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

## unequal dilemma :)

##### This topic has expert replies

- waltz2salsa
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- Geva@EconomistGMAT
- GMAT Instructor
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(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

- waltz2salsa
- Junior | Next Rank: 30 Posts
**Posts:**28**Joined:**28 Sep 2010**Thanked**: 3 times**Followed by:**1 members

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' ?????

- Geva@EconomistGMAT
- GMAT Instructor
**Posts:**905**Joined:**12 Sep 2010**Thanked**: 378 times**Followed by:**123 members**GMAT Score:**760

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.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' ?????