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If a, b and c are integers greater than one, and 615=a·bc, what is the

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If a, b and c are integers greater than one, and 615=a·bc, what is the [#permalink]

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If a, b and c are integers greater than one, and \(6^{15}=a·b^c\), what is the value of c?

(1) a is not divisible by 3.
(2) b is prime.
[Reveal] Spoiler: OA

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Re: If a, b and c are integers greater than one, and 615=a·bc, what is the [#permalink]

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New post 01 Oct 2015, 04:38
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reto wrote:
If a, b and c are integers greater than one, and \(6^{15}=a·b^c\), what is the value of c?

(1) a is not divisible by 3.
(2) b is prime.


Good question. +1

\(6^{15} = a.b^c\) , c=? Make sure to not straightaway assume that c= 15. This is not a must as shown below:

Statement 1, \(a\neq 3p\), p is an integer >1. Thus \(6^{15}\) could be factored as \((2^{15})*(3^{15})\), with c = 15, \(a= 2^{15}\)and b = 3 and also as \((2^3)*(6^4*3)^3\), giving you c=3.

Statement 2, b=prime. Again you can come up with 2 cases similar to statement 1, b=2 or 3 giving you different values of c. Hence not sufficient.

Combining, b=prime and \(a\neq 3p\), you get the only case as \((2^{15})*(3^{15})\) or \((3^{15})*(2^{15})\) , either way giving you c=15.

C is the correct answer.

Similar question to practice: if-a-b-and-c-are-integers-greater-than-one-154698.html

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Re: If a, b and c are integers greater than one, and 615=a·bc, what is the [#permalink]

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New post 07 Apr 2016, 19:05
reto wrote:
If a, b and c are integers greater than one, and \(6^{15}=a·b^c\), what is the value of c?

(1) a is not divisible by 3.
(2) b is prime.


6^15 = 2^15 x 3^15

1. a not divisible by 3
a can be 2^15, and b^c can be 3^15, in which c=15, or b^c can be 9^5 - c=5. A and D are out.

2. b is prime
b can be 2^1 and a=2^14 x 3^15 -> c=1
or b can be 3^15, and c=15
2 outcomes - no.

1+2
a is clearly 2^15, and b must be prime - so b must be 3, and c is 15.

C is sufficient.

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Re: If a, b and c are integers greater than one, and 615=a·bc, what is the [#permalink]

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Re: If a, b and c are integers greater than one, and 615=a·bc, what is the   [#permalink] 18 Oct 2017, 06:18
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