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

3^2a 11^b

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 5835
Followers: 93

Kudos [?]: 1143 [1] , given: 5441

3^2a 11^b [#permalink]  07 Aug 2017, 03:27
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 [1] , given: 66

Re: 3^2a 11^b [#permalink]  24 Sep 2017, 07:01
1
KUDOS
Here there is a missing OA!
Director
Joined: 20 Apr 2016
Posts: 824
WE: Engineering (Energy and Utilities)
Followers: 10

Kudos [?]: 601 [2] , given: 121

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

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

Kudos [?]: 7 [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?
Moderator
Joined: 18 Apr 2015
Posts: 5835
Followers: 93

Kudos [?]: 1143 [0], given: 5441

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