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06 Jan 2020, 06:59
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E
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Difficulty:
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Question Stats:
44% (01:48) correct
56%
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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.
Are You Up For the Challenge: 700 Level Questions
(1) a is not divisible by 5.
(2) b is not divisible by 3.
Are You Up For the Challenge: 700 Level Questions
06 Jan 2020, 09:10
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Bunuel
(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
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.
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.
