Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 06 Aug 2007
Posts: 30
Location: Montreal

For which of the following values of x is [#permalink]
Show Tags
Updated on: 16 May 2012, 03:53
Question Stats:
69% (00:49) correct 31% (00:40) wrong based on 998 sessions
HideShow timer Statistics
For which of the following values of x is \(\sqrt{1\sqrt{2\sqrt{x}}}\) NOT defined as a real number? A. 1 B. 2 C. 3 D. 4 E. 5
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Safiya on 24 Aug 2010, 12:41.
Last edited by Bunuel on 16 May 2012, 03:53, edited 1 time in total.
Edited the question



Math Expert
Joined: 02 Sep 2009
Posts: 46328

Re: NOT defined as a real number [#permalink]
Show Tags
24 Aug 2010, 12:49



Intern
Joined: 06 Aug 2007
Posts: 30
Location: Montreal

Re: NOT defined as a real number [#permalink]
Show Tags
24 Aug 2010, 13:04
It helped indeed, thank you very much!



Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 122
Concentration: Finance, General Management

Re: NOT defined as a real number [#permalink]
Show Tags
20 Dec 2010, 01:18
Bunuel 
So the approach to problems such as this one is to work your way from the most inner root, out toward the main root? Always keeping track of whether the underlying roots are (1) negative (2) are larger than the main root.



Math Expert
Joined: 02 Sep 2009
Posts: 46328

Re: NOT defined as a real number [#permalink]
Show Tags
20 Dec 2010, 01:35
tonebeeze wrote: Bunuel 
So the approach to problems such as this one is to work your way from the most inner root, out toward the main root? Always keeping track of whether the underlying roots are (1) negative (2) are larger than the main root. Consider another example: For which of the following values of x \(\sqrt{1\sqrt{4\sqrt{x}}}\) is NOT defined as a real number? A. 16 B. 12 C.10 D. 9 E. 4 First see whether \(4\sqrt{x}\) could be negative for some value of \(x\) so you should test max value of \(x\): \(4\sqrt{x_{max}}=4\sqrt{16}=0\). As it's not negative then see whether \(1\sqrt{4\sqrt{x}}\) can be negative for some value of \(x\), so you should test min value of \(x\) to maximize \(4\sqrt{x}\): \(1\sqrt{4\sqrt{x_{min}}}=1\sqrt{4\sqrt{4}}=11.41=0.41<0\). Answer E. Hope it's clear.
_________________
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: Current MBA Student
Joined: 19 Nov 2009
Posts: 122
Concentration: Finance, General Management

Re: NOT defined as a real number [#permalink]
Show Tags
20 Dec 2010, 02:02
Great visual explanation. I now understand. Thanks for taking the time to help.



Senior Manager
Joined: 29 Jan 2011
Posts: 317

Re: NOT defined as a real number [#permalink]
Show Tags
11 Jul 2011, 04:04
Bunuel wrote: Safiya wrote: I'd be glad if someone could explain the logic for this question;
For which of the following values of x is
\(\sqrt{1}\)\(\sqrt{2}\)\(\sqrt{x}\)
NOT defined as a real number?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Real Numbers are: Integers, Fractions and Irrational Numbers. Nonreal numbers are even roots (such as square roots) of negative numbers. We have \(\sqrt{1\sqrt{2\sqrt{x}}}\). For \({x=5}\) expression becomes:\(\sqrt{1\sqrt{2\sqrt{5}}}\) and \(2\sqrt{5}<0\), thus square root from this expression is not a real number. Answer: E. Hope it helps. Why is 4 not the correct answer as it would yield root ( 2  (root (4)) => root(2  2) = 0 .. Is root (0) not a real number?



Retired Moderator
Joined: 16 Nov 2010
Posts: 1471
Location: United States (IN)
Concentration: Strategy, Technology

Re: NOT defined as a real number [#permalink]
Show Tags
11 Jul 2011, 05:36
@siddhans, root(0) = 0, which is a real number, and the question is asking for a value that is not a real number. So 4 is not a correct choice.
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 16 Feb 2012
Posts: 200
Concentration: Finance, Economics

Re: For which of the following values of x is [#permalink]
Show Tags
16 May 2012, 04:27
I don't understand how did you came from \(\sqrt{1\sqrt{2\sqrt{5}}} to 2\sqrt{5}<0\) ? I would appreciate if you explain, because I'm obviously missing something.
_________________
Kudos if you like the post!
Failing to plan is planning to fail.



