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19 Nov 2019, 01:23
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
39% (01:47) correct
61%
(01:46)
wrong
based on 135
sessions
History
Date
Time
Result
Not Attempted Yet
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
(1) a is not divisible by 3.
(2) b is prime.
Are You Up For the Challenge: 700 Level Questions
19 Nov 2019, 03:47
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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
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
General Discussion
Updated on: 19 Nov 2019, 02:23
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.
Last edited by rajatchopra1994 on 19 Nov 2019, 02:23, edited 1 time in total.
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Bunuel
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
