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What is (x^2y^2)^1/2 if x < 0 and y > 0 ?

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What is (x^2y^2)^1/2 if x < 0 and y > 0 ?  [#permalink]

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26 Jun 2016, 00:36
$$\sqrt{x^2}=(-x)$$ because -x > 0
$$\sqrt{y^2}=y$$ because y > 0
$$\sqrt{x^2*y^2}= \sqrt{x^2} * \sqrt{y^2} = (-x)y$$
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$80/hour as of May 2018. http://www.facebook.com/HanoiGMATtutor HanoiGMATTutor@gmail.com Director Joined: 04 Jun 2016 Posts: 603 GMAT 1: 750 Q49 V43 What is (x^2y^2)^1/2 if x < 0 and y > 0 ? [#permalink] Show Tags Updated on: 15 Aug 2016, 07:06 nehamodak wrote: What is $$\sqrt{x^2*y^2}$$ if x < 0 and y > 0? (A) –xy (B) xy (C) –|xy| (D) |y|x (E) No solution ANSWER IS A take x as -2 and y as 2 $$\sqrt{-2^2*2^2}$$ $$\sqrt{4*4}$$ $$\sqrt{16}$$ = 4 Now see what option gives you 4 x*y= -2*2=-4 WRONG -(x)*y = -(-2)*2 = 2*2 = 4 CORRECT _________________ Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired. Originally posted by LogicGuru1 on 24 Jul 2016, 23:56. Last edited by LogicGuru1 on 15 Aug 2016, 07:06, edited 1 time in total. Manager Joined: 28 Apr 2016 Posts: 97 Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ? [#permalink] Show Tags 15 Aug 2016, 04:24 What's the difference between A and C? Both will give us the same answer right? A = - (of a positive xy) B = - (of a positive xy) Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8195 Location: Pune, India Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ? [#permalink] Show Tags 16 Aug 2016, 01:42 1 ameyaprabhu wrote: What's the difference between A and C? Both will give us the same answer right? A = - (of a positive xy) B = - (of a positive xy) You are given that x < 0 (say x is -2) and y > 0 (say y is 5). So xy will be -2*5 = -10. Hence xy will actually be a negative number. Option (A) = - xy = - (-10) = 10 (a positive number) Option (C) = - |xy| = - |-10| = -10 (a negative number) _________________ Karishma Veritas Prep GMAT Instructor Save up to$1,000 on GMAT prep through 8/20! Learn more here >

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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?  [#permalink]

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16 Aug 2016, 03:15
got it. Thanks

[quote="VeritasPrepKarishma"][quote="ameyaprabhu"]What's the difference between A and C?
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What is (x^2y^2)^1/2 if x < 0 and y > 0 ?  [#permalink]

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10 Sep 2016, 07:54
But isn't saying that |x| = -x contradictory?.. You are saying that "something always positive equals a negative umber"

How can this be?

Or is this something like |x| = - (X) , so "if X is negative then modulus is (obviously) positive and if you plug a negative X into a negative -> negative X you get a positive X ?

The way the choice A is written, is misleading imo. It looks as you are saying that a modulus is somehow equivalent to a negative number
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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?  [#permalink]

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10 Sep 2016, 09:35
iliavko wrote:
But isn't saying that |x| = -x contradictory?.. You are saying that "something always positive equals a negative umber"

How can this be?

Or is this something like |x| = - (X) , so "if X is negative then modulus is (obviously) positive and if you plug a negative X into a negative -> negative X you get a positive X ?

The way the choice A is written, is misleading imo. It looks as you are saying that a modulus is somehow equivalent to a negative number

|x| = -x implies what I have highlighted above.
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What is (x^2y^2)^1/2 if x < 0 and y > 0 ?  [#permalink]

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10 Sep 2016, 12:29
iliavko wrote:
But isn't saying that |x| = -x contradictory?.. You are saying that "something always positive equals a negative umber"

How can this be?

Or is this something like |x| = - (X) , so "if X is negative then modulus is (obviously) positive and if you plug a negative X into a negative -> negative X you get a positive X ?

The way the choice A is written, is misleading imo. It looks as you are saying that a modulus is somehow equivalent to a negative number

|x| actually behaves differently for values greater than 0 and less than 0.

In other words |x| has two cases
CASE 1) x>0;
for x >0 |x| = x
For example |4|= 4

Case 2) x<0;
for x<0 |x|= -x
For example |-4|= - of -4 or -(-4)= 4
so to generalise |-x| = -(x);
Now since x is a "variable" it is hiding a "Negative Polarity" inside itself in this case.

YOU HAVE TO BE ABSOLUTELY CLEAR ABOUT IT. A VARIABLE CAN LOOK POSITIVE BUT IT MAY CARRY A HIDDEN POLARITY .
For example x can be -9 but just looking at x you cannot quickly relate to -9. You will automatically see x as positive.
BUT REMEMBER X IS A VARIABLE THAT CAN HAVE ANY POLARITY AND VALUE.
THAT IS WHY SO MANY PEOPLE ARE GETTING CONFUSED IN THIS QUESTION.

