GMATPrep - Prime Factors

IMHO the answer is D, and I think as follows.

If we know that a number has only 2 prime factors that means that it has no other prime factors besides 1 and the same number, since any other possible factor can be converted to the primes and this may contradict the problem statement. That is, the positive factors of the number we are looking for are 1, prime factors given, and all possible products of the prime factors given, including their product that equals to the same number.

Therefore, if we are limited by 2 exact prime factors and by 6 total factors, we can say that the all factors of our numbers are 1, x, y, x*x, x*y, x*x*y, where the x and y are the prime factors given. You may notice and check that one of the 2 prime factors we have must be in the second power, since in the other way we cannot have exactly 6 factors.

Therefore we if we have these limits, to find our number we just need to know which of prime factors given is in the second power. Both of the statements given can help us with the solution, besides the statements do not contradict one another, and therefore both are sufficient.

Correct me, if I’m wrong, please.

I go with D

we have 3 and 7 as factors so k = (3^x)*(7^y)
k has 6 factors, it means that (x+1)(y+1)=6
if x=1, y=2
if x=2, y=1


(1)
3^2 is a factor of k. means that x=2 so y=1
to get 3^2 as a factor k can be
k = (3^x)*(7^y) = (3^2)*(7^1)
SUFF


(2)
7^2 is not a factor means that k has only one 7, making y=1, so x=2
so k = (3^2)*(7^1)
SUFF

Answer D


What is OA?

OA is D. Thanks for your explanation!

4meonly,

"k has 6 factors, it means that (x+1)(y+1)=6"

I did not get this statement...why cant 3*7*7 be the factor of k ?? [/list]

This is a very interesting trick
please refer
www.beatthegmat.com/factors-t12966.html
www.beatthegmat.com/prime-number-and-di ... 15095.html


If you want to work out how many positive divisors a number has:
-prime factorize
-look only at the powers
-add one to each power
-multiply what you get (don't add!)

we have 3 and 7 as prime factors so k = (3^x)*(7^y)
from the rule above we can conclude that if k has 6 factors, it means that (x+1)(y+1)=6
It means that k can have following factors:
1, 3, 3^2, 7, 3*7, 3^2*7 - if k=3^2*7
or 1, 3, 7, 7^2, 3*7, 7^2*3 - if k=7^2*3

hope now it is clear, tell me if not

Thanks buddy its clear now.