Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 20 Dec 2010
Posts: 1836

Re: modes and square root
[#permalink]
Show Tags
11 Feb 2011, 01:42
the question is: If x < 0, what is the value for \(sqrt{x*\mid x \mid}\): \(sqrt{(+x)*(+x)}\) \(sqrt{x^2}\) \(\pm x\) Reasoning is: Since x < 0; only x is the valid value. +x can be ignored. Ans: "A"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 754

Re: Square root and Mod Problem
[#permalink]
Show Tags
07 Mar 2011, 23:32
sqrt(x^2) = x if x <0 x = x x^2 = xx
Hence A



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1055

Re: Square root and Modulus
[#permalink]
Show Tags
14 Jun 2011, 02:07
A as root will always give positive value.



Intern
Joined: 25 Jun 2012
Posts: 36

Re: If x < 0, then root({x} •x) is
[#permalink]
Show Tags
29 Nov 2012, 14:10
x is < 0.
This makes sense, if it was positive, then it would be the square root of ()(+)(+)= . We can't have the square of a negative, not a real #
so x is . Let's pick x= 5. (1)(5)(5)= √25 = 5. answer is 5 which is x.



Board of Directors
Joined: 01 Sep 2010
Posts: 3305

Re: Square root and Modulus
[#permalink]
Show Tags
29 Nov 2012, 14:51
Bunuel wrote: udaymathapati wrote: If x < 0, then \sqrt{x} •x) is A. x B. 1 C. 1 D. x E. \sqrt{x} 1. If x<0, then \(\sqrt{x*x}\) equals:A. \(x\) B. \(1\) C. \(1\) D. \(x\) E. \(\sqrt{x}\) Remember: \(\sqrt{x^2}=x\). The point here is that square root function can not give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function! That is why \(\sqrt{x^2}=x\) Back to the original question:\(\sqrt{x*x}=\sqrt{(x)*(x)}=\sqrt{x^2}=x=x\) Or just substitute the value let \(x=5<0\) > \(\sqrt{x*x}=\sqrt{(5)*5}=\sqrt{25}=5=(5)=x\). Answer: A. Hope it's clear. Sorry Bunuel but the approach :\(\sqrt{x* x}\) if we put this one ^2 then we have simply \(x * x\). The latter is positive, so we have a quantity straight negative \( X\). or is wrong this simple way )) thanks
_________________
COLLECTION OF QUESTIONS AND RESOURCES Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection  The Next Generation 3. Bunuel Signature Collection ALLINONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Readingcomprehension_Oldy but goldy question banks



Board of Directors
Joined: 01 Sep 2010
Posts: 3305

Re: modes and square root
[#permalink]
Show Tags
29 Nov 2012, 14:55



Senior Manager
Joined: 13 Aug 2012
Posts: 431
Concentration: Marketing, Finance
GPA: 3.23

Re: If x < 0, then root({x} •x) is
[#permalink]
Show Tags
03 Dec 2012, 20:59
Since \(x < 0\), \(\sqrt{xx}\) \(\sqrt{x^2}=x\) Answer: x since x is of negative value.
_________________
Impossible is nothing to God.



Manager
Joined: 29 Mar 2010
Posts: 121
Location: United States
Concentration: Finance, International Business
GPA: 2.54
WE: Accounting (Hospitality and Tourism)

Re: If x < 0, then root({x} •x) is
[#permalink]
Show Tags
08 May 2013, 21:43
I said X before I read the very important point that x<1 I need to stop that
_________________
4/28 GMATPrep 42Q 36V 640



Senior Manager
Joined: 13 May 2013
Posts: 429

Re: Square root and Modulus
[#permalink]
Show Tags
15 Jun 2013, 09:19
How can the solution be negative if we're taking the square root of a positive number? Bunuel wrote: mbafall2011 wrote: udaymathapati wrote: If x < 0, then \sqrt{x} •x) is A. x B. 1 C. 1 D. x E. \sqrt{x} what is the source of this question. I havent seen any gmat question testing imaginary numbers GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers. So you won't see any question involving imaginary numbers. This question also does not involve imaginary numbers as expression under the square root is nonnegative (actually it's positive): we have \(\sqrt{x*x}\) > as \(x<0\) then \(x=positive\) and \(x=positive\), so \(\sqrt{x*x}=\sqrt{positive*positive}=\sqrt{positive}\). Hope it's clear.



