Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 01 Apr 2006
Posts: 169
Location: Toronto, Canada

Is root(x5)^2 = 5  x ?
[#permalink]
Show Tags
13 Jan 2007, 11:52
Question Stats:
64% (01:43) correct 36% (01:49) wrong based on 890 sessions
HideShow timer Statistics
Is \(\sqrt{(x5)^2} = 5  x\)? (1) xx > 0 (2) 5  x > 0
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 50005

Is root(x5)^2 = 5  x ?
[#permalink]
Show Tags
09 Sep 2009, 15:41
dhushan wrote: Just want to make sure that my line of thinking is right. I got D as well.
sqrt(x5)^2 = 5x ==> x5 = 5x
which means that if
x5<0, (x5) = 5x = no solution, therefore x<5
x5>0, x5 = 5x, which means that x>5 and x = 5
from (1) xx > 0, we know that x has to be negative (x)x is the only way to get a number greater than 0. Therefore, this means that of the three possible solutions for x, only this x<5 hold true.
from (2) 5x>0, therefore x<5.
Can someone please point out if there is something wrong with my reasoning. Is \(\sqrt{(x5)^2}=5x\)?First of all, recall that \(\sqrt{x^2}=x\). Is \(\sqrt{(x5)^2}=5x\)? > is \(x5=5x\)? > is \(x5\leq{0}\)? > is \(x\leq{5}\)? (1) \(xx > 0\) > \(x\) is never negative (positive or zero), so for \(xx\) to be positive, \(x\) must be positive \(x>0\) > \(x<0\). Sufficient. (2) \(5x>0\) > \(x<5\). Sufficient. Answer: D.
_________________
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




Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1211
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

Is sqrt(x5)^2 = 5x?
[#permalink]
Show Tags
06 Sep 2010, 12:20
Is \(\sqrt {(x5)^2} = 5x\) ? (1) xx > 0 (2) 5  x > 0 PS. Is always this true?: \(\sqrt{x^2}\) = lxl ?
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."
My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html
GMAT Club Premium Membership  big benefits and savings




SVP
Joined: 01 May 2006
Posts: 1777

For me (D)
sqrt( (x5)^2) = 5  x ?
<=> x5 = 5x ?
<=> 5x = 5x ?
This is true if 5x >= 0 <=> x =< 5
So we end up with checking if x =< 5 ?
Stat 1
x x > 0
<=> x < 0 < 5
SUFF.
Stat 2
5  x > 0
<=> x < 5
SUFF.



Intern
Joined: 30 Jul 2009
Posts: 18

Re: DS: Sqrt inequality
[#permalink]
Show Tags
09 Sep 2009, 12:01
Just want to make sure that my line of thinking is right. I got D as well.
sqrt(x5)^2 = 5x ==> x5 = 5x
which means that if
x5<0, (x5) = 5x = no solution, therefore x<5
x5>0, x5 = 5x, which means that x>5 and x = 5
from (1) xx > 0, we know that x has to be negative (x)x is the only way to get a number greater than 0. Therefore, this means that of the three possible solutions for x, only this x<5 hold true.
from (2) 5x>0, therefore x<5.
Can someone please point out if there is something wrong with my reasoning.



Manager
Joined: 25 Aug 2009
Posts: 133
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years

Re: Square root.
[#permalink]
Show Tags
31 Dec 2009, 09:40
The question basically wants to know if x<=5 else RHS will be x5 Statement 1 xx>0 or xx<0 (multiply by 1 both sides and reverse the sign) either x<0 or x<0 since x is always positive or 0 x<0 is true. if x<0 then x<5 hence sufficient Statement 2 5x>0 5>x This is what we are looking for hence sufficient Answer is D.
_________________
Rock On



