Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: NOT defined as a real number [#permalink]
24 Aug 2010, 11:49

1

This post received KUDOS

Expert's post

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. Non-real 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.

Re: NOT defined as a real number [#permalink]
20 Dec 2010, 00:18

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.

Re: NOT defined as a real number [#permalink]
20 Dec 2010, 00:35

5

This post received KUDOS

Expert's post

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 \(4-\sqrt{x}\): \(1-\sqrt{4-\sqrt{x_{min}}}=1-\sqrt{4-\sqrt{4}}=1-1.41=-0.41<0\).

Re: NOT defined as a real number [#permalink]
11 Jul 2011, 03:04

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. Non-real 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?

Re: NOT defined as a real number [#permalink]
11 Jul 2011, 04:36

@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)

Re: For which of the following values of x is [#permalink]
16 May 2012, 03:27

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. _________________

Re: For which of the following values of x is [#permalink]
16 May 2012, 03:41

1

This post received KUDOS

Expert's post

Stiv wrote:

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.

If \({x=5}\) then the expression becomes:\(\sqrt{1-\sqrt{2-\sqrt{5}}}\). The expression under the second square root is \(2-\sqrt{5}\). Now, since \(2-\sqrt{5}<0\) then the square root from this expression is not a real number.

Re: For which of the following values of x is [#permalink]
05 Jun 2013, 09:09

1

This post received KUDOS

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.

Re: For which of the following values of x is [#permalink]
11 Jul 2014, 21:19

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. _________________

Re: For which of the following values of x is [#permalink]
15 Jul 2015, 16:28

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. _________________

Contact for One-on-One LIVE Online (SKYPE Based) Quant/Verbal Demo ______________________________________________________ Please press the if you appreciate this post !!

gmatclubot

Re: For which of the following values of x is
[#permalink]
15 Jul 2015, 20:29

Interested in applying for an MBA? In the fourth and final part of our live QA series with guest expert Chioma Isiadinso, co-founder of consultancy Expartus and former admissions...