Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 24 Jun 2016
Posts: 259
GPA: 4

What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
[#permalink]
Show Tags
26 Jun 2016, 00:36
\(\sqrt{x^2}=(x)\) because x > 0 \(\sqrt{y^2}=y\) because y > 0 \(\sqrt{x^2*y^2}= \sqrt{x^2} * \sqrt{y^2} = (x)y\)
_________________
Offering top quality online and offline GMAT tutoring in SoCal and worldwide.
$80/hour as of May 2018.
http://www.facebook.com/HanoiGMATtutor HanoiGMATTutor@gmail.com



Director
Joined: 04 Jun 2016
Posts: 603

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) yx (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 semiretired.
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
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 >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Joined: 28 Apr 2016
Posts: 97

Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
[#permalink]
Show Tags
16 Aug 2016, 03:15
got it. Thanks [quote="VeritasPrepKarishma"][quote="ameyaprabhu"]What's the difference between A and C?



Senior Manager
Joined: 08 Dec 2015
Posts: 302

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



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
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.
_________________
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 Blog: Subscribe to Question of the Day Blog
GMAT Club Inbuilt Error Log Functionality  View More. New Visa Forum  Ask all your Visa Related Questions  here.
New! Best Reply Functionality on GMAT Club! Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free



Director
Joined: 04 Jun 2016
Posts: 603

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



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



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
20 Apr 2017, 00:30
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 isSo 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?
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION 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
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 isSo 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) yx (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 Blog: Subscribe to Question of the Day Blog
GMAT Club Inbuilt Error Log Functionality  View More. New Visa Forum  Ask all your Visa Related Questions  here.
New! Best Reply Functionality on GMAT Club! 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
VeritasPrepKarishmaam 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
LakerFan24 wrote: VeritasPrepKarishmaam 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



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: VeritasPrepKarishmaam 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 >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



NonHuman User
Joined: 09 Sep 2013
Posts: 7754

Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
[#permalink]
Show Tags
31 Jul 2018, 16:15
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ? &nbs
[#permalink]
31 Jul 2018, 16:15



Go to page
Previous
1 2
[ 38 posts ]



