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17 Mar 2021, 12:55
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Difficulty:
45%
(medium)
Question Stats:
67% (02:07) correct
33%
(02:30)
wrong
based on 302
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If xy ≠ 0, is x/y > 0?
(1) x|y| - |xy|/|x + y| < 0
(2) |x + y| = |x| + |y|
(1) x|y| - |xy|/|x + y| < 0
(2) |x + y| = |x| + |y|
17 Mar 2021, 18:26
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Given: xy \(\neq\) 0, is \(\frac{x}{y}\) > 0?
\(\frac{x}{y}\) > 0 if either both x and y are positive or both x and y are negative.
Statement 1:
\(\frac{x|y| - |xy|}{|x + y|}\) < 0
|x + y| is always positive so let us remove that from equation.
=> x|y| - |xy| < 0
From the above equation x < 0, because if x > 0 then x|y| - |xy| = 0.
But we cannot conclude anything on y.
=> If y > 0, then \(\frac{x}{y}\) < 0
and if y < 0, then \(\frac{x}{y}\) > 0.
Statement 1 is Not Sufficient.
Statement 2:
|x + y| = |x| + |y|
This is only possible when x and y are either both positive or both negative.
=> If x, y > 0, then \(\frac{x}{y}\) > 0
and if x, y < 0, then also \(\frac{x}{y}\) > 0.
Statement 2 is Sufficient.
So, correct answer is option B.
\(\frac{x}{y}\) > 0 if either both x and y are positive or both x and y are negative.
Statement 1:
\(\frac{x|y| - |xy|}{|x + y|}\) < 0
|x + y| is always positive so let us remove that from equation.
=> x|y| - |xy| < 0
From the above equation x < 0, because if x > 0 then x|y| - |xy| = 0.
But we cannot conclude anything on y.
=> If y > 0, then \(\frac{x}{y}\) < 0
and if y < 0, then \(\frac{x}{y}\) > 0.
Statement 1 is Not Sufficient.
Statement 2:
|x + y| = |x| + |y|
This is only possible when x and y are either both positive or both negative.
=> If x, y > 0, then \(\frac{x}{y}\) > 0
and if x, y < 0, then also \(\frac{x}{y}\) > 0.
Statement 2 is Sufficient.
So, correct answer is option B.
General Discussion
18 Mar 2021, 17:56
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Asked: If xy ≠ 0, is x/y > 0?
(1) x|y| - |xy|/|x + y| < 0
x|y| < |xy|/|x + y|
x may be positive or negative
Since signs of x & y can not be concluded
NOT SUFFICIENT
(2) |x + y| = |x| + |y|
In this case signs of both x & y should be same, i.e. both x & y are positive or both are negative
x/y > 0
SUFFICIENT
IMO B
(1) x|y| - |xy|/|x + y| < 0
x|y| < |xy|/|x + y|
x may be positive or negative
Since signs of x & y can not be concluded
NOT SUFFICIENT
(2) |x + y| = |x| + |y|
In this case signs of both x & y should be same, i.e. both x & y are positive or both are negative
x/y > 0
SUFFICIENT
IMO B
