It is currently 11 Dec 2018, 05:08
My Tests

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.

QOTD #1 81^3 + 27^4 is equivalent to which

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Moderator
Moderator
User avatar
Joined: 18 Apr 2015
Posts: 5130
Followers: 77

Kudos [?]: 1029 [0], given: 4636

CAT Tests
QOTD #1 81^3 + 27^4 is equivalent to which [#permalink] New post 27 Jun 2016, 08:42
Expert's post
00:00

Question Stats:

42% (01:30) correct 57% (01:14) wrong based on 19 sessions
\(81^3\) + \(27^4\) is equivalent to which of the following expressions?

Indicate all such expressions.

I) (\(3^7\))(\(2\))

II) (\(3^{12}\))(\(2\))

III) (\(9^6\))(\(2\))

IV) \(9^{12}\)

V) \(3^{24}\)

[Reveal] Spoiler: OA
II and III
[Reveal] Spoiler: OA

_________________

Get the 2 FREE GREPrepclub Tests

1 KUDOS received
Manager
Manager
Joined: 23 Jan 2016
Posts: 137
Followers: 3

Kudos [?]: 109 [1] , given: 15

Re: QOTD #1 81^3 + 27^4 is equivalent to which [#permalink] New post 04 Jul 2016, 21:20
1
This post received
KUDOS
The original expression can be written as 3^24; Choice ii 3^12(2) = 3^24 and Choice iii 9^6(2) = 3^12(2) = 3^24 are equivalent to original expression,hence answers
1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1232
Followers: 45

Kudos [?]: 1113 [1] , given: 7

Re: QOTD #1 81^3 + 27^4 is equivalent to which [#permalink] New post 05 Apr 2017, 12:07
1
This post received
KUDOS
Expert's post
Carcass wrote:
\(81^3\) + \(27^4\) is equivalent to which of the following expressions?

Indicate all such expressions.

I) (\(3^7\))(\(2\))

II) (\(3^{12}\))(\(2\))

III) (\(9^6\))(\(2\))

IV) \(9^{12}\)

V) \(3^{24}\)

[Reveal] Spoiler: OA
II and III


Scanning the answer choices, I can see that I should try to rewrite the original expression with base 3 and base 9.

BASE 3

\(81^3\) + \(27^4\) = \((3^4)^3\) + \((3^3)^4\)

= \(3^{12}\) + \(3^{12}\)

= (\(2\))(\(3^{12}\))

= II


BASE 9
Take the result from above:

\(81^3\) + \(27^4\) = (\(2\))(\(3^{12}\))

Notice that \(3^{12}\) can be rewritten as \((3^2)^6\), and also notice that \(3^2 = 9\)

So, we get: (\(2\))(\(3^{12}\)) = \((2)\)\((3^2)^6\)

= (\(2\))(\(9^6\))

= III

Answer:
[Reveal] Spoiler:
II and III


RELATED VIDEOS



_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

Re: QOTD #1 81^3 + 27^4 is equivalent to which   [#permalink] 05 Apr 2017, 12:07
Display posts from previous: Sort by

QOTD #1 81^3 + 27^4 is equivalent to which

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.