Math Expert
Joined: 02 Sep 2009
Posts: 49915

Re: Square root and Modulus
[#permalink]
Show Tags
15 Jun 2013, 09:23



Senior Manager
Joined: 13 May 2013
Posts: 429

Re: Square root and Modulus
[#permalink]
Show Tags
15 Jun 2013, 09:25
Ha! I got it just before I read your response. That is a very tricky problem  it's (x). Thanks! Bunuel wrote: WholeLottaLove wrote: How can the solution be negative if we're taking the square root of a positive number?
Please read the solution carefully: ifx0thenrootxxis100303.html#p773754The answer is A, which is \(x\), since \(x\) is negative then \(x=(negative)=positive\).



Manager
Joined: 01 Nov 2016
Posts: 67
Concentration: Technology, Operations

If x < 0, then root({x} •x) is
[#permalink]
Show Tags
03 Apr 2017, 10:42
Bunuel wrote: Square root function can not give negative result Bunuel, I do not understand this. When you graph \(x^2  9 = 0\) you will get a parabola with roots at 3 and 3. That is because \(\sqrt{9}\) is 3 or 3, not just 3. When you square root a number, the answer will always be plus/minus because when you square a negative number, it becomes positive. For example, \(\sqrt{25}\) is 5 or 5, not just 5. This is because \(5^2\) and \((5)^2\) both equal 25. Why is this different for this question? I think what fluke wrote is correct: fluke wrote: the question is: If x < 0, what is the value for \(sqrt{x*\mid x \mid}\):
\(sqrt{(+x)*(+x)}\) \(sqrt{x^2}\) \(\pm x\)
Reasoning is:
Since x < 0; only x is the valid value. +x can be ignored.
Ans: "A"



Math Expert
Joined: 02 Sep 2009
Posts: 49915

Re: If x < 0, then root({x} •x) is
[#permalink]
Show Tags
03 Apr 2017, 10:49
joondez wrote: Bunuel wrote: Square root function can not give negative result Bunuel, I do not understand this. When you graph \(x^2  9 = 0\) you will get a parabola with roots at 3 and 3. That is because \(\sqrt{9}\) is 3 or 3, not just 3. When you square root a number, the answer will always be plus/minus because when you square a negative number, it becomes positive. For example, \(\sqrt{25}\) is 5 or 5, not just 5. This is because \(5^2\) and \((5)^2\) both equal 25. Why is this different for this question? I think what fluke wrote is correct: fluke wrote: the question is: If x < 0, what is the value for \(sqrt{x*\mid x \mid}\):
\(sqrt{(+x)*(+x)}\) \(sqrt{x^2}\) \(\pm x\)
Reasoning is:
Since x < 0; only x is the valid value. +x can be ignored.
Ans: "A" What I said there is a fact. When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root. That is, \(\sqrt{16}=4\), NOT +4 or 4. Even roots have only a positive value on the GMAT.In contrast, the equation \(x^2=16\) has TWO solutions, +4 and 4. Odd roots have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{64} =4\).
_________________
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



Intern
Joined: 25 Jul 2018
Posts: 2

Re: If x < 0, then root({x} •x) is
[#permalink]
Show Tags
05 Aug 2018, 13:50
Bunuel wrote: udaymathapati wrote: If x < 0, then \sqrt{x} •x) is A. x B. 1 C. 1 D. x E. \sqrt{x} 1. If x<0, then \(\sqrt{x*x}\) equals:A. \(x\) B. \(1\) C. \(1\) D. \(x\) E. \(\sqrt{x}\) Remember: \(\sqrt{x^2}=x\). The point here is that square root function can not give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function! That is why \(\sqrt{x^2}=x\) Back to the original question:\(\sqrt{x*x}=\sqrt{(x)*(x)}=\sqrt{x^2}=x=x\) Or just substitute the value let \(x=5<0\) > \(\sqrt{x*x}=\sqrt{(5)*5}=\sqrt{25}=5=(5)=x\). Answer: A. Hope it's clear. I have a different theory here. They explicitly state that x is negative. Then they give us an eq. Your solution neglects the fact that x is negative. \(\sqrt{x*x}=\sqrt{(negative)*negative)}=\sqrt{positive*positive}=x=x\) There are two solutions for x and both of them are in the answers. Some thing is off with this question imho



