sana.noor wrote:Is x(y/z) > 0?
(1) xyz > 0
(2) yz > 0
Target question:
Is x(y/z) > 0?
Notice that x(y/z) = (xy)/z = (x)(y)(1/z) [you'll see why I did this later]
Rephrased target question:
Is (x)(y)(1/z) positive?
IMPORTANT CONCEPTS:
If z is positive, then 1/z is positive.
If z is negative, then 1/z is negative.
In other words, z and 1/z must have the same sign.
Statement 1: xyz > 0
In other words, the product (x)(y)(z) is positive.
Since z and 1/z have the same sign (positive or negative) we can conclude with certainty that
(x)(y)(1/z) is positive
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: yz > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: x=1, y=1, z=1, in which case
(x)(y)(1/z) is positive
Case b: x=-1, y=1, z=1, in which case
(x)(y)(1/z) is negative
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
