Rephrase |3x| > |4y| so that one of the variables is IN TERMS OF THE OTHER:asciijai wrote:If |3x| > |4y|, is x > y?
(1) x > 0
(2) y > 0
3|x| > 4|y|
Thus:
|y| < (3/4)|x|
and
|x| > (4/3)|y|
Statement 1: x > 0
Substituting positive values for x into |y| < (3/4)|x|, we get:
If x = 4, then |y| < 3, with the result that x > y.
If x = 1/2, then |y| < 3/8, with the result that x > y.
If x = 40, then |y| < 30, with the result that x > y.
In every case, x > y.
SUFFICIENT.
Statement 2: y > 0
Substituting y=3 into |x| > (4/3)|y|, we get:
|x| > 4.
Here, it's possible that x=5 and y=3 (with the result that x>y) or that x=-5 and y=3 (with the result that x<y).
INSUFFICIENT.
The correct answer is A.
