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Re: If a, b and c are integers greater than one [#permalink]

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24 Jun 2013, 20:54

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vyada wrote:

I thought the OA is D. Can someone explain it in detail.

If a, b and c are integers greater than one, and 15^8=a·b^c, what is the value of c?

Right away, we should split this into its prime factors: 15^8 = (3^8) * (5^8). (a, b, c) can take on a variety of values. Here are a few examples:

1) a = 3^8, b = 5, c = 8 2) a = 3^2, b = (3^3) * (5^4), c = 2 etc...

(1) a is not divisible by 5.

If a is not divisible by 5, all we know is that a cannot contain any 5s. A can contain anywhere from 1 to 8 '3's. Here are some examples:

1) a = 3^4, b = (3 * 5^2), c = 4 2) a = 3^4, b = (3^2 * 5^4), c = 2 etc...

(2) b is not divisible by 3.

Similar argument to (1): If b is not divisible by 3, all we know is that b cannot contain any 3s. B can contain anywhere from 1 to 8 '5's. Here are some examples:

1) a = 3^8, b = 5^4, c = 2 2) a = (3^8) * (5^2), b = 5, c = 6 etc...

Statements (1) and (2) together:

We know that A has no 5s, and B has no 3s. Thus all 3s must be in A and no 5s can be in A. Thus A must be equal to 3^8. Thus b^c must equal 5^8. However, many possible combinations of b and c could yield 5^8:

1) b = 5, c = 8 2) b = 5^2, c = 4 3) b = 5^4, c = 2 etc...

Re: If a, b and c are integers greater than one [#permalink]

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02 Apr 2017, 10:49

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If a, b and c are integers greater than one [#permalink]

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11 Aug 2017, 22:01

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dave785 wrote:

If the question was rephrased to have (A*B)^C then it would be D as the correct answer?

here as we are given that (a b)^c=15^8 therefore a= 3 or 5 and b=3 or 5 statement 1= a is not div by 5 gives us that a=3 and b= 5 Not Sufficient ) statement 2= b is not div by 3 which gives b=5 again not sufficient now when we combine both of the statements then we see that 3^8 gives c=8 (3^2)^4 gives c= 4 (3^4)^2 gives c=2 and same goes for 5^8 As we are getting multiple answers so our answer has to be E.