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

 It is currently 21 Feb 2019, 16:11

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

# If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c

Author Message
TAGS:

### Hide Tags

Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 504
If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c  [#permalink]

### Show Tags

01 May 2011, 06:42
2
8
00:00

Difficulty:

85% (hard)

Question Stats:

44% (01:29) correct 56% (01:23) wrong based on 332 sessions

### HideShow timer Statistics

If 3^a * 4^b = c, what is the value of b?

(1) 5^a = 25
(2) c = 36

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-3-a-4-b-c ... 06047.html

_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c  [#permalink]

### Show Tags

04 Feb 2012, 14:50
4
6
amit2k9 wrote:
straight B. 36 = 2 ^2 * 3^2

If 3^a*4^b = c, what is the value of b?

Note that we are not told that the variables are integers only.

(1) 5^a = 25 --> $$a=2$$, but we can not get the values of $$b$$. Not sufficient.

(2) c = 36 --> $$3^a*4^b = c$$: it's tempting to write $$3^2*4^1=36$$ and say that $$b=1$$ but again we are not told that the variables are integers only. So, for example it can be that $$3^a=36$$ for some non-integer $$a$$ and $$b=0$$, making $$4^b$$ equal to 1 --> $$3^a*4^b =36*1=36$$. Not sufficient.

(1)+(2) As $$a=2$$ and $$c = 36$$ then $$9*4^b=36$$ --> $$b=1$$. Sufficient.

Hope it's clear.
_________________
##### General Discussion
Director
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 999
Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c  [#permalink]

### Show Tags

02 May 2011, 03:45
straight B. 36 = 2 ^2 * 3^2
Manager
Joined: 10 Jul 2010
Posts: 171
Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c  [#permalink]

### Show Tags

09 Nov 2011, 07:52
I'm going to go with B

36 = $$3^2 and 2^2$$

you are given that $$3^a*4^b=c$$

we can break down 4 to 2^2b
So now we have

$$3^a*2^2b=2^2*3^2$$

so a= 2, b = 2
Intern
Joined: 07 Oct 2011
Posts: 27
Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c  [#permalink]

### Show Tags

09 Nov 2011, 08:41
1
a and b are not integers here.

consider this:

Now for every value of a, there is a different value of b.
Say, a = 1, then 4^b = 12 and b = 1.79 approx
a = 2, then 4^b = 4 and b = 1
a = 3, then 4^b = 36/27 and b = 0.2 approx

Intern
Status: Stay Hungry, Stay Foolish.
Joined: 05 Sep 2011
Posts: 34
Location: India
Concentration: Marketing, Social Entrepreneurship
Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c  [#permalink]

### Show Tags

13 Nov 2011, 08:20
2
The question does not mention a and b to be Integers.
Individually,none of the statements suffice to reach the value of b.

Both the statements when used together,give the value of b.
3^2 * 4^b = 36.
b=1

Hence C.
Intern
Joined: 21 Feb 2013
Posts: 6
Schools: Arizona State"19
Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c  [#permalink]

### Show Tags

19 Jun 2015, 07:15
Hi Bunnel in the above explantion how can 3^a=36 be possible for any value a, it has to have an even no. plz clarify my doubt
Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c  [#permalink]

### Show Tags

19 Jun 2015, 07:21
caster88 wrote:
Hi Bunnel in the above explantion how can 3^a=36 be possible for any value a, it has to have an even no. plz clarify my doubt

We are NOT told that a and b are integers. So, there exists some irrational a for which 3^a = 36: $$a= \frac{2 (log(2)+log(3))}{log(3)}\approx{3.2619}$$
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c  [#permalink]

### Show Tags

29 Dec 2017, 23:09
Baten80 wrote:
If 3^a * 4^b = c, what is the value of b?

(1) 5^a = 25
(2) c = 36

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-3-a-4-b-c ... 06047.html
_________________
Re: If 3^a * 4^b = c, what is the value of b? (1) 5^a = 25 (2) c   [#permalink] 29 Dec 2017, 23:09
Display posts from previous: Sort by