Math Expert
Joined: 02 Sep 2009
Posts: 50005

Re: Is sqrt(x5)^2 = 5x?
[#permalink]
Show Tags
06 Sep 2010, 12:30
metallicafan wrote: Is \(sqrt(x5)^2 = 5x?\)
(1) xlxl > 0 (2) 5x > 0
PS. Is always this true?: \(sqrt{x^2}\) = lxl ? Is \(\sqrt{(x5)^2}=5x\)? Remember: \(\sqrt{x^2}=x\). So "is \(\sqrt{(x5)^2}=5x\)?" becomes: is \(x5=5x\)? \(x5=5x\) is true only for \(x\leq{5}\), as in this case \(\{LHS=x5=5x\}=\{RHS=5x\}\). So we have that if \(x\leq{5}\), then \(x5=5x\) is true. Basically question asks is \(x\leq{5}\)? (1) \(xx > 0\) > \(x\) is never negative (positive or zero), so in order to have \(xx > 0\), \(x\) must be positive \(x>0\) > \(x<0\), so \(x\) is less than 5 too. Sufficient. (2) \(5x>0\) > \(x<5\). Sufficient. Answer: D. Hope it helps. P.S. Explanation of: \(\sqrt{x^2}=x\). The point here is that as square root function can not give negative result then \(\sqrt{some \ expression}\geq{0}\). 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: \(x=x\), if \(x\geq{0}\) and \(x=x\), if \(x<0\). That is why \(\sqrt{x^2}=x\).
_________________
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
Status: Last few days....Have pressed the throttle
Joined: 20 Jun 2010
Posts: 58
WE 1: 6 years  Consulting

Re: Is sqrt(x5)^2 = 5x?
[#permalink]
Show Tags
07 Sep 2010, 02:44
Bunuel wrote: metallicafan wrote: Is \(sqrt(x5)^2 = 5x?\)
(1) xlxl > 0 (2) 5x > 0
PS. Is always this true?: \(sqrt{x^2}\) = lxl ? Is \(\sqrt{(x5)^2}=5x\)? Remember: \(\sqrt{x^2}=x\). So "is \(\sqrt{(x5)^2}=5x\)?" becomes: is \(x5=5x\)? \(x5=5x\) is true only for \(x\leq{5}\), as in this case \(\{LHS=x5=5x\}=\{RHS=5x\}\). So we have that if \(x\leq{5}\), then \(x5=5x\) is true. Basically question asks is \(x\leq{5}\)? (1) \(xx > 0\) > \(x\) is never negative (positive or zero), so in order to have \(xx > 0\), \(x\) must be positive \(x>0\) > \(x<0\), so \(x\) is less than 5 too. Sufficient. (2) \(5x>0\) > \(x<5\). Sufficient. Answer: D. Hope it helps. Hi Bunuel, I get confused in the following concept. Can you please help me: \(xx > 0\) > \(x\) is never negative (positive or zero), so in order to have \(xx > 0\), \(x\) must be positive \(x>0\) > \(x<0\), so \(x\) is less than 5 too Can't we solve it as follows: As \(x\) is never negative > \(xx > 0\) = x*x = x^2 >0 = x^2<0 (multiplying by ve sign and flipping sign) x^2<0 => \(sqrt{x^2}\) <0 => lxl <0 (as \(sqrt{x^2}\) =lxl ) Since lxl cannot be negative and lxl <0 that implies X<0 I have reached to same conclusion as yours but wanted to confirm if my approach is right. Please explain.Thanks
_________________
Consider giving Kudos if my post helps in some way



