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

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

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21 Jun 2013, 13:08
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If a, b and c are integers greater than one, and 15^8=a·b^c, what is the value of c?

(1) a is not divisible by 5.

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

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

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21 Jun 2013, 14:01
If the question was rephrased to have (A*B)^C then it would be D as the correct answer?

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

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21 Jun 2013, 16:07
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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?

I suppose it would, by default, since neither statement would be required to solve for A, B, C.
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Re: If a, b and c are integers greater than one [#permalink]

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24 Jun 2013, 21:40
I thought the OA is D. Can someone explain it in detail.

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

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24 Jun 2013, 21:54
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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...

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

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11 May 2014, 15:48
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mattce wrote:
Another nice one..

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

(1) a is not divisible by 5.

(2) b is not divisible by 3.

I think the key to this problem is that we are not told that a,b,c must be prime factors

So 15^8 = 3^8*5^8

Now then, let's see

Statement 1

a is not divisible by 5

Now a=3^8 and b=5^8 in which case c=8
But also a=3^8 and b=25^4, c=4

Insufficient

Statement 2

Same here

b=5^8
a=3^8

Therefore c=8

Or b=25^4, c=4

Both together we have the same cases

b=5^8
a=3^8

Therefore c=8

Or b=25^4, c=4

Cheers!
J

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

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30 Nov 2014, 08:28

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

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02 Apr 2017, 11:49
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If a, b and c are integers greater than one [#permalink]

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11 Aug 2017, 23:01
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.

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If a, b and c are integers greater than one   [#permalink] 11 Aug 2017, 23:01
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