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

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chetan2u
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Is |x|*|y|>x*y? [#permalink] New post   30 May 2016, 07:26
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A
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E

Difficulty:

75% (hard)

Question Stats:

39% (01:34) correct 61% (01:12) wrong based on 117 sessions
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Is \(|x|*|y|>x*y\)?

(1) \(|x|>x\)
(2) \(|y|=y\)


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E
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Re: Is |x|*|y|>x*y? [#permalink] New post   30 May 2016, 08:18
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|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

Answer: E
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adiagr
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Re: Is |x|*|y|>x*y? [#permalink] New post   30 May 2016, 08:59
chetan2u wrote:
Is \(|x|*|y|>x*y\)?
(1) \(|x|>x\)
(2) \(|y|=y\)


Self Made



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.

E is the answer.
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Re: Is |x|*|y|>x*y? [#permalink] New post   03 Jun 2016, 11:27
chetan2u wrote:
Is \(|x|*|y|>x*y\)?
(1) \(|x|>x\)
(2) \(|y|=y\)


Self Made


|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
E is the answer
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Re: Is |x|*|y|>x*y? [#permalink] New post   05 Jun 2016, 05:57
Expert Reply
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? [#permalink] New post   19 Aug 2023, 03:10
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Re: Is |x|*|y|>x*y? [#permalink]
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