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Intern  Joined: 06 May 2015
Posts: 7
If x<0 and y>0 what will be the value of  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 56% (00:47) correct 44% (00:55) wrong based on 465 sessions

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If x<0 and y>0 what will be the value of $$\sqrt{x^2*y^2}$$

a. -xy
b. xy
c. -|xy|
d. |y|x
e. No solution.

I put my best on C as it will give the negative value which we are looking for. But he said that because of square root, we want a non negative value and so a -xy is the answer.
I am still not able to get it Can anyone explain why is it A? He said, its a question from Veritas.

Originally posted by skyfarer on 01 Mar 2016, 17:26.
Last edited by Bunuel on 09 Jan 2017, 00:05, edited 5 times in total.
Reformatted the question and added the OA.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: If x<0 and y>0 what will be the value of  [#permalink]

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3
9
skyfarer wrote:
If x<0 and y>0 what will be the value of $$\sqrt{x^2*y^2}$$

a. -xy
b. xy
c. -|xy|
d. |y|x
e. No solution.

I put my best on C as it will give the negative value which we are looking for. But he said that because of square root, we want a non negative value and so a -xy is the answer.
I am still not able to get it Can anyone explain why is it A? He said, its a question from Veritas.

A few definitions will help solve such questions easily:

$$\sqrt{x^2} = |x|$$

|x| = x if x >= 0 (x is 0 or positive)
|x| = -x if x < 0 (x is negative)

$$\sqrt{x^2*y^2}$$

$$= \sqrt{x^2} * \sqrt{y^2}$$

$$= |x| * |y|$$

Since x < 0, |x| = -x
Since y > 0, |y| = y

|x| * |y| = -x * y

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Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
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Re: If x<0 and y>0 what will be the value of  [#permalink]

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3
2
skyfarer wrote:
If x<0 and y>0 what will be the value of $$\sqrt{x^2*y^2}$$

a. -xy
b. xy
c. -|xy|
d. |y|x
e. No solution.

I put my best on C as it will give the negative value which we are looking for. But he said that because of square root, we want a non negative value and so a -xy is the answer.
I am still not able to get it Can anyone explain why is it A? He said, its a question from Veritas.

Follow posting guidelines (link in my signatures). Select the proper forum to post your question and put all your analyses either in the next post or under "spoilers". Do format the question properly.

An alternate method is to assume particular values based on the information in the question. It is given that x<0 and y>0, so assume x=-2 and y=3. Thus $$\sqrt{x^2*y^2} = \sqrt{36} = +6$$. Now check which of the options give you the same value when you put x=-2 and y=3.

a. -xy = -(-2)*3=6. Keep.
b. xy = -2*3=-6. Eliminate.
c. -|xy| = -|-6| = -6 . Eliminate.
d. |y|x = 3*(-2)=-6. Eliminate.
e. No solution. Not possible as both x^2 and y^2 are positive and hence there will be a solution. Eliminate.

Hence A is the correct answer.

Hope this helps.
General Discussion
Math Expert V
Joined: 02 Aug 2009
Posts: 7957
Re: If x<0 and y>0 what will be the value of  [#permalink]

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skyfarer wrote:
Hi,
I have a question which my Friend asked me. IF x<0 and y>0 what will be the value of \sqrt{X^2.Y^2}
Choices
a. -xy
b. xy
c. -|xy|
d. |y|x
e. No solution.

I put my best on C as it will give the negative value which we are looking for. But he said that because of square root, we want a non negative value and so a -xy is the answer.
I am still not able to get it Can anyone explain why is it A? He said, its a question from Veritas.

Hi,
Firstly, the Q has not been posted in correct format..

Now on your Q..
$$\sqrt{x^2*y^2}$$...
$$\sqrt{x^2}*\sqrt{y^2}$$...
$$\sqrt{a^2}$$ will always be positive a..
so $$\sqrt{x^2}*\sqrt{y^2}$$= positive x*positive y....
since y<0, we have to add a -ive sign so our ansewr becomes x*(-y)=-xy

Hope it clears your doubt

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Posts: 226
Location: United States
Concentration: Entrepreneurship, Marketing
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Re: If x<0 and y>0 what will be the value of  [#permalink]

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1
x < 0
y > 0
assume x = -2 , y = 3
$$substitute \sqrt{x^{2} y^{2}}$$
$$\sqrt{36}$$
6
Substitute in options
-xy = -(-2x3) = 6
A
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Senior Manager  S
Joined: 12 Sep 2017
Posts: 301
Re: If x<0 and y>0 what will be the value of  [#permalink]

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chetan2u wrote:
skyfarer wrote:
Hi,
I have a question which my Friend asked me. IF x<0 and y>0 what will be the value of \sqrt{X^2.Y^2}
Choices
a. -xy
b. xy
c. -|xy|
d. |y|x
e. No solution.

I put my best on C as it will give the negative value which we are looking for. But he said that because of square root, we want a non negative value and so a -xy is the answer.
I am still not able to get it Can anyone explain why is it A? He said, its a question from Veritas.

Hi,
Firstly, the Q has not been posted in correct format..

Now on your Q..
$$\sqrt{x^2*y^2}$$...
$$\sqrt{x^2}*\sqrt{y^2}$$...
$$\sqrt{a^2}$$ will always be positive a..
so $$\sqrt{x^2}*\sqrt{y^2}$$= positive x*positive y....
since y<0, we have to add a -ive sign so our ansewr becomes x*(-y)=-xy

Hope it clears your doubt

Hello chetan2u !

Where does the +/- after rooting a number enter in your explanation?

$$\sqrt{x^2}$$

Why in some exercises you must consider +x and -x?

Kind regards!
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: If x<0 and y>0 what will be the value of  [#permalink]

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1
jfranciscocuencag wrote:
chetan2u wrote:
skyfarer wrote:
Hi,
I have a question which my Friend asked me. IF x<0 and y>0 what will be the value of \sqrt{X^2.Y^2}
Choices
a. -xy
b. xy
c. -|xy|
d. |y|x
e. No solution.

I put my best on C as it will give the negative value which we are looking for. But he said that because of square root, we want a non negative value and so a -xy is the answer.
I am still not able to get it Can anyone explain why is it A? He said, its a question from Veritas.

Hi,
Firstly, the Q has not been posted in correct format..

Now on your Q..
$$\sqrt{x^2*y^2}$$...
$$\sqrt{x^2}*\sqrt{y^2}$$...
$$\sqrt{a^2}$$ will always be positive a..
so $$\sqrt{x^2}*\sqrt{y^2}$$= positive x*positive y....
since y<0, we have to add a -ive sign so our ansewr becomes x*(-y)=-xy

Hope it clears your doubt

Hello chetan2u !

Where does the +/- after rooting a number enter in your explanation?

$$\sqrt{x^2}$$

Why in some exercises you must consider +x and -x?

Kind regards!

Check this post: https://www.veritasprep.com/blog/2016/0 ... oots-gmat/
It discusses when to take both positive and negative values and when to take only positive values.
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Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Re: If x<0 and y>0 what will be the value of   [#permalink] 21 Feb 2019, 00:47
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