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

It is currently 18 Oct 2019, 20:13

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.

Close

Request Expert Reply

Confirm Cancel

If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 26 Nov 2009
Posts: 621
Location: Singapore
Concentration: General Management, Finance
Schools: Chicago Booth - Class of 2015
GMAT ToolKit User
If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 10 Dec 2010, 01:00
5
23
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

53% (01:11) correct 47% (01:15) wrong based on 408 sessions

HideShow timer Statistics

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


(1) \(5^a = 25\)

(2) \(c = 36\)
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 10 Dec 2010, 01:33
7
6
nusmavrik wrote:
Q1 If 3^a*4^b = c, what is the value of b?

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


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.

Answer: C.

Hope it's clear.
_________________
General Discussion
SVP
SVP
User avatar
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1824
Concentration: General Management, Nonprofit
GMAT ToolKit User
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 10 Dec 2010, 02:00
Excellent clarification bunuel!

Image Posted from GMAT ToolKit
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 26 Nov 2009
Posts: 621
Location: Singapore
Concentration: General Management, Finance
Schools: Chicago Booth - Class of 2015
GMAT ToolKit User
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 10 Dec 2010, 02:34
Bunuel:
Pls correct my reasoning.

for Q1) my reasoning was since 3^a*4^b = c and base 3 is "even" and base 4 is "odd" then there wont be any other answer except a=2 and b=1. But I was wondering what are the other values of a and b can be for this equation to be true. Sorry, I am asking too much ;-)

Thanks for the awesome explanation. You rock Bunuel!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 10 Dec 2010, 02:53
3
nusmavrik wrote:
Bunuel
Pls correct my reasoning.

for Q1) my reasoning was since 3^a*4^b = c and base 3 is "even" and base 4 is "odd" then there wont be any other answer except a=2 and b=1. But I was wondering what are the other values of a and b can be for this equation to be true. Sorry, I am asking too much ;-)


For 1: equation \(3^a*4^b = 36\) (if there is no restrictions on a and b) has infinitely many solutions for a and b: a=0 --> 4^b=36 --> b=log_4(36); a=1 --> 4^b=12 --> b=log_4(12), ...

Hope it's clear.
_________________
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 26 Nov 2009
Posts: 621
Location: Singapore
Concentration: General Management, Finance
Schools: Chicago Booth - Class of 2015
GMAT ToolKit User
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 10 Dec 2010, 03:18
Thanks Bunuel. Makes sense, the power of logarithms! I was wondering whether the first question was 700+. This is a new perspective. I havent really used logs in any of questions. Awesome !
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 26 Nov 2009
Posts: 621
Location: Singapore
Concentration: General Management, Finance
Schools: Chicago Booth - Class of 2015
GMAT ToolKit User
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 10 Dec 2010, 05:12
Very enlightening ! Thanks
Senior Manager
Senior Manager
User avatar
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 340
Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross) - Class of 2014
GMAT 1: 730 Q49 V39
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 10 Dec 2010, 07:06
Thanks for the explanation!
_________________
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 12 Apr 2011, 19:00
kamalkicks wrote:
If \(3^a4^b = c\), what is the value of b?

(1) \(5^a = 25\)

(2) c = 36

IS OA CORRECT!!

i will go by B, what do you say


If you are wondering why stmnt 2 alone is not sufficient, think of it this way:

\(3^a4^b = c\)
(2) c = 36

So
\(3^a4^b = 36\)
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
and so on...

If we were given that a and b are integers, then answer would have been (B)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
User avatar
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 175
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 13 Apr 2011, 11:19
VeritasPrepKarishma wrote:
kamalkicks wrote:
If \(3^a4^b = c\), what is the value of b?

(1) \(5^a = 25\)

(2) c = 36

IS OA CORRECT!!

i will go by B, what do you say


If you are wondering why stmnt 2 alone is not sufficient, think of it this way:

\(3^a4^b = c\)
(2) c = 36

So
\(3^a4^b = 36\)
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
and so on...

