IMO E.

stmnt1 - divisible by primes 3, 5, nsf
stmnt2 - divisible by primes 2, 5, nsf

combining, nsf

Statement 1:
15 breaks down to 3*5..So K can simply have just 2 prime factors or more--Insuff
Statement 2:
10 breaks down to 2*5..So K can simply have just 2 prime factors or more--Insuff

Together..K must have at least one 2, one 3 and one 5 to be divisible by 15 and 10--Therefore it has at least 3 different prime factors.

Ans: C

1) k = 1*3*5, 2*3*5, 3*3*5, 2*2*3*5, 2*3*3*5, 7*3*5,...... NS as first value has less than 3 prime factors
2) k = 1*2*5, 2*2*5, 3*2*5, 2*2*2*5, 5*2*5, 2*3*2*5,............NS as first value has less than 3 prime factors


Comibing two

k= 2*3*5, 2*2*3*5,.......

k will always have at least three prime factors, hence C.

1 is a factor of every single integer, but it is NOT a prime factor. (Prime factors are 2,3,5,7....)

-this is a Least Common Multiple Problem guys……Right off the top, based on question alone, K could not be “0” because the question asks if integer K have at least 3 different positive prime numbers (btw, there is no such things as a non-positive prime number by definition of what a prime number is……recall the first prime number is 2….), in which “0” doesn’t have factors…………

What number evenly divides into zero? What number is a factor of zero?


Check it out:

(i) K/15 is an integer….means that K has to be a most 15 in order for it to be an integer, however, K could be 30, 45, 60, etc

-statement one also states that K/15 is an integer which implies that 15 is a factor of K. the least factor in which K/15 is an integer is 15 and if you were to perform prime factorization on 15 you get 15=3x5…..only two prime factors. INSUFFICIENT BECAUSE WE DON’T KNOW IF K = 15, 30, ETC…..

(ii) assess statement (ii) similar to one and you will see the same result. The only prime factors in which K has to be at least 10 in order to be an integer is 10. and the prime factorization of 10 = 5x2….only two prime factors.

Taking (i) and (ii) together in which K/15 = an integer and K/10 is an integer, the least common multiple of K=2*3*5=30, which means that K has at least 3 positive prime factors (2,3,5)


C

surely answer is E.
K=0
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C.

1. Not suff --> 3,5
2. Not suff --> 2,5

Both together means x is divisible 30, which has 2,3,5 as factors

All numbers are factors of 0. Therefore, all primes are factors of 0.
Answer is C.

Combining statements 1 and 2 we know that 2, 3 and 5 are all prime factors of k.

Thus integer k has "at least three different positive prime factors".

Yes.

Answer is C.

Footnote: if k were 0 then the answer would still be Yes, as all numbers are factors of 0, and all primes are factors of 0. Therefore integer k would still have "at least three different positive prime factors".
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Agree with you. In a topic, someone said that, GMAC's cost per question is about 2 thousand dollars; so, these questions are very well designed.