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

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Bunuel
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If a, b and c are integers greater than one, and 15^8=a·b^c, what is [#permalink] New post   06 Jan 2020, 06:59
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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.


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E
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chetan2u
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If a, b and c are integers greater than one, and 15^8=a·b^c, what is [#permalink] New post   06 Jan 2020, 09:10
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Bunuel wrote:
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.


Are You Up For the Challenge: 700 Level Questions


(1) a is not divisible by 5.
\(15^8 = a*b^c=3^2(3^35^4)^2=5^83^8\), so c can be 8 or 2
Insuff

(2) b is not divisible by 3.
\(15^8 = a*b^c=(5^33^4)^25^2=3^85^8\), so c can be 8 or 2
Insuff

Combined
a contains all 3s and b contains all 5s, so possible answers.
\(15^8=3^85^8\), but \(5^8=25^4=625^2\).
Thus c can be 2, 4 or 8.
Insufficient

E
Edited... kudos VeritasKarishma
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shiva1325
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If a, b and c are integers greater than one, and 15^8=a·b^c, what is [#permalink] New post   Updated on: 14 Jan 2020, 21:41
Consider only statement 1:
a is not divisible by 5.
15^8=a∗b^c=(3^2)*(3^3*5^4)2 or 3^8*5^8
here c can be either 2 or 8
no unique answer

Consider only statement 2:
b is not divisible by 3.
15^8=a∗b^c =3^8*5^8 or (3^8*5)*5^7 or (3^8*5^2)*5^6 ....
here c can be 8 or 7 or 6 or ....
hence no unique answer

Consider both statements 1&2:
we get answers for a=3^8 ,b=5 ,c=8
or b=25 then c=4
hence more than one answer

hence choice E is answer.

Originally posted by shiva1325 on 06 Jan 2020, 21:59.
Last edited by shiva1325 on 14 Jan 2020, 21:41, edited 1 time in total.
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Re: If a, b and c are integers greater than one, and 15^8=a·b^c, what is [#permalink] New post   14 Jan 2020, 21:18
VeritasKarishma Can you help with this qu.?

I got C.

But the OA is E. my method:

statement 1 says a is not div by 5.

so, possibilities can be: 3^8 * 5^8 c=8
(3^4) * (3^2 * 5^4)^2 c=2

same for statement 2.

If we combine, it leaves us only with 1 possibility, 3^8 * 5^8 (a, b, c are integers greater than 1). so, c=8
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Re: If a, b and c are integers greater than one, and 15^8=a·b^c, what is [#permalink] New post   14 Jan 2020, 21:19
chetan2u wrote:
Bunuel wrote:
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.


Are You Up For the Challenge: 700 Level Questions


(1) a is not divisible by 5.
\(15^8 = a*b^c=3^2(3^35^4)^2=5^83^8\), so c can be 8 or 2
Insuff

(2) b is not divisible by 3.
\(15^8 = a*b^c=(5^33^4)^25^2=3^85^8\), so c can be 8 or 2
Insuff

Combined
a contains all 3s and b contains all 5s, so ONLY possibility is \(3^85^8\)
c= 8

C



I solved in the same manner. But the OA is E
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Re: If a, b and c are integers greater than one, and 15^8=a·b^c, what is [#permalink] New post   15 Jan 2020, 00:36
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Bunuel wrote:
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.


Are You Up For the Challenge: 700 Level Questions


\(15^8 = a*b^c\)

\(3^8 * 5^8 = a * b^c\)

Stmnt 1: Since a is not divisible by 5, all 5s belong to b. Some 3s may belong to b too such as

\(a = 3^4\)
\(b^c = (3*5*5)^4\)
or
\(a = 3^8\)
\(b^c = 5^8\)
or
\(a = 3^8\)
\(b^c = (25)^4\)
c can take various values.

Stmnt 2: Since b is not divisible by 3, all 3s belong to a. Some 5s may belong to a.

Note that the last two cases work here too.
\(a = 3^8\)
\(b^c = 5^8\)
or
\(a = 3^8\)
\(b^c = (25)^4\)
c can take various values.

Using both statements, we get
\(a = 3^8\)
\(b^c = 5^8 or 25^4 or 625^2\)
c can take various values.

Answer (E)
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Re: If a, b and c are integers greater than one, and 15^8=a·b^c, what is [#permalink] New post   25 Jan 2023, 13:45
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Re: If a, b and c are integers greater than one, and 15^8=a·b^c, what is [#permalink]
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