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Does the integer k have at least three different positive [#permalink]
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09 Jul 2012, 04:51
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Re: Does the integer k have at least three different positive [#permalink]
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09 Jul 2012, 04:51
SOLUTIONDoes 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. Answer: C.
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Re: Does the integer k have at least three different positive [#permalink]
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09 Jul 2012, 05:44
Bunuel 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.
Hi, For integer k to have atleast 3 different positive prime factors, k = a.b.c, where a, b, c are prime numbers. Using (1), k/15 is an integer, least value of k =15, which has two different prime factors 3 & 5. Insufficient. Using (2), k/10 is an integer, least value of k =10 which has two different prime factors 2 & 5. Insufficient. Using both, least value of k =30 which has two different prime factors 2, 3 & 5. Sufficient. Answer is (C) Regards,



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Re: Does the integer k have at least three different positive [#permalink]
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13 Jul 2012, 03:53
SOLUTIONDoes 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. Answer: C.
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Re: Does the integer k have at least three different positive [#permalink]
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17 Jul 2012, 00:46
If a divides b, then all the primes in a along with their powers are in b
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Does the integer k... [#permalink]
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14 Nov 2013, 15:45
This is in the official GMAT review book. 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 book says , but shouldn't the answer be E? Couldn't k = 0?



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Re: Does the integer k... [#permalink]
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14 Nov 2013, 15:49



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Re: Does the integer k... [#permalink]
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14 Nov 2013, 16:08
Bunuel wrote: jdiamond wrote: This is in the official GMAT review book. 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 book says , but shouldn't the answer be E? Couldn't k = 0? Merging similar topics. Please refer to the solutions above. I didn't know this was here already. I don't think my issue with the question is answered in the solutions above.



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Re: Does the integer k... [#permalink]
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14 Nov 2013, 16:12



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Re: Does the integer k have at least three different positive [#permalink]
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03 Dec 2016, 20:10
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
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Re: Does the integer k have at least three different positive [#permalink]
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12 Dec 2016, 14:51
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, 04:45
Here is my solution: Question: Does K have atleast 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]
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18 Feb 2017, 19:12
Hi, does 1 counted as a prime factor?



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Re: Does the integer k have at least three different positive [#permalink]
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19 Feb 2017, 00:33




Re: Does the integer k have at least three different positive
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