Prime Factors

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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

Ans D

[sana.noor]

answer must be D, how? we know that K has 6 factors including 1 and k, 3 and 7 are its two positive prime factors. it means either k has 2 3's or one 7 or 2 7's or one 3
1)statement one says that k has 2 3's----> sufficient. it means k has total 6 factors as 1,3,7,9, 21 and k (21.9) itself
2) statement two says that it has one 7, it means it has 2 3's and one 7

[[email protected]]

Not really- the factors include 63 as well and k = 63

answer must be D, how? we know that K has 6 factors including 1 and k, 3 and 7 are its two positive prime factors. it means either k has 2 3's or one 7 or 2 7's or one 3
1)statement one says that k has 2 3's----> sufficient. it means k has total 6 factors as 1,3,7,9, 21 and k (21.9) itself
2) statement two says that it has one 7, it means it has 2 3's and one 7

[theCodeToGMAT]

k = (3)^a (7)^b

k has total of 6 factors that means (a+1)(b+1) = 6

To find: Value of "k"

Statement 1:
3^2 is a factor o "k"
i.e. a=2
So, (2+1)(b+1) = 6
b = 1
SUFFICIENT

Statement 2:
7^2 is not a factor
B != 2
Assume b=1..So, (a+1)(1+1) = 6 ==> a = 2
Assume b=3..so, (a+1)(3+1) = 6 ==> a will be in decimals..
So, b=1
SUFFICIENT

Answer [spoiler]{D}[/spoiler]

[sana.noor]

oh yeah! i wrote k= (21.9) which is wrong, k must be equal to 63 and the six factors will be 1,3,7,9, 21, 63
thanks by the way