Math Expert
Joined: 02 Sep 2009
Posts: 46328

Re: For which of the following values of x is [#permalink]
Show Tags
16 May 2012, 04:41



Manager
Joined: 16 Feb 2012
Posts: 200
Concentration: Finance, Economics

Re: For which of the following values of x is [#permalink]
Show Tags
16 May 2012, 05:58
O yes,yes,yes... thanks! Sometimes I just look at numbers and don't see anything no matter how obvious it is. I need a break!
_________________
Kudos if you like the post!
Failing to plan is planning to fail.



Math Expert
Joined: 02 Sep 2009
Posts: 46328

Re: For which of the following values of x is [#permalink]
Show Tags
05 Jun 2013, 04:28



Intern
Joined: 28 Apr 2013
Posts: 16
GMAT Date: 08032013
GPA: 3.3
WE: Supply Chain Management (Military & Defense)

Re: For which of the following values of x is [#permalink]
Show Tags
05 Jun 2013, 10:09
Can we not simply take each value (calculated or not) under a radical, inside to out, and test if it's less than zero?
\(x<0\)  no answer choice satisfies
\(2\sqrt{x}<0\)  otherwise reads \(2<\sqrt{x}\) so \(x>2^2\)or 4....answer is E, no need to test [m]1\sqrt{2[square_root]x}[/square_root] as we have only one answer choice that meets this criteria. This approach is very similar to what Bunuel did but seems much quicker upfront in this case.



SVP
Joined: 08 Jul 2010
Posts: 2115
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: For which of the following values of x is [#permalink]
Show Tags
15 Jul 2015, 21:29
Safiya wrote: For which of the following values of x is \(\sqrt{1\sqrt{2\sqrt{x}}}\) NOT defined as a real number?
A. 1 B. 2 C. 3 D. 4 E. 5 CONCEPT: Any Number is considered NONREAL if the number under the square root is negative (i.e.√(ve)) .Such questions require us to check the smallest or highest values among option because at the extremes only the number will result in Real or NONReal Here, We need to check the highest value because x is being subtracted from other numbers @x=5 (Option E) √[1−√(2−√x)] = √[1−√(2−√5)] = √[1−√(2−2.2)] = √[1− √(ve)] i.e. NONREAL NumberHence, Correct Option Answer: Option E
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Current Student
Joined: 04 Sep 2015
Posts: 27
Location: United Arab Emirates
GPA: 3.21

Re: For which of the following values of x is [#permalink]
Show Tags
11 Jun 2016, 10:48
Nwsmith11 wrote: Can we not simply take each value (calculated or not) under a radical, inside to out, and test if it's less than zero?
\(x<0\)  no answer choice satisfies
\(2\sqrt{x}<0\)  otherwise reads \(2<\sqrt{x}\) so \(x>2^2\)or 4....answer is E, no need to test [m]1\sqrt{2[square_root]x}[/square_root] as we have only one answer choice that meets this criteria. This approach is very similar to what Bunuel did but seems much quicker upfront in this case. How would you solve this (the question mentioned by buneul above): Consider another example: For which of the following values of x 1−4−x√‾‾‾‾‾‾‾√‾‾‾‾‾‾‾‾‾‾‾‾‾√1−4−x is NOT defined as a real number? A. 16 B. 12 C.10 D. 9 E. 4



Director
Joined: 09 Mar 2016
Posts: 615

For which of the following values of x is [#permalink]
Show Tags
09 Jun 2018, 04:46
Bunuel wrote: tonebeeze wrote: Bunuel 
So the approach to problems such as this one is to work your way from the most inner root, out toward the main root? Always keeping track of whether the underlying roots are (1) negative (2) are larger than the main root. Consider another example: For which of the following values of x \(\sqrt{1\sqrt{4\sqrt{x}}}\) is NOT defined as a real number? A. 16 B. 12 C.10 D. 9 E. 4 First see whether \(4\sqrt{x}\) could be negative for some value of \(x\) so you should test max value of \(x\): \(4\sqrt{x_{max}}=4\sqrt{16}=0\). As it's not negative then see whether \(1\sqrt{4\sqrt{x}}\) can be negative for some value of \(x\), so you should test min value of \(x\) to maximize \(4\sqrt{x}\): \(1\sqrt{4\sqrt{x_{min}}}=1\sqrt{4\sqrt{4}}=11.41=0.41<0\). Answer E. Hope it's clear. hi pushpitkccan you please explain the technique of taking square root, when one radical is under another radical sign ? i am kinda confused:) do we take square root \(\sqrt{1}\) by multiplying by exponent 2 ? ? then we get \(1\sqrt{4\sqrt{x}}\) and after we get this \(12\sqrt{x}\) and then again multiply by exponent 2 and get \(12x\)



