 It is currently 20 Mar 2019, 19:47 ### 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. # 3^2a 11^b  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Moderator  Joined: 18 Apr 2015
Posts: 5835
Followers: 93

Kudos [?]: 1143  , given: 5441

1
KUDOS
Expert's post 00:00

Question Stats: 80% (01:14) correct 19% (01:18) wrong based on 26 sessions

If $$3^{2a}$$$$11^b$$= $$27^{4x}$$ $$33^{2x}$$ then x must equal which of the following ?

Indicate all that apply.

❑ 2a

❑ 2b

❑ 7a - 2b

❑ $$\frac{a}{7}$$

❑ $$\frac{b}{2}$$
[Reveal] Spoiler: OA

_________________ Director Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 344  , given: 66

Re: 3^2a 11^b [#permalink]
1
KUDOS
Here there is a missing OA! Director Joined: 20 Apr 2016
Posts: 824
WE: Engineering (Energy and Utilities)
Followers: 10

Kudos [?]: 601  , given: 121

Re: 3^2a 11^b [#permalink]
2
KUDOS
Carcass wrote:
If $$3^{2a}$$$$11^b$$= $$27^{4x}$$ $$33^{2x}$$ then x must equal which of the following ?

Indicate all that apply.

❑ 2a

❑ 2b

❑ 7a - 2b

❑ $$\frac{a}{7}$$

❑ $$\frac{b}{2}$$

[Reveal] Spoiler: OA

Here given

$$3^{2a}$$$$11^b$$= $$27^{4x}$$ $$33^{2x}$$

$$3^{2a}$$$$11^b$$ = $$3^{12x}$$ $$3^{2x}$$ $$11^{2x}$$ (Since $$27^{4x}$$ = $${3^{(3x)}}^{4}$$ = $$3^{12x}$$)

or $$3^{2a}$$$$11^b$$ = $$3^{14x}$$ $$11^{2x}$$

Since prime bases are same, the exponents must also be equal.
14x = 2a,

or x= $$\frac{2}{14}$$

or a =$$\frac{a}{7}$$

And 2x = b, or x= $$\frac{b}{2}$$

Therefore only choices (D) and (E) must be true
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting https://greprepclub.com/forum/rules-for ... -1083.html

Intern Joined: 14 Jun 2018
Posts: 36
Followers: 0

Kudos [?]: 7 , given: 100

Re: 3^2a 11^b [#permalink]
pranab01 wrote:
Carcass wrote:
If $$3^{2a}$$$$11^b$$= $$27^{4x}$$ $$33^{2x}$$ then x must equal which of the following ?

Indicate all that apply.

❑ 2a

❑ 2b

❑ 7a - 2b

❑ $$\frac{a}{7}$$

❑ $$\frac{b}{2}$$

[Reveal] Spoiler: OA

Here given

$$3^{2a}$$$$11^b$$= $$27^{4x}$$ $$33^{2x}$$

$$3^{2a}$$$$11^b$$ = $$3^{12x}$$ $$3^{2x}$$ $$11^{2x}$$ (Since $$27^{4x}$$ = $${3^{(3x)}}^{4}$$ = $$3^{12x}$$)

or $$3^{2a}$$$$11^b$$ = $$3^{14x}$$ $$11^{2x}$$

Since prime bases are same, the exponents must also be equal.
14x = 2a,

or x= $$\frac{2}{14}$$

or a =$$\frac{a}{7}$$

And 2x = b, or x= $$\frac{b}{2}$$

Therefore only choices (D) and (E) must be true

I know that one base equal to another will have the same exponent, but here we have two different bases. How that could be true to equate them as you did?
Moderator  Joined: 18 Apr 2015
Posts: 5835
Followers: 93

Kudos [?]: 1143 , given: 5441

Re: 3^2a 11^b [#permalink]
Expert's post
Actuallly

$$3^{2a}= 3^{14x}$$

AND

$$11^b = 11^{2x}$$

Hope you spot the gist of the problem.

Regards
_________________ Re: 3^2a 11^b   [#permalink] 08 Jul 2018, 09:51
Display posts from previous: Sort by

# 3^2a 11^b  Question banks Downloads My Bookmarks Reviews Important topics 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®.