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 :)
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- waltz2salsa
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- Geva@EconomistGMAT
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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
- waltz2salsa
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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' ?????
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
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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' ?????