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# I thought this would be good for learning: The integers k

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Director
Joined: 29 Aug 2005
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I thought this would be good for learning: The integers k  [#permalink]

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14 Jun 2009, 01:47
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I thought this would be good for learning:

The integers k and n are such that 4 2?

1. The greatest common factor of k and n is 4.
2. The least common multiple of k and n is 84.

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Director
Joined: 23 May 2008
Posts: 739
Re: DS: number prop  [#permalink]

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14 Jun 2009, 03:21
seofah wrote:
I thought this would be good for learning:

The integers k and n are such that 4 < k < n and k is not a factor of n. If r is the remainder when n is divided by k, is r > 2?

1. The greatest common factor of k and n is 4.
2. The least common multiple of k and n is 84.

D i think

1) GCF of k and n is 4. k and n each have 2 2's. in order for k not to be a factor of n, the rest of the primes between k and n have to be different. for every diference of 2 between the remaining primes, it will be multiplied by 4 sine there are 2 2's present in k and n, so the remainder is always greater than 2

2) LCM of k and n is 84, just as in statement 1, the primes not shered bhy k and n account for a difference that will make r>2
Director
Joined: 05 Jun 2009
Posts: 678
WE 1: 7years (Financial Services - Consultant, BA)
Re: DS: number prop  [#permalink]

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14 Jun 2009, 11:46
bigtreezl wrote:
seofah wrote:
I thought this would be good for learning:

The integers k and n are such that 4 < k < n and k is not a factor of n. If r is the remainder when n is divided by k, is r > 2?

1. The greatest common factor of k and n is 4.
2. The least common multiple of k and n is 84.

D i think

1) GCF of k and n is 4. k and n each have 2 2's. in order for k not to be a factor of n, the rest of the primes between k and n have to be different. for every diference of 2 between the remaining primes, it will be multiplied by 4 sine there are 2 2's present in k and n, so the remainder is always greater than 2

2) LCM of k and n is 84, just as in statement 1, the primes not shered bhy k and n account for a difference that will make r>2

Can you please explain me your reasoning. Especially of the 2nd part.
what if the LCM given is 132 and not 84. How will you explain it?
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Manager
Joined: 30 May 2009
Posts: 202
Re: DS: number prop  [#permalink]

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14 Jun 2009, 12:13
I think answer should be A. What is the OA???

(1) The greatest common factor of k and n is 4.Some of the possible combinations for (k, n) such that GCF is 4 and K<n are - (8,12) (12,16) (12,20) (16,20) (20,24) (20,28) etc etc....

Take any combination you will get remainder r as either 4 or 8, both of which are greater than 2. Hence SUFF.

(2) The least common multiple of k and n is 84. Some of the possible combinations for (k,n) such that LCM is 84 and k<n are - (1,84) (7,12) (12,21) (12,14).

If k=7, n=12 , then the remainder is 4
If k=12, n=14, then the reaminder is 2

So we cannot say for sure that the remainder is = 2 always. INSUFF.

Hence answer should be A........unless I missed something...Please correct if you see anything wrong.
Director
Joined: 23 May 2008
Posts: 739
Re: DS: number prop  [#permalink]

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14 Jun 2009, 12:24
sdrandom1 wrote:
I think answer should be A. What is the OA???

(1) The greatest common factor of k and n is 4.Some of the possible combinations for (k, n) such that GCF is 4 and K<n are - (8,12) (12,16) (12,20) (16,20) (20,24) (20,28) etc etc....

Take any combination you will get remainder r as either 4 or 8, both of which are greater than 2. Hence SUFF.

(2) The least common multiple of k and n is 84. Some of the possible combinations for (k,n) such that LCM is 84 and k<n are - (1,84) (7,12) (12,21) (12,14).

If k=7, n=12 , then the remainder is 4
If k=12, n=14, then the reaminder is 2

So we cannot say for sure that the remainder is = 2 always. INSUFF.

Hence answer should be A........unless I missed something...Please correct if you see anything wrong.

yes, I believe you are right...i overlooked the (12,14) combo

should be A
Manager
Joined: 28 Jan 2004
Posts: 198
Location: India
Re: DS: number prop  [#permalink]

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14 Jun 2009, 22:29
I think the answer is A.But i also used the hit and trial method by picking some numbers.
Is there any other way of doing this ?
Intern
Joined: 02 Jun 2008
Posts: 4
Re: DS: number prop  [#permalink]

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15 Jun 2009, 11:41
stmt1 is alone sufficient.: shortcut: the remainder when a number is divided by another number is always a multiple of their HCF.... for eg; 27 when divided by 18 will leave a remainder 9 which is a multiple of 9 itself you can try different combination and will find this result true..

The same logic doesn't hold true when we know the LCM for two different numbers... because we can't separate out the primes...

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Re: DS: number prop &nbs [#permalink] 15 Jun 2009, 11:41
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# I thought this would be good for learning: The integers k

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