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# Is |x|*|y|>x*y?

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Math Expert
Joined: 02 Aug 2009
Posts: 7036

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30 May 2016, 06:26
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Difficulty:

85% (hard)

Question Stats:

42% (01:44) correct 58% (01:17) wrong based on 84 sessions

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Is $$|x|*|y|>x*y$$?
(1) $$|x|>x$$
(2) $$|y|=y$$

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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30 May 2016, 07:18
2
|x| * |y| > x * y when the product of x and y is negative

St1: |x| > x --> x is negative
If y is negative then Is |x| * |y| > x * y ? No
If y is positive then Is |x| * |y| > x * y ? Yes
Not Sufficient

St2: |y| = y --> $$y \geq {0}$$
Insufficient as it depends on the sign of x.

Combining St1 and St2: $$y \geq {0}$$ and x is negative
If y > 0 and x is negative then Is |x| * |y| > x * y ? Yes
If y = 0 then Is |x| * |y| > x * y ? No
Not Sufficient

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30 May 2016, 07:59
chetan2u wrote:
Is $$|x|*|y|>x*y$$?
(1) $$|x|>x$$
(2) $$|y|=y$$

Statement 1

$$|x|>x$$
This means that x <0.
But there is no info about y. So not sufficient.

Statement 2

$$|y|=y$$
This means that y>0; or y=0
But there is no info about x. So not sufficient.

Combining the two

x is negative and y is positive or y is zero.

xy will always be negative or zero.

|x|*|y| will always be more than xy when y not equal to zero

|x|*|y| will be equal to xy when y = 0

Hence Not sufficient.

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03 Jun 2016, 10:27
chetan2u wrote:
Is $$|x|*|y|>x*y$$?
(1) $$|x|>x$$
(2) $$|y|=y$$

|x|*|y|>x*y can be possible if either x or y is -ve. Its not possible if both x and y have same sign or any one is 0

(1) $$|x|>x$$ x is -ve. We don't know the sign of y

(2) $$|y|=y$$ Y can be 0 or +ve

Combining both statements:-
x is -ve and y can be +ve or 0
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05 Jun 2016, 04:57
If we modify the original condition and the question, the question becomes |xy|>xy?, which is same as xy<0?.
There are 2 variables (x and y). In order to match the number of variables to the number of equations, we need 2 equations. Hence, there is high chance that C is the correct answer. Using both the condition 1) and the condition 2), we get the answer as yes when x=-1, y=1. Yet, the answer becomes no when x=-1 y=0. The conditions are not sufficient and the correct answer is E.
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Re: Is |x|*|y|>x*y? &nbs [#permalink] 05 Jun 2016, 04:57
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