S1 says that k/15 is an integer, this means that k is divisible by 15
since 15 = 5*3, k is divisible by 5 & 3 both being prime

S2 says that k/10 is an integer, this means that k is divisible by 10
since 10 = 5*2, k is divisible by 5 & 2 both being prime

We already have 3 primes 5, 3 and 2 which can divide k

meparashar wrote:Please help me with this question

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

1) k/15 is an integer

2) k/10 is an integer

The Answer is C

ankur.agrawal wrote:

meparashar wrote:Please help me with this question

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

1) k/15 is an integer

2) k/10 is an integer

The Answer is C

1) k/15 is an integer . Lets take numbers .

30 = 5*3*2 ( 3 DIFF. + prime factors) YES

45= 5*3 *3 ( Only two diff + prime factors) NO

Clearly not Sufficient..

2) k/30 . Take 20 & 30 & check . U will get a no & a yes. again not sufficient..

Taking together 1 & 2 . Check with 30, 60 , 90 , all have minimum 3 different positive prime factors.

Hence sufficient. C

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

1) k/15 is an integer

2) k/10 is an integer

We need to determine whether k has at least three different prime factors.

Statement One Alone:

k/15 is an integer.

Statement one alone is not sufficient to answer the question. If k = 15, then k has two different prime factors; however, if k = 30, then k has three different prime factors.

Statement Two Alone:

k/10 is an integer.

Statement two alone is not sufficient to answer the question. If k = 10, then k has two different prime factors; however, if k = 30, then k has three different prime factors.

Statements One and Two Together:

Using statements one and two, we see that k is a multiple of both 10 and 15, and thus it is a multiple of their least common multiple, which is 30. Since all multiples of 30 have at least three different prime factors, the two statements together are sufficient.

Answer: C