If x and y are nonzero integers, is [x^(-1)+y^(-1)]^(-1) > [x^(-1) * y^(-1)]^(-1)?
i. x=2y
ii. x+y >0
OA: A
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Inequality
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Rephrasing will result into: Is (xy/x+y) > xy?
Statement 1) x=2y , this implies that x and y both have same signs. So, xy is always positive.
(xy/x+y) > xy becomes 1/(x+y) > 1 as we can cancel positive xy from both sides.
And as x=2y, so Is 1/3y > 1 ? i.e. Is 1/y > 3 ?
Whether y is positive or negative. 1/y will always be less than 3. Sufficient!!!
Statement 2) x+y>0 , this does not provide any information as both x and y either have same signs
(2 + 3 = 5 > 0) or opposite signs ( 3 - 2 = 1 > 0). Not Sufficient!!!
Answer:- A
Statement 1) x=2y , this implies that x and y both have same signs. So, xy is always positive.
(xy/x+y) > xy becomes 1/(x+y) > 1 as we can cancel positive xy from both sides.
And as x=2y, so Is 1/3y > 1 ? i.e. Is 1/y > 3 ?
Whether y is positive or negative. 1/y will always be less than 3. Sufficient!!!
Statement 2) x+y>0 , this does not provide any information as both x and y either have same signs
(2 + 3 = 5 > 0) or opposite signs ( 3 - 2 = 1 > 0). Not Sufficient!!!
Answer:- A
