If xy0 and y

Question

If xy>0 and y<0, which of the following must be positive?
(A) x-y
(B) x+y 
(C) (x+10)/y 
(D) (y-2)/x 
(E) None of these

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nick1816 · Answer

Since xy>0 and y<0, x must be -ve.

A. x and y are both -ve, but we have no idea about whether x is greater than y. x-y can be -ve or +ve.

B. x+y is definitely -ve

C. If x<-10, (x+10)/y is +ve.

D. y<0, so y-2 is always less than 0. Also, x<0. Hence, (y-2)/x is always +ve.

D

Kinshook · Answer

Asked: If xy>0 and y<0, which of the following must be positive?

x < 0
y < 0

(A) x-y; may be positive or negative
(B) x+y; negative
(C) (x+10)/y ; may be positive or negative
(D) (y-2)/x ; positive 
(E) None of these

IMO D

If xy>0 and y<0, which of the following must be positive?