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# Does the integer k have at least three different positive

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

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27 Mar 2012, 02:57
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Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer.
(2) k/10 is an integer.
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Re: Does the integer k have at least three different positive  [#permalink]

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27 Mar 2012, 03:07
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.

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

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24 Mar 2013, 08:42
hi
I understand the example
1. since K is divisible by 15, 3 AND 5 are the factors but what about 1?can't it be considered as one of the factors?
Or it is not considered as one of the factors because the question mentions prime factor and 1 is not a prime no.?

Bunuel wrote:
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.

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

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24 Mar 2013, 11:49
4112019 wrote:
hi
I understand the example
1. since K is divisible by 15, 3 AND 5 are the factors but what about 1?can't it be considered as one of the factors?
Or it is not considered as one of the factors because the question mentions prime factor and 1 is not a prime no.?

1 is one of the factors of K, but we are looking for "different positive prime factors", so 1 cannot be considered as it is not a prime number.
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Re: Does the integer k have at least three different positive  [#permalink]

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25 Mar 2013, 01:28
dzodzo85 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.

Maybe it is just me but I feel the answer should be E.

The question stem asks whether integer k has atleast 3 different ..... SO it is either a Yes or a No.

Now, taking F.S 1, we have k/15 is an integer. Thus, for k=0, we have a NO for the question stem. But, for k=30, we have a YES. Insufficient.

From F.S 2 , we have k/10 is an integer. Just as above, Insufficient. Taking both fact statements together, we have for k=0, a NO. Again, taking both statements together, for k=30 we have a YES. Insufficient

Might be a blonde moment.
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Re: Does the integer k have at least three different positive  [#permalink]

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25 Mar 2013, 01:33
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vinaymimani wrote:
dzodzo85 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.

Maybe it is just me but I feel the answer should be E.

The question stem asks whether integer k has atleast 3 different ..... SO it is either a Yes or a No.

Now, taking F.S 1, we have k/15 is an integer. Thus, for k=0, we have a NO for the question stem. But, for k=30, we have a YES. Insufficient.

From F.S 2 , we have k/10 is an integer. Just as above, Insufficient. Taking both fact statements together, we have for k=0, a NO. Again, taking both statements together, for k=30 we have a YES. Insufficient

Might be a blonde moment.

If k=0, then k is a multiple of all prime numbers: zero is a multiple of every integer (except zero itself).
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Re: Does the integer k have at least three different positive  [#permalink]

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25 Mar 2013, 02:14
Bunuel wrote:
vinaymimani wrote:
dzodzo85 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.

Maybe it is just me but I feel the answer should be E.

The question stem asks whether integer k has atleast 3 different ..... SO it is either a Yes or a No.

Now, taking F.S 1, we have k/15 is an integer. Thus, for k=0, we have a NO for the question stem. But, for k=30, we have a YES. Insufficient.

From F.S 2 , we have k/10 is an integer. Just as above, Insufficient. Taking both fact statements together, we have for k=0, a NO. Again, taking both statements together, for k=30 we have a YES. Insufficient

Might be a blonde moment.

Indeed a blonde moment!Thanks!
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Re: Does the integer k have at least three different positive  [#permalink]

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17 Jul 2017, 20:34
dzodzo85 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.

Simple

St 1

K is multiple of 15

K =5 x 3 x some integer C

Insuff - C could be 1 or many other values

St 2

K is a multiple of 10

K = 5 x 2 x some integer C

Insuff C could be 2 or 1 or many other values

St 1 & 2

Knowing that K is multiple of 15 and 10 just find the LCM and then draw a conclusion

LCM(15,10) = 5 x 3 x 2

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

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30 Jul 2017, 17:40
dzodzo85 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.

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Re: Does the integer k have at least three different positive   [#permalink] 30 Jul 2017, 17:40
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