If xy ≠ 0, is x/y 0? (1) x|y| - |xy|/|x + y|

Question

If xy ≠ 0, is x/y > 0?

(1) x|y| - |xy|/|x + y| < 0
(2) |x + y| = |x| + |y|

MarmikUpadhyay · Accepted Answer

Given: xy eq 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 .

Kinshook · Answer

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

NeoNguyen1989 · Answer

If xy ≠ 0, is x/y > 0?

(1) x|y| - |xy|/|x + y| < 0
(2) |x + y| = |x| + |y|

(1) assume x & y same positive sign
(1) <=> xy - xy/(x+y) <0 <=> xy <1 and x+y<1 => x & y can be the same sign

Assume x<0 and y>0 => (1) can still happen

(1) is not enoughr

(2) if x and y have different sign => |x+y| = |y| - |x| or = |x| - |y|. Either is contradict with (2) => x and y have the same sign

B is correct answer

Posted from my mobile device

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If xy ≠ 0, is x/y > 0? (1) x|y| - |xy|/|x + y| < 0 (2) |x + y| = |x|

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