It is useless to rote or memorize the formula that |x|= x until and unless how it works in case of x>0 and x<0

Again to revise

IF x>0 then |x|= x {plain and simple to remember}
If x<0 then |x|=-x {You need to understand the concept of hidden polarity inside a variable}.
In this case particular example -x will ultimately be a positive numerical value but if the question does not involve substitution of numerical values to x and -x then you have to be solve the question very carefuly.

Hope its clear to all now .
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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?  [#permalink]

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19 Apr 2017, 21:45
VeritasPrepKarishma, I don't understand your explanation:

$$\sqrt{(x^2*y^2)}$$ = |x|*|y| --> I understand this part, but how do you then go here: "Now, if x < 0, |x|=−x"

Let me rephrase:
- if I told you that I know x=-2, when you take |-2|, you get 2.
- if, on the other hand, I told you that the value of x changed, and is now 25, then when you take |25|, you get 25.
* The point here being: the absolute value will give you the positive value of whatever is inside the brackets, regardless of what sign the content inside the bracket is

So I'm having a hard time rationalizing this: |x|=−x. How can the absolute value of a variable ever be negative?
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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?  [#permalink]

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20 Apr 2017, 00:30
1
LakerFan24 wrote:
VeritasPrepKarishma, I don't understand your explanation:

$$\sqrt{(x^2*y^2)}$$ = |x|*|y| --> I understand this part, but how do you then go here: "Now, if x < 0, |x|=−x"

Let me rephrase:
- if I told you that I know x=-2, when you take |-2|, you get 2.
- if, on the other hand, I told you that the value of x changed, and is now 25, then when you take |25|, you get 25.
* The point here being: the absolute value will give you the positive value of whatever is inside the brackets, regardless of what sign the content inside the bracket is

So I'm having a hard time rationalizing this: |x|=−x. How can the absolute value of a variable ever be negative?

What makes you say that -x is a negative quantity?
Note that the absolute value is -x when x itself is negative. So x itself will have a negative sign and the two negatives will cancel off each other to give you a positive value.
-x is a way of expressing a positive quantity when x itself is negative.