If we were given that a and b are integers, then answer would have been (B)


Dear Karishma Agreed with your approach i also think that way

but wanted to ask you one thing that does GMAT wants us to seriously think the nos to be real nos until specifically stated to be integers :?:
or this kind of confusion is rare in real GMAT :?:
or these kind of questions are actually TRAP questions :?:
_________________
WarLocK
_____________________________________________________________________________
The War is oNNNNNNNNNNNNN for 720+
see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html
do not hesitate me giving kudos if you like my post. :)
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 13 Apr 2011, 18:37
1
Warlock007 wrote:

Dear Karishma Agreed with your approach i also think that way

but wanted to ask you one thing that does GMAT wants us to seriously think the nos to be real nos until specifically stated to be integers :?:
or this kind of confusion is rare in real GMAT :?:
or these kind of questions are actually TRAP questions :?:


Sorry to say but yes, GMAT wants you to consider whether the number can be non-integer and if so, how your answer could vary. Also, GMAT is not above laying such and many other traps for you e.g. the easy C. This is one of the reasons why DS questions are considered much harder than PS questions. You have to analyze the problem from every aspect and consider every possibility. That is why it takes more time to do DS questions even though the concepts behind PS and DS questions are exactly the same. While practicing these questions, there will be many times when you will feel like pulling your hair out because you overlooked one tiny thing e.g. 'what if x is 0' or something like that and all effort was wasted because you got the answer wrong. Hence, try and be aware of these traps and practice as much as you can.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
avatar
Joined: 03 Jun 2010
Posts: 120
Location: Dubai, UAE
Schools: IE Business School, Manchester Business School, HEC Paris, Rotterdam School of Management, Babson College
GMAT ToolKit User
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 14 Apr 2011, 00:11
Karishma, Please tell me where exactly im going wrong

Statement 1)
a=2
Insufficient

Statement 2)
insufficient

Both taken together
b=1
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 14 Apr 2011, 14:03
scbguy wrote:
Karishma, Please tell me where exactly im going wrong

Statement 1)
a=2
Insufficient

Statement 2)
insufficient

Both taken together
b=1


You are not wrong. The answer is (C).
You need both statements to get the value of b.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Senior Manager
Senior Manager
User avatar
S
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 422
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 29 May 2011, 20:36
VeritasPrepKarishma wrote:
kamalkicks wrote:
If \(3^a4^b = c\), what is the value of b?

(1) \(5^a = 25\)

(2) c = 36

IS OA CORRECT!!

i will go by B, what do you say


If you are wondering why stmnt 2 alone is not sufficient, think of it this way:

\(3^a4^b = c\)
(2) c = 36

So

\(3^a4^b = 36\)
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
and so on...

If we were given that a and b are integers, then answer would have been (B)


If I solved the problem as:
3^a * 4^b = 36
3^a*2^2b = 3^2*2^2 [a = 2, b = 2]
What is the problem?

What is the difference between 3^a * 4^b = 36 and 5^21 x 4^11 =2x10^n
_________________
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36  [#permalink]

Show Tags

New post 30 May 2011, 03:50
Baten80 wrote:
VeritasPrepKarishma wrote:
kamalkicks wrote:
If \(3^a4^b = c\), what is the value of b?

(1) \(5^a = 25\)

(2) c = 36

IS OA CORRECT!!

i will go by B, what do you say


If you are wondering why stmnt 2 alone is not sufficient, think of it this way:

\(3^a4^b = c\)
(2) c = 36

So

\(3^a4^b = 36\)
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
and so on...

If we were given that a and b are integers, then answer would have been (B)


If I solved the problem as:
3^a * 4^b = 36
3^a*2^2b = 3^2*2^2 [a = 2, b = 2]
What is the problem?

What is the difference between 3^a * 4^b = 36 and 5^21 x 4^11 =2x10^n


There is nothing wrong with the solution (a = 2, b = 1) except that it doesn't say that a and b are integers (as mentioned above) hence it is just one of the infinite solutions. a and b can be any real numbers and for every value of a, b will have a corresponding real value.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13263
Re: If (3^a)*(4^b)=c , then what is the value of b? 1. 5^a=25 2.  [#permalink]

Show Tags

New post 01 Oct 2019, 07:11
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: If (3^a)*(4^b)=c , then what is the value of b? 1. 5^a=25 2.   [#permalink] 01 Oct 2019, 07:11
Display posts from previous: Sort by

If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = 36

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne