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

(1) k/15 is an integer --> since k is divisible by 3*5=15, then it's divisible by 3 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(2) k/10 is an integer --> since k is divisible by 2*5=10, then it's divisible by 2 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(1)+(2) At least 3 primes are factors of k: 2, 3, and 5. Sufficient.

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

(1) k/15 is an integer --> since k is divisible by 3*5=15, then it's divisible by 3 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(2) k/10 is an integer --> since k is divisible by 2*5=10, then it's divisible by 2 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(1)+(2) At least 3 primes are factors of k: 2, 3, and 5. Sufficient.

Re: Does the integer k have at least three different positive [#permalink]

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03 Dec 2016, 19:10

Here is my solution-> We need to check if the number of prime factors of p are atleast 3 i.e.≥3 Statement 1 p=15 => no p=15*17 => yes Not sufficient Statement 2 p=10 => no p=10*13 => yes Not sufficient Combining the two statements we can say that p=2*3*5*x for some integer x. Clearly p must have atleast 3 prime factors Hence C

Re: Does the integer k have at least three different positive [#permalink]

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12 Dec 2016, 13:51

I solved this problem using Plug In

1, If k=30, have 2,3,5 prime factors If K=75, have 3,5 only Insufficient 2, If k = 70 , have 2,5,7 prime factors If k = 80, Only 2,5 prime factors Insufficient 3, K/15 and K/10 If k=30 2,3,5 K=90 2,3,5 prime factors

Irrespective K value , these only both meet conditions C

Is my approach Right? Thanks
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Re: Does the integer k have at least three different positive [#permalink]

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13 Dec 2016, 03:45

Here is my solution:

Question: Does K have at-least 3 different positive prime factors.

Statement 1: \(\frac{k}{15}\) is an integer.

Hence the values of k are multiples of 15 such as 15,30,45... Factors of 15 = 5 and 3 (2 factors) Factors of 30 = 5 , 3 and 2 (3 factors) Hence not sufficient.

Statement 2: \(\frac{k}{10}\) is an integer

Hence the values of k are multiples of 10 such as 10,20,30 Factors of 10 = 5 and 2 (2 factors) Factors of 30 = 5 , 3 and 2 (3 factors) Hence not sufficient.

Stmt 1 + Stmt 2:

k should be multiples of 10 and 15 such as 30,60... All these values have atleast 3 positive different prime factors.

Hence C.
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Re: Does the integer k have at least three different positive
[#permalink]
13 Dec 2016, 03:45

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