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Is x|y|=|xy|?

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Is x|y|=|xy|?  [#permalink]

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New post 24 Aug 2018, 00:52
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[Math Revolution GMAT math practice question]

Is x|y|=|xy|?

1) x>0
2) y>0

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Re: Is x|y|=|xy|?  [#permalink]

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New post 24 Aug 2018, 00:55
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is x|y|=|xy|?

1) x>0
2) y>0
Imo A
Attachment:
1535097408235.jpg
1535097408235.jpg [ 71.3 KiB | Viewed 1666 times ]


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Re: Is x|y|=|xy|?  [#permalink]

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New post 24 Aug 2018, 00:56
Given x|y| = |xy|

From statement 1:

x>0. Then x|y| = |xy| becomes x|y|. Hence LHS = RHS. 1 is sufficient.

From statement 2:

y>0. Then xy = y|x|. Since we don't have any info about x. 2 is insufficient.

A is the answer.
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Re: Is x|y|=|xy|?  [#permalink]

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New post 24 Aug 2018, 11:19
My solution is presented in the image attached.
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Re: Is x|y|=|xy|?  [#permalink]

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New post 26 Aug 2018, 18:21
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Modifying the question:
x|y|=|xy|
=> x|y|-|xy| = 0
=> x|y|-|x||y| = 0
=> |y|(x-|x|) = 0
=> |y|=0 or x-|x| = 0
=> y=0 or x=|x|
=> y=0 or x≥0

Condition 1) is sufficient.
Condition 2) is not sufficient since it tells us nothing about the value of x.

Therefore, A is the answer.
Answer: A
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Re: Is x|y|=|xy|?  [#permalink]

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New post 27 Aug 2018, 03:55
I solved this within 5 secs using a different approach. Pls let me know if Its a correct approach... MathRevolution
I modified the question by dividing modulus Y on both sides and translated the question to is x positive? And option A answered the question straight away...

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Re: Is x|y|=|xy|?  [#permalink]

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New post 29 Aug 2018, 08:43
Kem12 wrote:
I solved this within 5 secs using a different approach. Pls let me know if Its a correct approach... MathRevolution
I modified the question by dividing modulus Y on both sides and translated the question to is x positive? And option A answered the question straight away...

Posted from my mobile device


We can't both sides of the question by y, since we don't know if y is zero or not.
If y is zero, we can't divide them by y.

This kind of divisions is one of common mistakes in algebra.
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Is x|y|=|xy|?  [#permalink]

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New post 29 Aug 2018, 15:55
MathRevolution wrote:
Kem12 wrote:
I solved this within 5 secs using a different approach. Pls let me know if Its a correct approach... MathRevolution
I modified the question by dividing modulus Y on both sides and translated the question to is x positive? And option A answered the question straight away...

Posted from my mobile device


We can't both sides of the question by y, since we don't know if y is zero or not.
If y is zero, we can't divide them by y.

This kind of divisions is one of common mistakes in algebra.

Hi thanks for your reply but you seem to misinterpret me. I said I divided by 'modulus y' not just ' y'...i felt. Since it's not an inequality the sign would not matter... The right hand side will always be positive. MathRevolution
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Re: Is x|y|=|xy|?  [#permalink]

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New post 17 Sep 2018, 08:46
1
Kem12 wrote:
MathRevolution wrote:
Kem12 wrote:
I solved this within 5 secs using a different approach. Pls let me know if Its a correct approach... MathRevolution
I modified the question by dividing modulus Y on both sides and translated the question to is x positive? And option A answered the question straight away...

Posted from my mobile device


We can't both sides of the question by y, since we don't know if y is zero or not.
If y is zero, we can't divide them by y.

This kind of divisions is one of common mistakes in algebra.

Hi thanks for your reply but you seem to misinterpret me. I said I divided by 'modulus y' not just ' y'...i felt. Since it's not an inequality the sign would not matter... The right hand side will always be positive. MathRevolution


The modulus of y might be zero.
That's why we cannot divide both sides by 'the modulus of y' either.
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Re: Is x|y|=|xy|?  [#permalink]

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New post 18 Sep 2018, 04:37
Kem12 wrote:
I solved this within 5 secs using a different approach. Pls let me know if Its a correct approach... MathRevolution
I modified the question by dividing modulus Y on both sides and translated the question to is x positive? And option A answered the question straight away...

Posted from my mobile device


We can't both sides of the question by y, since we don't know if y is zero or not.
If y is zero, we can't divide them by y.

This kind of divisions is one of common mistakes in algebra.[/quote]
Hi thanks for your reply but you seem to misinterpret me. I said I divided by 'modulus y' not just ' y'...i felt. Since it's not an inequality the sign would not matter... The right hand side will always be positive. MathRevolution[/quote]

The modulus of y might be zero.
That's why we cannot divide both sides by 'the modulus of y' either.[/quote]

Very clear sir.
Thank you
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Re: Is x|y|=|xy|?  [#permalink]

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New post 16 Nov 2018, 17:59
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is x|y|=|xy|?

1) x>0
2) y>0



At first glimpse it is clear that the only variable that has any impact on the equation is x

As y is inside the modulus sign on both the sides of equations, the position of y on number-line will not affect the result.

So, value of x will suffice to tell us whether x|y|=|xy|

So A is sufficient.

Experts may suggests limitations of my approach.
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Re: Is x|y|=|xy|?   [#permalink] 16 Nov 2018, 17:59
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