Max@Math Revolution wrote:If |2x|>|3y|, is x >y?
1) x>0
2) y>0
Statement 1:
Test x=3.
Plugging x=3 into |2x|>|3y|, we get:
|2*3|>|3y|
6 > 3|y|
|y| < 2
-2 < y < 2
Since x=3 and -2 < y < 2, we get:
x > y.
Test x=1/2.
Plugging x=1/2 into |2x|>|3y|, we get:
|2 * 1/2|>|3y|
1 > 3|y|
|y| < 1/3
-1/3 < y < 1/3
Since x=1/2 and -1/3 < y < 1/3, we get:
x > y.
Whether x is close to 0 or farther to the right of 0, x > y.
Implication:
Regardless of the value of x, the answer to the question stem is YES.
SUFFICIENT.
Statement 2:
Test y=2.
Plugging y=2 into |2x|>|3y|, we get:
|2x|>|3*2|
2|x| > 6
|x| > 3
Case 1: x=4, with the result that x > y.
Case 2: x=-4, with the result that x < y.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
The correct answer is
A.
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