer the question.
Eliminate A and D.
Statement 2
(2) y > 0
As y is greater than 0, the value of x must be equal to zero for the condition in the premise to hold true.
Hence, we have a definite answer to the question - "What is the value of x?". x = 0.
Option B
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