• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

unequal dilemma :)

This topic has expert replies
User avatar
Junior | Next Rank: 30 Posts
Posts: 28
Joined: 28 Sep 2010
Thanked: 3 times
Followed by:1 members

unequal dilemma :)

by waltz2salsa » Wed Nov 03, 2010 12:22 am
If 3^a * 4^b = c, what is the value of b?

(1) 5^a = 25

(2) c = 36

i dont have the OA ... but as quoted by an expert here https://www.beatthegmat.com/exponent-values-t69282.htmlit should be [spoiler] 'c[/spoiler]'

According to me it should be [spoiler]'e' [/spoiler] . Can someone please tell me where am i going wrong.

stmt 1 is clearly insufficient ( it just gives a=2)

stmt 2 :

3^a * 4^b = 36 = 3^2 * 4^1

or (3^a * 4^b)/ (3^2 * 4^1) = integer

i.e. 3^(a-2) * 4^(b-1) = int

or a>=2 and b > = 1

clearly insufficient

stmt 1 & stmt 2 for choice 'c': a = 2 , b>=1

'again insufficient as we can have infinite values for 'b' (greater than equal to 1)

Can some one please clarify :(

Regards,
Shashwat

User avatar
GMAT Instructor
Posts: 905
Joined: 12 Sep 2010
Thanked: 378 times
Followed by:123 members
GMAT Score:760

by Geva@EconomistGMAT » Wed Nov 03, 2010 2:07 am
waltz2salsa wrote:If 3^a * 4^b = c, what is the value of b?

(1) 5^a = 25

(2) c = 36

i dont have the OA ... but as quoted by an expert here https://www.beatthegmat.com/exponent-values-t69282.htmlit should be [spoiler] 'c[/spoiler]'

According to me it should be [spoiler]'e' [/spoiler] . Can someone please tell me where am i going wrong.

stmt 1 is clearly insufficient ( it just gives a=2)

stmt 2 :

3^a * 4^b = 36 = 3^2 * 4^1

or (3^a * 4^b)/ (3^2 * 4^1) = integer
In this step you're dividing both sides of the equation by 3^2 * 4^1. but if you're dividing the right side by itself, the answer is not "integer" but simply "1".

i.e. 3^(a-2) * 4^(b-1) = int

or a>=2 and b > = 1

clearly insufficient

stmt 1 & stmt 2 for choice 'c': a = 2 , b>=1

'again insufficient as we can have infinite values for 'b' (greater than equal to 1)

Can some one please clarify :(

Regards,
Shashwat
Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com

User avatar
Junior | Next Rank: 30 Posts
Posts: 28
Joined: 28 Sep 2010
Thanked: 3 times
Followed by:1 members

by waltz2salsa » Wed Nov 03, 2010 2:37 am
Thanks Geva, but does that mean :

if (3^a * 4^b)/ (3^2 * 4^1) = 1

3^(a-2) * 4^(b-1) = 1

that means a=2 and b= 1

ans 'b' ?????

User avatar
GMAT Instructor
Posts: 905
Joined: 12 Sep 2010
Thanked: 378 times
Followed by:123 members
GMAT Score:760

by Geva@EconomistGMAT » Wed Nov 03, 2010 3:02 am
waltz2salsa wrote:Thanks Geva, but does that mean :

if (3^a * 4^b)/ (3^2 * 4^1) = 1

3^(a-2) * 4^(b-1) = 1

that means a=2 and b= 1

ans 'b' ?????
I actually sort of agree. Rahul's explanation for why stat. (2) is insufficient is that you do not know that a and b are integers, which opens the way for a and b to equal logrithms. Since I've never seen a GMAT question resort to Lns (too advanced), I believe the original question should state that a and b are integers, in which case B would be the right answer.
Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com