If $\sqrt{\sqrt{\sqrt{5x}}}=\sqrt[6]{4x},$ what is the range of the possible values of $x?$

Expert replies

Previous Topic Next Topic

Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sun Mar 14, 2021 7:36 am

Timer

00:00

Answers

Stats

Difficulty—

If $\sqrt{\sqrt{\sqrt{5x}}}=\sqrt[6]{4x},$ what is the range of the possible values of $x?$

A. $0$

B. $14$

C. $\dfrac{125}{256}$

D. $\dfrac12$

E. $\dfrac{131}{256}$

Answer: C

Source: GMAT Club Tests

Like this post

Source: Beat The GMAT — Problem Solving | Sun Mar 14, 2021 7:36 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: If $\sqrt{\sqrt{\sqrt{5x}}}=\sqrt[6]{4x},$ what is the range of the possible values of $x?$

by deloitte247 » Wed Mar 17, 2021 12:33 am

What is the range of the possible value of x?
$$\left(5x\right)^{\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}}=\left(4x\right)^{\frac{1}{6}}$$
$$\left(5x\right)^{\frac{1}{8}}=\left(4x\right)^{\frac{1}{6}}$$
$$5x=\left[\left(4x\right)^{\frac{1}{6}}\right]^8$$
$$5x=\left(4x\right)^{\frac{8}{6}}$$
$$5x=\left(4x\right)^{\frac{4}{3}}$$
$$5x=4^{\frac{4}{3}}\cdot x^{\frac{4}{3}}$$
$$\frac{5x}{x\cdot4^{\frac{4}{3}}}=\frac{\left(4^{\frac{4}{3}}\cdot x^{\frac{4}{3}}\right)}{x\cdot4^{\frac{4}{3}}}$$
$$\frac{5}{4^{\frac{4}{3}}}=\frac{x^{\frac{4}{3}}}{x^1}$$ $$\frac{5}{4^{\frac{4}{3}}}=x^{\frac{4}{3}-1}$$ $$\frac{5}{4^{\frac{4}{3}}}=x^{\frac{4-3}{3}}$$
$$x^{\frac{1}{3}}=\frac{5}{4^{\frac{4}{3}}}$$
$$\left(x^{\frac{1}{3}}\right)^3=\left(\frac{5}{4^{\frac{4}{3}}}\right)^3$$
$$x=\frac{5^3}{4^{\frac{4}{3}\cdot3}}=\frac{5^3}{4^4}=\frac{125}{256}$$

Answer = C

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review