clock60 wrote:hi guys
my question is rather silly, but i still confused, and want somebody clarify my doubts
Does integer k have at least three different positive prime factors?
(1) k/15 is an integer
(2) k/10 is an integer
oa C

with some efforts i can solve this problem, finding LCM(10,15) and regarding that k=30m, where m is +ve integer
my question is
what if k=0, then 0/15, as well as 0/10=0 (we are not given any restrictions on k, for example k>0) , and the answer will be E
what i am missing here?

Do it this way:

(1)

Since k/15 --> k has all the prime factors of 15. Therefore, the prime factors of K are 5,3....and more.... More because we do not know ALL the prime factors of K because we don't know what K is. We can only say that it has the prime factors of 15 because it is divisible by 15.

So 5,3.....more

Therefore this one is insufficient because we have 2 factors of K but we don't know whether there are more or not.

(2) k/10 --> so the prime factors of K are 5,2. Again these are only 2 and there might be more.

So this one is also insufficient.

Together:

We have 5,5,3,2, ...... more. Even though we might have more, we certainly have 3 distinct factors.

Therefore the answer is (C).

hi gurpinder
thank you for you reply, i will follow your way,
but what if K=0? many factors does 0 have?

clock60 wrote:hi gurpinder
thank you for you reply, i will follow your way,
but what if K=0? many factors does 0 have?

Well..... if k = 0 then the denominator can be anything, you will always get a zero. So there is an infinite number of factors. Every real number can be part of a factor pair with 0. So there are infinite factors and infinite factor pairs. So I dont think GMAT would test such thing.


Hmmm....you got me thinking.

well, come to think about it. the problem, the way it is worded now, is similar to the question you raised.

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

so the prime factors of K include 5,3,5,2................more. < this list could be infinitive since we dont know what K is. all we care about is 3 distinct prime factors. which we have. so i guess just dont worry about it. lol.

does that help a little?

i am still not convinced, but don`t want to look stubborn,
let us imply that if k=0 the,the problem does not have meaning,
but for me the it will looks better if they add :where k is +ve integer

clock60 wrote:i am still not convinced, but don`t want to look stubborn,
let us imply that if k=0 the,the problem does not have meaning,
but for me the it will looks better if they add :where k is +ve integer

But to me k=0 doesn't rationalize. If it were 0, then it wouldnt even matter what statement 1,2 said because regardless of what information they give us, since technically zero is a multiple of every number, any number is a factor of zero. That wouldn't really be much of a question rather just knowing a rule!

Gurpinder wrote:

clock60 wrote:i am still not convinced, but don`t want to look stubborn,
let us imply that if k=0 the,the problem does not have meaning,
but for me the it will looks better if they add :where k is +ve integer

But to me k=0 doesn't rationalize. If it were 0, then it wouldnt even matter what statement 1,2 said because regardless of what information they give us, since technically zero is a multiple of every number, any number is a factor of zero. That wouldn't really be much of a question rather just knowing a rule!

it seems that it is exactly the same what i want to hear, i missed this point
thank you!!

clock60 wrote:

Gurpinder wrote:

clock60 wrote:i am still not convinced, but don`t want to look stubborn,
let us imply that if k=0 the,the problem does not have meaning,
but for me the it will looks better if they add :where k is +ve integer

But to me k=0 doesn't rationalize. If it were 0, then it wouldnt even matter what statement 1,2 said because regardless of what information they give us, since technically zero is a multiple of every number, any number is a factor of zero. That wouldn't really be much of a question rather just knowing a rule!

it seems that it is exactly the same what i want to hear, i missed this point
thank you!!

hahaha np!