Math Expert
Joined: 02 Sep 2009
Posts: 49915

Re: If x < 0, then root({x} •x) is
[#permalink]
Show Tags
05 Aug 2018, 22:27
nobilisrex wrote: Bunuel wrote: udaymathapati wrote: If x < 0, then \sqrt{x} •x) is A. x B. 1 C. 1 D. x E. \sqrt{x} 1. If x<0, then \(\sqrt{x*x}\) equals:A. \(x\) B. \(1\) C. \(1\) D. \(x\) E. \(\sqrt{x}\) Remember: \(\sqrt{x^2}=x\). The point here is that square root function can not give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function! That is why \(\sqrt{x^2}=x\) Back to the original question:\(\sqrt{x*x}=\sqrt{(x)*(x)}=\sqrt{x^2}=x=x\) Or just substitute the value let \(x=5<0\) > \(\sqrt{x*x}=\sqrt{(5)*5}=\sqrt{25}=5=(5)=x\). Answer: A. Hope it's clear. I have a different theory here. They explicitly state that x is negative. Then they give us an eq. Your solution neglects the fact that x is negative. \(\sqrt{x*x}=\sqrt{(negative)*negative)}=\sqrt{positive*positive}=x=x\) There are two solutions for x and both of them are in the answers. Some thing is off with this question imho To check your theory, I'd suggest to plug some negative number and check what you'd get. P.S. The question as well as the solution is fine.
_________________
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



Manager
Joined: 29 May 2017
Posts: 72
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability

Re: If x < 0, then root({x} •x) is
[#permalink]
Show Tags
19 Sep 2018, 18:38
Bunuel wrote: udaymathapati wrote: If x < 0, then \sqrt{x} •x) is A. x B. 1 C. 1 D. x E. \sqrt{x} 1. If x<0, then \(\sqrt{x*x}\) equals:A. \(x\) B. \(1\) C. \(1\) D. \(x\) E. \(\sqrt{x}\) Remember: \(\sqrt{x^2}=x\). The point here is that square root function can not give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function! That is why \(\sqrt{x^2}=x\) Back to the original question:\(\sqrt{x*x}=\sqrt{(x)*(x)}=\sqrt{x^2}=x=x\) Or just substitute the value let \(x=5<0\) > \(\sqrt{x*x}=\sqrt{(5)*5}=\sqrt{25}=5=(5)=x\). Answer: A. Hope it's clear. since we are given x<0, this means x is ve. therefore: 1. x> (x) > x so, 2. sqrt(x . x) > sqrt(x . x) can you explain what is wrong with stmt 1? i lose the plot on stmt 2....can you explain why x> x? it should be +x thanks



Intern
Joined: 07 Jul 2018
Posts: 11

If x < 0, then root({x} •x) is
[#permalink]
Show Tags
20 Sep 2018, 09:35
Bunuel wrote: udaymathapati wrote: If x < 0, then \sqrt{x} •x) is A. x B. 1 C. 1 D. x E. \sqrt{x} 1. If x<0, then \(\sqrt{x*x}\) equals:A. \(x\) B. \(1\) C. \(1\) D. \(x\) E. \(\sqrt{x}\) Remember: \(\sqrt{x^2}=x\). The point here is that square root function can not give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function! That is why \(\sqrt{x^2}=x\) Back to the original question:\(\sqrt{x*x}=\sqrt{(x)*(x)}=\sqrt{x^2}=x=x\) Or just substitute the value let \(x=5<0\) > \(\sqrt{x*x}=\sqrt{(5)*5}=\sqrt{25}=5=(5)=x\). Answer: A. Hope it's clear. I understood the concept, However I don't understand how you did this \(\sqrt{x*x}=\sqrt{(x)*(x)}\) Inside mod X can be either positive or negative, how can you assume it to be negative?




If x < 0, then root({x} •x) is &nbs
[#permalink]
20 Sep 2018, 09:35



Go to page
Previous
1 2
[ 37 posts ]



