We have to determine whether |xy| > x^2*y^2.Mo2men wrote:Is |xy| > x^2*y^2 ?
(1) 0 < x^2 < 1/4
(2) 0 < y^2 < 1/9
OA: C
|xy| > x^2*y^2 can be written as |xy| > (xy)^2.
We see that the LHS = |xy| and the RHS = (xy)^2 are positive irrespective of whether one or both of x and y are negative.
|xy| > x^2*y^2 in the following conditions.
1. None of x and y is 0.
2. The product of |x| and |y| = |xy| < 1.
Let's take each statement one by one.
(1) 0 < x^2 < 1/4
=> 0 < |x| < 1/2, but we do not have any information about y. Insufficient.
(2) 0 < y^2 < 1/9
=> 0 < |y| < 1/2, but we do not have any information about x. Insufficient.
(1) and (2) together
We have 0 < |x| < 1/2 and 0 < |y| < 1/3, thus 0 < |xy| < 1/6 and 0 < (xy)^2 < (1/2*1/3)^2 => 0 < (xy)^2 < (1/6)^2 => 0 < (xy)^2 < 1/36.
We see that |xy| < (xy)^2. The answer is yes. Sufficient.
The correct answer: C
Hope this helps!
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