GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 01:55 GMAT Club Daily Prep

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

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.  If 12th root of x is equal to 12, 8th root of y equals to 8

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Senior Manager  V
Joined: 25 Sep 2018
Posts: 422
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30 GPA: 3.97
WE: Investment Banking (Investment Banking)
If 12th root of x is equal to 12, 8th root of y equals to 8  [#permalink]

Show Tags

2 00:00

Difficulty:   55% (hard)

Question Stats: 60% (02:29) correct 40% (03:09) wrong based on 20 sessions

HideShow timer Statistics

If $$\sqrt{x} = 12$$, $$\sqrt{y}$$ = 8, $$\sqrt{z} = 6$$ then which of the following is the median of$$\sqrt{x^{12}}$$ , $$\sqrt{y^8}$$ and$$\sqrt{z^6}$$

A) $$8^{98}$$

B)$$2^{96}$$

C)$$6^{18}$$

D)$$8^{10}$$

E)$$4^{12}$$

_________________
Why do we fall?...So we can learn to pick ourselves up again

Originally posted by Abhi077 on 13 Apr 2019, 01:01.
Last edited by Abhi077 on 13 Apr 2019, 01:55, edited 2 times in total.
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2974
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
If 12th root of x is equal to 12, 8th root of y equals to 8  [#permalink]

Show Tags

Abhi077 wrote:
If $$\sqrt{x} = 2$$, $$\sqrt{y}$$ = 8, $$\sqrt{z} = 6$$ then which of the following is the median of$$\sqrt{x^{12}}$$ , $$\sqrt{y^8}$$ and$$\sqrt{z^6}$$

A) $$8^{98}$$

B)$$2^{96}$$

C)$$6^{18}$$

D)$$8^{10}$$

E)$$4^{12}$$

$$x^{1/12} = 12$$
i.e.$$x = 12^{12}$$

i.e. $$\sqrt{x^{12}}$$ $$= x^6 = 12^{72}$$

Now, $$\sqrt{y}$$ = 8
i.e.$$y^{1/8} = 8$$

i.e. $$y = 8^8$$

i.e. $$\sqrt{y^8} = y^4 = 8^{32} = 2^{96}$$

Also, $$\sqrt{z} = z^{1/6} = 6$$

i.e. $$z = 6^6$$

i.e. $$\sqrt{z^6} = z^3 = 6^{18}$$

$$\sqrt{z^6} = 6^{18}$$ is the smallest number

and $$12^{72} = 2^{144}*3^{72}$$ is even bigger than $$2^{96}$$

So median = Middle term in increasing order of these numbers = $$2^{96}$$

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Originally posted by GMATinsight on 13 Apr 2019, 01:51.
Last edited by GMATinsight on 13 Apr 2019, 05:44, edited 1 time in total.
Senior Manager  V
Joined: 25 Sep 2018
Posts: 422
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30 GPA: 3.97
WE: Investment Banking (Investment Banking)
Re: If 12th root of x is equal to 12, 8th root of y equals to 8  [#permalink]

Show Tags

GMATinsight i'm sorry there was an error in typing. it's 12th root of x = 12 and not 2. I have corrected it. answer is B
_________________
Why do we fall?...So we can learn to pick ourselves up again Re: If 12th root of x is equal to 12, 8th root of y equals to 8   [#permalink] 13 Apr 2019, 01:58
Display posts from previous: Sort by

If 12th root of x is equal to 12, 8th root of y equals to 8

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  