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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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01 Oct 2015, 04:11
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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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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.

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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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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18 Oct 2017, 06:18
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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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