aspiregmat wrote:I tried searching in the forum with little success. If its already discussed can you plz point me to that thread.



Does the integer k have at least three different positive prime factors ?

(1) k/15 is an integer
(2) k/10 is an integer

OA : C

I understand why the answer is so. But it ignores the case k=0. 0 is an integer and 0/15 and 0/10 is also an integer. So IMO the answer should be E.

Any thoughts.

tnaim wrote:Hi,
Is 1 not considered a factor?
in this case if we have k/15=I => k=15*I => k=1*3*5*I
thanks for your help!

Testluv wrote:

tnaim wrote:Hi,
Is 1 not considered a factor?
in this case if we have k/15=I => k=15*I => k=1*3*5*I
thanks for your help!

1 is a factor but it is not a prime factor. The smallest prime factor is 2 (2 is also the only even prime factor).

Testluv wrote:Not only is 0 not a prime factor, in fact it is not a factor of any number at all because you can't divide by 0. 0 is, however, a multiple of all numbers.

Does the integer k have at least three different positive prime factors ?

(1) k/15 is an integer

Yes, k can be 0, in which case k does have at least three different positive prime factors. But it doesn't have to be. In order for k/15 to be an integer k has to have at least 3 and 5 as prime factors. Otherwise it wouldn't be divisible by 15.

(2) k/10 is an integer

By similar reasoning, k has to have at least 2 and 5 as prime factos. Otherwise, it wouldn't be divisible by 10.

Together, you know that k has at least 2, 3 and 5 as prime factors.

Choose C.

Testluv wrote:

tnaim wrote:Hi,
Is 1 not considered a factor?
in this case if we have k/15=I => k=15*I => k=1*3*5*I
thanks for your help!

1 is a factor but it is not a prime factor. The smallest prime factor is 2 (2 is also the only even prime factor).

aspiregmat wrote:Its not given that K is positive integer. It just asks that if K has 3 distinct positive prime factors. We cannot assume K to be positive.

life is a test wrote:aspiregmat - the requirements are that k must be positive (hence k=0 and k = negative number is out). Moreover there has to be three distinct prime factors

(1) k/15 is an integer--> k = 15x --> 3*5*x--> insuff
(2) k/10 is an integer--> k = 10x--> 2*5*x-->insuff

llynx wrote:

aspiregmat wrote:Its not given that K is positive integer. It just asks that if K has 3 distinct positive prime factors. We cannot assume K to be positive.

life is a test wrote:aspiregmat - the requirements are that k must be positive (hence k=0 and k = negative number is out). Moreover there has to be three distinct prime factors

(1) k/15 is an integer--> k = 15x --> 3*5*x--> insuff
(2) k/10 is an integer--> k = 10x--> 2*5*x-->insuff

I don't understand how you come to the assumption that k must be positive. This assumption is not stated anywhere in the question.

If you are given that k/15 and k/10 are integers, they are allowed to be negative integers and thus neither (1) nor (2) are sufficient without knowing that k is positive.