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Is a positive integer n a multiple of 6?

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Is a positive integer n a multiple of 6? [#permalink]

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New post 15 May 2017, 01:00
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Is a positive integer n a multiple of 6?

1) n is the product of the 4 consecutive integers
2) n is a multiple of 12
[Reveal] Spoiler: OA

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Re: Is a positive integer n a multiple of 6? [#permalink]

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New post 15 May 2017, 01:32
Statement 1: If n is a product of 4 consecutive integers it must have a multiple of 2 and 4. Also 3 consecutive integers must have a multiple of 3. So n has to be a multiple of 6.
Sufficient.
Statement 2: If n is divisible by 12 it has to be divisible by 6 and 2.
Sufficient
D

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Re: Is a positive integer n a multiple of 6? [#permalink]

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New post 17 May 2017, 01:30
==> In the original condition, there is 1 variable, and in order to match the number of variables to the number of equations, there must be 1 more equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer.
For con 1), the product of consecutive 4 number is always the multiple of 24, hence yes, it is sufficient.
For con 2), if it is a multiple of 12, it is also a multiple of 6, hence yes, it is sufficient.

Therefore, D is the answer.
Answer: D
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Re: Is a positive integer n a multiple of 6? [#permalink]

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New post 21 Aug 2017, 08:25
Very simple question.

1. Among 4 consecutive integers we have multiples of 2 & 3. Hence the number is divisible by 6.

2. The number is multiple of 12-hence it is obviously a multiple of 6.

Answer is D.
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Re: Is a positive integer n a multiple of 6? [#permalink]

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New post 02 Sep 2017, 19:43
MathRevolution wrote:
Is a positive integer n a multiple of 6?

1) n is the product of the 4 consecutive integers
2) n is a multiple of 12



Please reword statement 1 for clarity... anyways nice question OP

Stmnt 1

If N is the product of 4 consecutive integers then it must necessarily be a multiple of 6 - this is one of those things just like how the product of 3 consecutive integers is a multiple of 3
The statement isn't worded correctly but if you start with

1,2,3,4 for example you have 3 and 2 in there and you could go on infinitely - 2,3,4,5 ... etc and it would be a multiple of 6

Suff

Stmnt 2

Yes because

A multiple of 12
n= 3 x 2 x 2 x some constant k

A multiple of 6
n= 3 x 2 x some constant k

there's enough 3's and 2's in N according to stmnt 2 so

suff

D

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Re: Is a positive integer n a multiple of 6?   [#permalink] 02 Sep 2017, 19:43
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