Does this make sense?
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[#permalink] Show Tags 20 Apr 2017, 19:41 VeritasPrepKarishma wrote: LakerFan24 wrote: VeritasPrepKarishma, I don't understand your explanation: $$\sqrt{(x^2*y^2)}$$ = |x|*|y| --> I understand this part, but how do you then go here: "Now, if x < 0, |x|=−x" Let me rephrase: - if I told you that I know x=-2, when you take |-2|, you get 2. - if, on the other hand, I told you that the value of x changed, and is now 25, then when you take |25|, you get 25. * The point here being: the absolute value will give you the positive value of whatever is inside the brackets, regardless of what sign the content inside the bracket is So I'm having a hard time rationalizing this: |x|=−x. How can the absolute value of a variable ever be negative? What makes you say that -x is a negative quantity? Note that the absolute value is -x when x itself is negative. So x itself will have a negative sign and the two negatives will cancel off each other to give you a positive value. -x is a way of expressing a positive quantity when x itself is negative. Does this make sense? Let me see if I understand this correctly: |x| is always positive, and since we know that x is a negative number, in order to express a positive quantity, we need to add a negative to "cancel out" the negatives to make positive? This way, |x| = -(negative value,x). If I were to substitute values for x (let's say, -2), then: |2| = -(-2) Manager Joined: 26 May 2013 Posts: 95 What is (x^2y^2)^1/2 if x < 0 and y > 0 ? [#permalink] Show Tags 06 Jul 2017, 21:16 VeritasPrepKarishma wrote: nehamodak wrote: What is \sqrt{x^2*y^2} if x < 0 and y > 0? (A) –xy (B) xy (C) –|xy| (D) |y|x (E) No solution Please explain how do we solve this Note that $$\sqrt{x^2} = |x|$$. It is not x, it is |x|. When we talk about square root, it implies the principal square root i.e. just the positive square root. $$\sqrt{x^2*y^2} = |x|*|y|$$ Now, if x < 0, $$|x| = -x$$ If y > 0, $$|y| = y$$ Hence, $$|x|*|y| = -x*y$$ Answer (A) $$\sqrt{x^2} = |x|$$ ^ in the above equation, if the X value is not specified, can you know for certain whether X is positive or negative? i.e. - the only way we know |X| is negative is because the stem tells us x<0. Without this information, are we unable to determine the sign of X? Manager Joined: 26 May 2013 Posts: 95 What is (x^2y^2)^1/2 if x < 0 and y > 0 ? [#permalink] Show Tags 06 Jul 2017, 21:19 LogicGuru1 wrote: iliavko wrote: But isn't saying that |x| = -x contradictory?.. You are saying that "something always positive equals a negative umber" How can this be? Or is this something like |x| = - (X) , so "if X is negative then modulus is (obviously) positive and if you plug a negative X into a negative -> negative X you get a positive X ? The way the choice A is written, is misleading imo. It looks as you are saying that a modulus is somehow equivalent to a negative number |x| actually behaves differently for values greater than 0 and less than 0. In other words |x| has two cases CASE 1) x>0; for x >0 |x| = x For example |4|= 4 Case 2) x<0; for x<0 |x|= -x For example |-4|= - of -4 or -(-4)= 4 so to generalise |-x| = -(x); Now since x is a "variable" it is hiding a "Negative Polarity" inside itself in this case. YOU HAVE TO BE ABSOLUTELY CLEAR ABOUT IT. A VARIABLE CAN LOOK POSITIVE BUT IT MAY CARRY A HIDDEN POLARITY . For example x can be -9 but just looking at x you cannot quickly relate to -9. You will automatically see x as positive. BUT REMEMBER X IS A VARIABLE THAT CAN HAVE ANY POLARITY AND VALUE. THAT IS WHY SO MANY PEOPLE ARE GETTING CONFUSED IN THIS QUESTION. It is useless to rote or memorize the formula that |x|= x until and unless how it works in case of x>0 and x<0 Again to revise IF x>0 then |x|= x {plain and simple to remember} If x<0 then |x|=-x {You need to understand the concept of hidden polarity inside a variable}. In this case particular example -x will ultimately be a positive numerical value but if the question does not involve substitution of numerical values to x and -x then you have to be solve the question very carefuly. Hope its clear to all now . This helps and I just want to clarify that without the added information that x<0, there would be no way of determining whether X is positive or negative? Correct? Board of Directors Status: Stepping into my 10 years long dream Joined: 18 Jul 2015 Posts: 3692 Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ? [#permalink] Show Tags 06 Jul 2017, 23:42 ak1802 wrote: This helps and I just want to clarify that without the added information that x<0, there would be no way of determining whether X is positive or negative? Correct? Hi ak1802 , Yes, that's true. We cannot find the nature of x unless we are given such condition. _________________ My GMAT Story: From V21 to V40 My MBA Journey: My 10 years long MBA Dream My Secret Hacks: Best way to use GMATClub | Importance of an Error Log! Verbal Resources: All SC Resources at one place | All CR Resources at one place GMAT Club Inbuilt Error Log Functionality - View More. New Visa Forum - Ask all your Visa Related Questions - here. Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free Senior Manager Joined: 26 Dec 2015 Posts: 277 Location: United States (CA) Concentration: Finance, Strategy WE: Investment Banking (Venture Capital) Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ? [#permalink] Show Tags 27 Jul 2017, 16:50 VeritasPrepKarishma am i correct in saying that $$\sqrt{x^{2}}$$ is NOT the same as writing $$\sqrt{(x^{2})}$$, so is this the reason here that $$\sqrt{x^{2}}$$ = (-x)? is this what the problem is testing? because otherwise, i cannot understand how an absolute value is negative -- an absolute value can never be negative, because it is the measure of how far away numbers are on a number line Math Expert Joined: 02 Sep 2009 Posts: 47983 Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ? [#permalink] Show Tags 27 Jul 2017, 21:04 1 LakerFan24 wrote: VeritasPrepKarishma am i correct in saying that $$\sqrt{x^{2}}$$ is NOT the same as writing $$\sqrt{(x^{2})}$$, so is this the reason here that $$\sqrt{x^{2}}$$ = (-x)? is this what the problem is testing? because otherwise, i cannot understand how an absolute value is negative -- an absolute value can never be negative, because it is the measure of how far away numbers are on a number line $$\sqrt{x^{2}}$$ is the same as $$\sqrt{(x^{2})}$$. $$\sqrt{x^{2}}=|x|$$. We are given that x is negative. When x < 0, we know that |x| = -x, so $$\sqrt{x^{2}}=|x|=-x$$. Notice that since x is negative, -x = -negative = positive, thus both the square root and the absolute value return positive result. _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8195 Location: Pune, India Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ? [#permalink] Show Tags 27 Jul 2017, 21:17 LakerFan24 wrote: VeritasPrepKarishma am i correct in saying that $$\sqrt{x^{2}}$$ is NOT the same as writing $$\sqrt{(x^{2})}$$, so is this the reason here that $$\sqrt{x^{2}}$$ = (-x)? is this what the problem is testing? because otherwise, i cannot understand how an absolute value is negative -- an absolute value can never be negative, because it is the measure of how far away numbers are on a number line In addition to what Bunuel said above, let me also add a line on how I explain this in words: You are right. An absolute value can never be negative. So |x| will never be negative. But it can be equal to -x. When? When x itself is negative. Note that a variable x CAN stand for a negative value too. So if x itself is negative, -x becomes POSITIVE. And that is the case in which |x| is equal to -x (which is positive). _________________ Karishma Veritas Prep GMAT Instructor Save up to$1,000 on GMAT prep through 8/20! Learn more here >

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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?  [#permalink]

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