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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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09 Jul 2012, 04:51
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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.

Diagnostic Test
Question: 42
Page: 26
Difficulty: 600

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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
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SOLUTION

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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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.

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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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Re: Does the integer k...  [#permalink]

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14 Nov 2013, 16:12
2
jdiamond wrote:
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.

0 is a multiple of all integers except 0 itself. Thus if k=0 it still has at least three different positive prime factors.
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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 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]

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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
2
brightandamen wrote:
Hi, does 1 counted as a prime factor?

No, 1 is not a prime number. The smallest prime is 2.
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Re: Does the integer k have at least three different positive  [#permalink]

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21 Feb 2018, 21:23
1
This concept is discussed in detail here:
https://www.veritasprep.com/blog/2014/0 ... r-factors/
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Re: Does the integer k have at least three different positive  [#permalink]

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07 Jul 2019, 05:21
Could integer k be 0?

If so, both conditions (k/10 is an integer) and (k/15 is an integer) would both be met as 0/anything = 0. Does 0 have an infinite number of prime factors?

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

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07 Jul 2019, 06:38
TriumphKai wrote:
Could integer k be 0?

If so, both conditions (k/10 is an integer) and (k/15 is an integer) would both be met as 0/anything = 0. Does 0 have an infinite number of prime factors?

Thank you all!

Hello,

0 is a multiple of all integers except 0 itself. Thus if k=0 it still has at least three different positive prime factors.

Hope it helps !!
Re: Does the integer k have at least three different positive   [#permalink] 07 Jul 2019, 06:38
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