Math Expert
Joined: 02 Sep 2009
Posts: 50005

Re: Is sqrt(x5)^2 = 5x?
[#permalink]
Show Tags
07 Sep 2010, 05:01
oldstudent wrote: Bunuel wrote: metallicafan wrote: Is \(sqrt(x5)^2 = 5x?\)
(1) xlxl > 0 (2) 5x > 0
PS. Is always this true?: \(sqrt{x^2}\) = lxl ? Is \(\sqrt{(x5)^2}=5x\)? Remember: \(\sqrt{x^2}=x\). So "is \(\sqrt{(x5)^2}=5x\)?" becomes: is \(x5=5x\)? \(x5=5x\) is true only for \(x\leq{5}\), as in this case \(\{LHS=x5=5x\}=\{RHS=5x\}\). So we have that if \(x\leq{5}\), then \(x5=5x\) is true. Basically question asks is \(x\leq{5}\)? (1) \(xx > 0\) > \(x\) is never negative (positive or zero), so in order to have \(xx > 0\), \(x\) must be positive \(x>0\) > \(x<0\), so \(x\) is less than 5 too. Sufficient. (2) \(5x>0\) > \(x<5\). Sufficient. Answer: D. Hope it helps. Hi Bunuel, I get confused in the following concept. Can you please help me: \(xx > 0\) > \(x\) is never negative (positive or zero), so in order to have \(xx > 0\), \(x\) must be positive \(x>0\) > \(x<0\), so \(x\) is less than 5 too Can't we solve it as follows: As \(x\) is never negative > \(xx > 0\)= x*x = x^2 >0 = x^2<0 (multiplying by ve sign and flipping sign) x^2<0 => \(sqrt{x^2}\) <0=> lxl <0 (as \(sqrt{x^2}\) =lxl ) Since lxl cannot be negative and lxl <0 that implies X<0 I have reached to same conclusion as yours but wanted to confirm if my approach is right. Please explain.Thanks This approach is not right. The red parts are not correct. \(xx > 0\) can not be written as \(x*x>0\), as \(x\geq{0}\) does not mean \(x\) itself can not be negative > \(x=x\) if \(x\geq{0}\) and \(x=x\) if \(x\leq{0}\), so when you are writing \(x\) instead of \(x\) you are basically assuming that \(x\geq{0}\) and then in the end get the opposite result \(x<0\). Next, \(x^2<0\) has no solution, square of a number can not be negative, so no \(x\) can make this inequality hold true.
_________________
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: 17 Mar 2010
Posts: 145

Re: Is sqrt(x5)^2 = 5x?
[#permalink]
Show Tags
07 Sep 2010, 23:42
I think for this question we dont need any statement... without statement itself it is possible to say if the equality is correct or wrong. Can someone comment on this... Bunuel please?



Math Expert
Joined: 02 Sep 2009
Posts: 50005

Re: Is sqrt(x5)^2 = 5x?
[#permalink]
Show Tags
08 Sep 2010, 06:59



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India

Re: Square root.
[#permalink]
Show Tags
19 Mar 2011, 20:20
arjunrampal wrote: Please explain the approach to solve the problem and point to any relevant material available in the GMAT club. Attachment: square_root_D.JPG Let me point out something here: You cannot square both sides to get Is \((\sqrt{(x5)^2})^2 = (5x)^2\) ? People sometimes get confused here. Why can you not square it? It is a question similar to 'Is x = 5?' Can you square both sides here and change the question to 'Is \(x^2 = 25\)?' Please remember, they are not the same. x^2 can be 25 even if x is not 5 ( when x = 5, even then x^2 = 25). Only if it is given to you that x = 5, then you can say that x^2 = 25. You can rephrase the question in the following manner (and many more ways) Is \((\sqrt{(x5)^2}) = (5x)\) ? Is \(x5 = (5x)\) ? or Is \(5x = (5x)\)? We know that x = x only when x >= 0 So \(5x = (5x)\) only when 5  x >= 0 or when x <= 5 Stmnt 1: xx > 0 Since x is always positive (or zero), x must be positive too. So x must be negative. If x < 0, then x is obviously less than 5. Sufficient. Stmnt 2: 5  x> 0 x < 5. Sufficient Answer D
_________________
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 >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 04 Jan 2015
Posts: 7

Re: Is root(x5)^2 = 5  x ?
[#permalink]
Show Tags
12 Jul 2015, 08:32
kshitij89Modulus always results in an positive value. If x5>0 then x−5 should be equal to x5 However, If x5<0 then modulus would result the positive value of it i.e. (x5)=5x Thus, is x−5=5−x? > is x−5<0? > is x<5? Solving as Bunuel ,you'll get D.




Re: Is root(x5)^2 = 5  x ? &nbs
[#permalink]
12 Jul 2015, 08:32






