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 500,000 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:

Since the answer choices are dissimilar, we can estimate the answer choice here. The \(\sqrt[2]{20}\) is somewhere between 4 and 5. Suppose it's 5, then we'll get \(\sqrt[2]{20+\sqrt[2]{20+5}\)=\(\sqrt[2]{20+5}\)=\(5\)

2: From third sqrt: sqrt 20 = 4 and a fraction of 1. From second sqrt: sqrt (20+4.00 = 24) = 4 and a fraction of 1. From first sqrt: sqrt (20+4.00 = 24) = 4 and a fraction of 1. which is definitely close to none other than 5.

3: Using POE:

A: it cannot be 20 cuz for 20, the value under root must be 400, which is impossible. so A is ruled out. B: It could be 5 as done above in method 2. 3. 2 is also not possible because even if we consider first 20 under root, the value must not be smaller than 4. 4. 8 is not possible because for 8, the value under root must be 64. Even if we add up all three 20s, the sum would not be more than 60. so it is also not possible. So left with 5.

Bunuel, would you be so kind and look at this question. Is there any other way to solve it rather than elimination? Can you describe elimination in greater detail? Thank you.

Bunuel, would you be so kind and look at this question. Is there any other way to solve it rather than elimination? Can you describe elimination in greater detail? Thank you.

Find the value of x

\(x= \sqrt{20+\sqrt{20+\sqrt{20}}}\)

1. 20 2. 5 3. 2 4. 8

Question should be what is the approximate value of \(x\).

Obviously answer choice C (2) is out as \(\sqrt{20+some \ #}>4\).

Now, \(4<\sqrt{20}<5\): \(x= \sqrt{20+\sqrt{20+\sqrt{20}}}= \sqrt{20+\sqrt{20+(# \ less \ than \ 5)}}= \sqrt{20+\sqrt{# \ less \ than \ 25}}= \sqrt{20+(# \ less \ than \ 5)}=\)

\(=\sqrt{# \ less \ than \ 25}=# \ less \ than \ 5\approx{5}\).

Answer: B.

Next, exactly 5 to be the correct answer question should be:

If the expression \(x=\sqrt{20+{\sqrt{20+\sqrt{20+\sqrt{20+...}}}}}\) extends to an infinite number of roots and converges to a positive number x, what is x?

\(x=\sqrt{20+{\sqrt{20+\sqrt{20+\sqrt{20+...}}}}}\) --> \(x=\sqrt{20+({\sqrt{20+\sqrt{20+\sqrt{20+...})}}}}\), as the expression under square root extends infinitely, then expression in brackets would equal to \(x\) itself so we can rewrite given expression as \(x=\sqrt{20+x}\). Square both sides \(x^2=20+x\) --> \(x=5\) or \(x=-4\). As given that \(x>0\) then only one solution is valid: \(x=5\).

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. _________________

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.

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. _________________

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. _________________

This is the kickoff for my 2016-2017 application season. After a summer of introspect and debate I have decided to relaunch my b-school application journey. Why would anyone want...

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

Time is a weird concept. It can stretch for seemingly forever (like when you are watching the “Time to destination” clock mid-flight) and it can compress and...