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Updated on: 16 Feb 2020, 01:27
Originally posted by QuantMadeEasy on 13 Feb 2020, 23:48.
Last edited by QuantMadeEasy on 16 Feb 2020, 01:27, edited 1 time in total.
Last edited by QuantMadeEasy on 16 Feb 2020, 01:27, edited 1 time in total.
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E
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Difficulty:
95%
(hard)
Question Stats:
35% (02:06) correct
65%
(01:44)
wrong
based on 122
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If xy ≠ 0, is x/y greater than y/x ?
(1) x - y> 0
(2) \(x^2 - y^2\) > 0
(1) x - y> 0
(2) \(x^2 - y^2\) > 0
14 Feb 2020, 01:21
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The question basically asks to compare x/y and y/x
Statement 1: x - y > 0
=> x > y
Apparently it seems x/y is greater than 1 and y/x is less than 1; implying x/y is greater than y/x.
However, it isn't that simple.
Say we have x = 4 and y = -1
x/y = -4 and y/x = -1/4
Here y/x is greater than x/y
Hence, the statement is insufficient
Statement 2:
x² - y² > 0
=> x² > y²
Again, it seems that, after taking square root, we get: x > y
Apparently it seems x/y is greater than 1 and y/x is less than 1; implying x/y is greater than y/x.
However, we can also have:
x = 4 and y = -1
x/y = -4 and y/x = -1/4
Here y/x is greater than x/y
Hence, the statement is insufficient
Combining:
We still have both the above situations
Answer E
Posted from my mobile device
Statement 1: x - y > 0
=> x > y
Apparently it seems x/y is greater than 1 and y/x is less than 1; implying x/y is greater than y/x.
However, it isn't that simple.
Say we have x = 4 and y = -1
x/y = -4 and y/x = -1/4
Here y/x is greater than x/y
Hence, the statement is insufficient
Statement 2:
x² - y² > 0
=> x² > y²
Again, it seems that, after taking square root, we get: x > y
Apparently it seems x/y is greater than 1 and y/x is less than 1; implying x/y is greater than y/x.
However, we can also have:
x = 4 and y = -1
x/y = -4 and y/x = -1/4
Here y/x is greater than x/y
Hence, the statement is insufficient
Combining:
We still have both the above situations
Answer E
Posted from my mobile device
16 May 2021, 17:28
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QuantMadeEasy
"Is \(\frac{x}{y} > \frac{y}{x}?\)" We don't want to simplify this yet without knowing the signs of x and y. Knowing if they are the same sign or opposite sign is enough to take one step further in simplifying.
Statement 1:
If both positive, the question is if \(x^2 > y^2\) and \(x > y > 0\) guarantees \(x^2 > y^2\) is true.
If x positive and y negative, the question is if \(x^2 < y^2\), which we can say "no" to when x has a higher absolute value than y. Insufficient.
Statement 2:
\(x^2 > y^2\) but we don't know the signs of x and y. Therefore this can give us a yes or no depending on the signs. Insufficient.
Combined:
We have \((x - y)(x + y) > 0\) and \(x - y > 0\), it must follow that \(x + y > 0\). Then add the two shorter inequalities together to get \(2x > 0\) but note that we cannot tell the sign of y. Then we still have the problem from statement 2, insufficient.
Ans: E
