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

It is currently 19 Aug 2018, 12:17

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

What is the decreasing order from left to right of the following numbe

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

Hide Tags

Director
Director
User avatar
G
Status: Learning stage
Joined: 01 Oct 2017
Posts: 526
WE: Supply Chain Management (Energy and Utilities)
Premium Member CAT Tests
What is the decreasing order from left to right of the following numbe  [#permalink]

Show Tags

New post 14 Jul 2018, 06:36
2
1
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

47% (02:40) correct 53% (02:19) wrong based on 19 sessions

HideShow timer Statistics

What is the decreasing order from left to right of the following numbers?

\(\sqrt[4]{3}, \sqrt[5]{6},\sqrt[10]{12},\sqrt[15]{45}\)

(A) \(\sqrt[4]{3}, \sqrt[5]{6}, \sqrt[10]{12}, \sqrt[15]{45}\)
(B) \(\sqrt[5]{6}, \sqrt[10]{12}, \sqrt[15]{45}, \sqrt[4]{3}\)
(C) \(\sqrt[5]{6}, \sqrt[15]{45}, \sqrt[4]{3}, \sqrt[10]{12}\)
(D) \(\sqrt[5]{6}, \sqrt[4]{3}, \sqrt[15]{45}, \sqrt[10]{12}\)
(E) \(\sqrt[4]{3}, \sqrt[15]{45}, \sqrt[5]{6} , \sqrt[10]{12}\)
Manager
Manager
avatar
B
Joined: 09 Jun 2014
Posts: 56
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
GMAT 1: 720 Q50 V38
CAT Tests
Re: What is the decreasing order from left to right of the following numbe  [#permalink]

Show Tags

New post 14 Jul 2018, 09:50
Good question. No idea how to approach.Any help would be great !!

Posted from my mobile device
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6554
What is the decreasing order from left to right of the following numbe  [#permalink]

Show Tags

New post 14 Jul 2018, 09:59
2
PKN wrote:
What is the decreasing order from left to right of the following numbers?

\(\sqrt[4]{3}, \sqrt[5]{6},\sqrt[10]{12},\sqrt[15]{45}\)

(A) \(\sqrt[4]{3}, \sqrt[5]{6}, \sqrt[10]{12}, \sqrt[15]{45}\)
(B) \(\sqrt[5]{6}, \sqrt[10]{12}, \sqrt[15]{45}, \sqrt[4]{3}\)
(C) \(\sqrt[5]{6}, \sqrt[15]{45}, \sqrt[4]{3}, \sqrt[10]{12}\)
(D) \(\sqrt[5]{6}, \sqrt[4]{3}, \sqrt[15]{45}, \sqrt[10]{12}\)
(E) \(\sqrt[4]{3}, \sqrt[15]{45}, \sqrt[5]{6} , \sqrt[10]{12}\)



since the roots are 5, 10 and 15 we can easily compare these

1) let's compare \(\sqrt[5]{6}-and-\sqrt[15]{45}\)

\(\sqrt[5]{6}=\sqrt[15]{6^3}=\sqrt[15]{216}......................\sqrt[15]{45}\)............\(216>45\) so \(\sqrt[5]{6}>\sqrt[15]{45}\)..

2) lets compare \(\sqrt[10]{12}-and-\sqrt[15]{45}\)

\(\sqrt[10]{12}=\sqrt[30]{12^3}=\sqrt[30]{3^3*4^3}................\sqrt[15]{45}=\sqrt[30]{45^2}=\sqrt[30]{3^4*5^2}\) \(3^45^2>3^34^3\) hence
\(\sqrt[10]{12}<\sqrt[15]{45}\)

3) finally lets compare \(\sqrt[4]{3}-and-\sqrt[15]{45}\)

\(\sqrt[4]{3}=\sqrt[60]{3^{15}}.................. \sqrt[15]{45}=\sqrt[60]{45^4}=\sqrt[60]{3^8*5^4},\)...
\(3^{15}=3^83^7,3^85^4\).....3^7>5^4
hence \(\sqrt[4]{3}> \sqrt[15]{45},\)

\(\sqrt[5]{6}> \sqrt[4]{3}> \sqrt[15]{45}> \sqrt[10]{12}\)

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Manager
Manager
avatar
B
Joined: 09 Jun 2014
Posts: 56
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
GMAT 1: 720 Q50 V38
CAT Tests
Re: What is the decreasing order from left to right of the following numbe  [#permalink]

Show Tags

New post 14 Jul 2018, 10:17
chetan2u wrote:
PKN wrote:
What is the decreasing order from left to right of the following numbers?

\(\sqrt[4]{3}, \sqrt[5]{6},\sqrt[10]{12},\sqrt[15]{45}\)

(A) \(\sqrt[4]{3}, \sqrt[5]{6}, \sqrt[10]{12}, \sqrt[15]{45}\)
(B) \(\sqrt[5]{6}, \sqrt[10]{12}, \sqrt[15]{45}, \sqrt[4]{3}\)
(C) \(\sqrt[5]{6}, \sqrt[15]{45}, \sqrt[4]{3}, \sqrt[10]{12}\)
(D) \(\sqrt[5]{6}, \sqrt[4]{3}, \sqrt[15]{45}, \sqrt[10]{12}\)
(E) \(\sqrt[4]{3}, \sqrt[15]{45}, \sqrt[5]{6} , \sqrt[10]{12}\)



since the roots are 5, 10 and 15 we can easily compare these

1) let's compare \(\sqrt[5]{6}-and-\sqrt[15]{45}\)

\(\sqrt[5]{6}=\sqrt[15]{6^3}=\sqrt[15]{216}......................\sqrt[15]{45}\)............\(216>45\) so \(\sqrt[5]{6}>\sqrt[15]{45}\)..

2) lets compare \(\sqrt[10]{12}-and-\sqrt[15]{45}\)

\(\sqrt[10]{12}=\sqrt[30]{12^3}=\sqrt[30]{3^3*4^3}................\sqrt[15]{45}=\sqrt[30]{45^2}=\sqrt[30]{3^4*5^2}\) \(3^45^2>3^34^3\) hence
\(\sqrt[10]{12}<\sqrt[15]{45}\)

3) finally lets compare \(\sqrt[4]{3}-and-\sqrt[15]{45}\)

\(\sqrt[4]{3}=\sqrt[60]{3^{15}}.................. \sqrt[15]{45}=\sqrt[60]{45^4}=\sqrt[60]{3^8*5^4},\)...
\(3^{15}=3^83^7,3^85^4\).....3^7>5^4
hence \(\sqrt[4]{3}> \sqrt[15]{45},\)

\(\sqrt[5]{6}> \sqrt[4]{3}> \sqrt[15]{45}> \sqrt[10]{12}\)

D


Thank you so much Chetan sir!!This is great ..

Posted from my mobile device
Re: What is the decreasing order from left to right of the following numbe &nbs [#permalink] 14 Jul 2018, 10:17
Display posts from previous: Sort by

What is the decreasing order from left to right of the following numbe

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.