non-zero numbers

[sanju09]

a, b, c, and d are four non-zero numbers. Is (a b)/(c d) positive?

(1) a d + b c = 0

(2) a b c d = -4

[bluementor]

(a b)/(c d) will be positive if:

1. all numbers are positive
2. 2 of the numbers are positive, and the other 2 negative
3. all 4 numbers are negative.

statement 1: ad = -bc

if ad is positive, then bc is negative. in this case, 1 or 3 of the numbers must be negative. the same can be said if ad is negative. therefore, we can definitely conclude that (a b)/(c d) is negative. sufficient.

statement 2: abcd = -4

either 1 or 3 of the numbers are negative. therefore, we can conclude that (ab)/(cd) is negative. sufficient.

choose d.

-BM-