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2841
Location: India
GPA: 3.12

For which of the following values of x is [#permalink]
Show Tags
09 Jun 2018, 05:00
dave13 wrote: Bunuel wrote: tonebeeze wrote: Bunuel 
So the approach to problems such as this one is to work your way from the most inner root, out toward the main root? Always keeping track of whether the underlying roots are (1) negative (2) are larger than the main root. Consider another example: For which of the following values of x \(\sqrt{1\sqrt{4\sqrt{x}}}\) is NOT defined as a real number? A. 16 B. 12 C.10 D. 9 E. 4 First see whether \(4\sqrt{x}\) could be negative for some value of \(x\) so you should test max value of \(x\): \(4\sqrt{x_{max}}=4\sqrt{16}=0\). As it's not negative then see whether \(1\sqrt{4\sqrt{x}}\) can be negative for some value of \(x\), so you should test min value of \(x\) to maximize \(4\sqrt{x}\): \(1\sqrt{4\sqrt{x_{min}}}=1\sqrt{4\sqrt{4}}=11.41=0.41<0\). Answer E. Hope it's clear. hi pushpitkccan you please explain the technique of taking square root, when one radical is under another radical sign ? i am kinda confused:) do we take square root \(\sqrt{1}\) by multiplying by exponent 2 ? ? then we get \(1\sqrt{4\sqrt{x}}\) and after we get this \(12\sqrt{x}\) and then again multiply by exponent 2 and get \(12x\) Hi dave13Whenever we have a square root under another square root, for example \(\sqrt{7 + \sqrt{81}}\) First step will be to do the square root of the number underneath. The expression now becomes \(\sqrt{7 + 9}\)  because \(\sqrt{81} = 9\) Now, after adding the two integers(in this case) under the radical sign, we need to perform the second square root operation (\(\sqrt{16} = 4\)) Hope this helps you!
_________________
You've got what it takes, but it will take everything you've got



Director
Joined: 09 Mar 2016
Posts: 615

For which of the following values of x is [#permalink]
Show Tags
Updated on: 09 Jun 2018, 07:56
pushpitkc thanks for explanation if you say "First step will be to do the square root of the number underneath." then why Bunuel after this \(\sqrt{1\sqrt{4\sqrt{x}}}\) gets this \(1\sqrt{4\sqrt{x}}\) why he takes square root of 1 and not x which is underneath hello generis, i ve decided to have rest and relax by switching to number properties questions today I thought perhaps you can explain ?:) I still dont get, though pushpitkc tried to explain pushpitkc says "First step will be to do the square root of the number underneath." this is how i tackled question \((\sqrt{1\sqrt{4\sqrt{x}}})^2\) ( square to get rid of the root ) we get this \((1\sqrt{4\sqrt{x}})^2\) (square again) we get this \(14\sqrt{x}\) > \((3\sqrt{x} )^2\) square again we get \(9x\):? now what ? ... that`s strange when we square (as you see above) first we get rid of external radical signs for example, Bunuel after this \(\sqrt{1\sqrt{4\sqrt{x}}}\) get this \(1\sqrt{4\sqrt{x}}\) this means he squared and got rid of bigger radical sign... on the other hand pushpitkc says First step will be to do the square root of the number underneath which is \(x\) can you please investigate this case generis007
Originally posted by dave13 on 09 Jun 2018, 05:22.
Last edited by dave13 on 09 Jun 2018, 07:56, edited 1 time in total.



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2841
Location: India
GPA: 3.12

Re: For which of the following values of x is [#permalink]
Show Tags
09 Jun 2018, 05:37
dave13 wrote: pushpitkc thanks for explanation if you say "First step will be to do the square root of the number underneath." then why Bunuel after this \(\sqrt{1\sqrt{4\sqrt{x}}}\) gets this \(1\sqrt{4\sqrt{x}}\) why he takes square root of 1 and not x which is underneath Hi dave13If you read the solution that Bunuel has written, it is also saying exactly what I said. Read this post for more clarity: https://gmatclub.com/forum/forwhichof ... ml#p838260Hope this helps you!
_________________
You've got what it takes, but it will take everything you've got



Director
Joined: 09 Mar 2016
Posts: 615

Re: For which of the following values of x is [#permalink]
Show Tags
12 Jun 2018, 06:10
pushpitkc what if it were like this \(\sqrt{7 + \sqrt{11}}\) how would you solve it ? thanks!:)




Re: For which of the following values of x is
[#permalink]
12 Jun 2018, 06:10



Go to page
1 2
Next
[ 22 posts ]



