The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of k?
(1) 3^2 is a factor of k.
(2) 7^2 is NOT a factor of k.
OA is D
The range of set A is r. If a number
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Source: Beat The GMAT — Data Sufficiency |
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cramya
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Total number of factors of an integer can be obtained by breaking down the integer in to its prime factors, adding 1 to each of the powers to which the individual prime factors are raised and multiplying them together
Eg: 6 = (3^1) * (2^1)
Total # factors of 6 = (1+1)*(1+1)
= 4
4 factors namely 1,2,3,6
Coming to the problem since k has 6 factors including 1 and k and 3 and 7 are its only prime factors k can either be
(3^2) *(7^1) => (2+1) (1+1) = 6 factors
or
(3^1) * (7^2) => (1+1) (2+1) = 6 factors
Stmt I
3^2 is a factor of k so k is 3^2 * 7^1
SUFF
Stmt II
7^2 is not a factor of k
so k again = 3^2 * 7^1
SUFF
D
Hope this helps!
Regards,
CR
Eg: 6 = (3^1) * (2^1)
Total # factors of 6 = (1+1)*(1+1)
= 4
4 factors namely 1,2,3,6
Coming to the problem since k has 6 factors including 1 and k and 3 and 7 are its only prime factors k can either be
(3^2) *(7^1) => (2+1) (1+1) = 6 factors
or
(3^1) * (7^2) => (1+1) (2+1) = 6 factors
Stmt I
3^2 is a factor of k so k is 3^2 * 7^1
SUFF
Stmt II
7^2 is not a factor of k
so k again = 3^2 * 7^1
SUFF
D
Hope this helps!
Regards,
CR
