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# Does the integer k have at least three different positive

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

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19 Apr 2009, 10:24
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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

Official Guide 12 Question

 Question: 42 Page: 26 Difficulty: 700

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Video Explanations:

OPEN DISCUSSION OF THIS QUESTION IS HERE: does-the-integer-k-have-at-least-three-different-positive-135551.html
[Reveal] Spoiler: OA

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Manager
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Re: interger K gmat Official guide [#permalink]

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19 Apr 2009, 10:47
IMO E.

stmnt1 - divisible by primes 3, 5, nsf
stmnt2 - divisible by primes 2, 5, nsf

combining, nsf

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Re: interger K gmat Official guide [#permalink]

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19 Apr 2009, 10:52
I have a doubt. Can K/15 =0 ? as 0 is also an integer.

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Re: interger K gmat Official guide [#permalink]

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19 Apr 2009, 23:20
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Statement 1:
15 breaks down to 3*5..So K can simply have just 2 prime factors or more--Insuff
Statement 2:
10 breaks down to 2*5..So K can simply have just 2 prime factors or more--Insuff

Together..K must have at least one 2, one 3 and one 5 to be divisible by 15 and 10--Therefore it has at least 3 different prime factors.

Ans: C

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Re: interger K gmat Official guide [#permalink]

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20 Apr 2009, 12:20
Yes, of course it's C, I don't know how I did not see that.
Thanks!

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Re: interger K gmat Official guide [#permalink]

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23 Apr 2009, 12:08
1) k = 1*3*5, 2*3*5, 3*3*5, 2*2*3*5, 2*3*3*5, 7*3*5,...... NS as first value has less than 3 prime factors
2) k = 1*2*5, 2*2*5, 3*2*5, 2*2*2*5, 5*2*5, 2*3*2*5,............NS as first value has less than 3 prime factors

Comibing two

k= 2*3*5, 2*2*3*5,.......

k will always have at least three prime factors, hence C.

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Re: interger K gmat Official guide [#permalink]

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30 Apr 2009, 22:47
The prime factors of 15 are 1,3 and 5 hence there are 3 prime factors. Is 1 not considered a prime factor ?

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Re: interger K gmat Official guide [#permalink]

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30 Apr 2009, 22:58
mdfrahim wrote:
The prime factors of 15 are 1,3 and 5 hence there are 3 prime factors. Is 1 not considered a prime factor ?

1 is a factor of every single integer, but it is NOT a prime factor. (Prime factors are 2,3,5,7....)

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Re: interger K gmat Official guide [#permalink]

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05 May 2009, 22:08
bandit wrote:
Q. Does the integer K have at least three different positive prime factors?

1. K/15 is an integer
2. K/10 is an integer

Will post OA after some time.

C cannot be it.
It should be E because K could be 0 or 30 or any multiple of 30.
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Re: interger K gmat Official guide [#permalink]

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07 May 2009, 14:56
-this is a Least Common Multiple Problem guys……Right off the top, based on question alone, K could not be “0” because the question asks if integer K have at least 3 different positive prime numbers (btw, there is no such things as a non-positive prime number by definition of what a prime number is……recall the first prime number is 2….), in which “0” doesn’t have factors…………

What number evenly divides into zero? What number is a factor of zero?

Check it out:

(i) K/15 is an integer….means that K has to be a most 15 in order for it to be an integer, however, K could be 30, 45, 60, etc

-statement one also states that K/15 is an integer which implies that 15 is a factor of K. the least factor in which K/15 is an integer is 15 and if you were to perform prime factorization on 15 you get 15=3x5…..only two prime factors. INSUFFICIENT BECAUSE WE DON’T KNOW IF K = 15, 30, ETC…..

(ii) assess statement (ii) similar to one and you will see the same result. The only prime factors in which K has to be at least 10 in order to be an integer is 10. and the prime factorization of 10 = 5x2….only two prime factors.

Taking (i) and (ii) together in which K/15 = an integer and K/10 is an integer, the least common multiple of K=2*3*5=30, which means that K has at least 3 positive prime factors (2,3,5)

C

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Re: interger K gmat Official guide [#permalink]

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19 Aug 2009, 13:14
I disagree with the previous poster.
k could be 0.
If k=0 then k has "at least three different positive prime factors", as every number is a factor of 0.

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Re: interger K gmat Official guide [#permalink]

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19 Aug 2009, 16:50
K=0
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Re: interger K gmat Official guide [#permalink]

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20 Aug 2009, 09:39
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Re: interger K gmat Official guide [#permalink]

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21 Aug 2009, 18:21
C.

1. Not suff --> 3,5
2. Not suff --> 2,5

Both together means x is divisible 30, which has 2,3,5 as factors

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Re: interger K gmat Official guide [#permalink]

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21 Aug 2009, 19:13
I believe answer should be E.

K=0
K/15=0 is an integer
K/10=0 is still an integer

but 0 has no prime factor.

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Re: interger K gmat Official guide [#permalink]

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21 Aug 2009, 20:05
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defeatgmat wrote:
I believe answer should be E.

K=0
K/15=0 is an integer
K/10=0 is still an integer

but 0 has no prime factor.

All numbers are factors of 0. Therefore, all primes are factors of 0.

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Re: interger K gmat Official guide [#permalink]

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31 Aug 2009, 22:56
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GMAT TIGER wrote:
bandit wrote:
Q. Does the integer K have at least three different positive prime factors?

1. K/15 is an integer
2. K/10 is an integer

Will post OA after some time.

C cannot be it.
It should be E because K could be 0 or 30 or any multiple of 30.

But the question is "Does the integer K has at least three different positive prime factors?". And the answer is "Yes".
0 - infinitely number of factors.
30 - 2*3*5 (3 factors).

Am I right, GT or am I missing something here?
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Re: interger K gmat Official guide [#permalink]

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01 Sep 2009, 00:29
Combining statements 1 and 2 we know that 2, 3 and 5 are all prime factors of k.

Thus integer k has "at least three different positive prime factors".

Yes.

Footnote: if k were 0 then the answer would still be Yes, as all numbers are factors of 0, and all primes are factors of 0. Therefore integer k would still have "at least three different positive prime factors".
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Re: interger K gmat Official guide [#permalink]

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01 Sep 2009, 10:54
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Expert's post
If this were a real GMAT question, it would ask "Does the positive integer K have at least three different positive prime factors?" GMAT questions about divisibility are always restricted to positive integers only. That said, zero is not an exception here anyway, as has been pointed out above, but you won't need to worry about that on the real test.
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Re: interger K gmat Official guide [#permalink]

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01 Sep 2009, 11:33
IanStewart wrote:
If this were a real GMAT question, it would ask "Does the positive integer K have at least three different positive prime factors?" GMAT questions about divisibility are always restricted to positive integers only. That said, zero is not an exception here anyway, as has been pointed out above, but you won't need to worry about that on the real test.

Agree with you. In a topic, someone said that, GMAC's cost per question is about 2 thousand dollars; so, these questions are very well designed.

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Re: interger K gmat Official guide   [#permalink] 01 Sep 2009, 11:33

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