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22 Feb 2017, 06:26
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
52% (01:28) correct
48%
(01:37)
wrong
based on 668
sessions
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Not Attempted Yet
For positive integers a, b, and c, where a<b<c, the product abc has exactly three prime factors. What is the maximum number of prime factors of a?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
22 Feb 2017, 06:48
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Answer : D
If product a*b*c has exactly 3 prime factors,
a can have maximum 3 prime factors.
eg.
a= 2^1 * 3^1 * 5^1
b = 2^2 * 3^2 * 5^2
c = 2^3 * 3^3 * 5^3
Now a * b* c = 2^6 * 3^6 * 5^6
If product a*b*c has exactly 3 prime factors,
a can have maximum 3 prime factors.
eg.
a= 2^1 * 3^1 * 5^1
b = 2^2 * 3^2 * 5^2
c = 2^3 * 3^3 * 5^3
Now a * b* c = 2^6 * 3^6 * 5^6
General Discussion
22 Feb 2017, 08:13
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Bunuel
For positive integers a, b, and c, where a<b<c, the product abc has exactly three prime factors. What is the maximum number of prime factors of a?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
for maximum no. of prime factors of a , it should be multiple of three prime nos.(since abc has only three prime factors)
and b &c could have any number of those three prime factors in a.
say if a =5^x * 7^y * 2^z
then b = 5^x * 7^y or any such prime combinations
& c= 5^x or 7^y or any combination as per condition a<b<c
thus a have max. of 3 prime factors
Ans D
