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If a, b and c are integers greater than one, and 6^15 = a*b^c, what is

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If a, b and c are integers greater than one, and 6^15 = a*b^c, what is  [#permalink]

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New post 19 Nov 2019, 01:23
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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.


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Spoiler: OA

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If a, b and c are integers greater than one, and 6^15 = a*b^c, what is  [#permalink]

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New post Updated on: 19 Nov 2019, 02:23
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Bunuel 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.


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Answer is A

Given, 6^15=a*b^C

6^15=2^15*3^15

1. a can be 2^15 or 3^15, but given that a is not divisible by 3, hence a is 2^15. So C is 15. Sufficient alone.

2. Again, b can be 2 or 3 which is prime numbers. So not sufficient

Pls give kudos, if you find my explanation good enough :please

Originally posted by rajatchopra1994 on 19 Nov 2019, 02:03.
Last edited by rajatchopra1994 on 19 Nov 2019, 02:23, edited 1 time in total.
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Re: If a, b and c are integers greater than one, and 6^15 = a*b^c, what is  [#permalink]

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New post 19 Nov 2019, 02:17
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IMO A

6^15 = (3*2)^15 = 3^15 * 2^15 = a * b^c

1) a is not divisible be 3, which implies that b^c = 3^15 ==> c= 15

2) bis a prime number, but in the equation we can deduce from 3^15 * 2^15 = a * b^c that so is a and hence not enough

Answer A
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Re: If a, b and c are integers greater than one, and 6^15 = a*b^c, what is  [#permalink]

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New post 19 Nov 2019, 03:47
2
Statement 1-

Case 1-

\(6^{15}= 2^{15}*3^{15}\)

where \(a= 2^{15}\), \(b=3\) and \(c=15\)

Case 2-

\(6^{15}= 2^3*2^{12}*3^{15}= 2^3 * (2^4*3^5)^3\)

where \(a=2^3\), \(b=2^4*3^5\) and \(c=3\)

Insufficient

Statement 2-

b is a prime number

Case 1-

\(6^{15}= 2^{15}*3^{15}\)

where \(a= 2^{15}\), \(b=3\) and \(c=15\)

Case 2-

\(6^{15}= 2^3*2^{12}*3^{15}= (2^4*3^5)^3 *2^3 \)

where \(b=2\), \(a=(2^4*3^5)^3\) and \(c=3\)

Insufficient


Combining both equations
a is not divisible by 3, and b is prime

hence, a must be \(2^{15}\) and b =3 and c=15

Sufficient


Bunuel 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.


Are You Up For the Challenge: 700 Level Questions
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If a, b and c are integers greater than one, and 6^15 = a*b^c, what is  [#permalink]

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New post 20 Nov 2019, 09:40
1
Bunuel 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.



\(6^{15}=a*b^c…2^{15}3^{15}=ab^c\)

(1) a is not divisible by 3. insufic

\(2^{15}3^{15}=ab^c…a=2^{something}…b=(2•3)^{something}…b=3^{something}\)
\(a=2^3…b^c=2^{12}3^15=(2^43^5)^3\)
\(a=2^5…b^c=2^{10}3^15=(2^23^3)^5\)
\(a=2^{15}…b^c=3^{15}\)

(2) b is prime. insufic

\(b^c=3^{something}…b^c=2^{something}\)

(1&2) sufic

\(a=2^{15}…b^c=3^{15}…c=15\)

Ans (C)
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If a, b and c are integers greater than one, and 6^15 = a*b^c, what is   [#permalink] 20 Nov 2019, 09:40
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