It is currently 19 Sep 2020, 14:01

### 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

# 3^2a 11^b

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 13306
Followers: 286

Kudos [?]: 3369 [3] , given: 12171

3^2a 11^b [#permalink]  07 Aug 2017, 03:27
3
KUDOS
Expert's post
00:00

Question Stats:

82% (01:17) correct 17% (01:30) wrong based on 67 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

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Director
Joined: 03 Sep 2017
Posts: 518
Followers: 2

Kudos [?]: 432 [1] , given: 66

Re: 3^2a 11^b [#permalink]  24 Sep 2017, 07:01
1
KUDOS
Here there is a missing OA!
VP
Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
Followers: 22

Kudos [?]: 1308 [2] , given: 251

Re: 3^2a 11^b [#permalink]  24 Sep 2017, 07:32
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

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

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

Kudos [?]: 8 [0], given: 100

Re: 3^2a 11^b [#permalink]  08 Jul 2018, 08:19
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?
Founder
Joined: 18 Apr 2015
Posts: 13306
Followers: 286

Kudos [?]: 3369 [0], given: 12171

Re: 3^2a 11^b [#permalink]  08 Jul 2018, 09:51
Expert's post
Actuallly

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

AND

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

Hope you spot the gist of the problem.

Regards
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

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

# 3^2a 11^b

 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®.