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# Is 4 + n/6 an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 49915
Is 4 + n/6 an integer?  [#permalink]

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13 Dec 2015, 05:33
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Difficulty:

5% (low)

Question Stats:

84% (00:40) correct 16% (01:19) wrong based on 87 sessions

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Is 4 + n/6 an integer?

(1) n is a multiple of 3.
(2) n divided by 6 has a remainder of 0.

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Re: Is 4 + n/6 an integer?  [#permalink]

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13 Dec 2015, 05:37
St1: n = 3k --> Not sufficient
St2: n = 6k --> Sufficient

Intern
Joined: 06 Oct 2013
Posts: 45
Re: Is 4 + n/6 an integer?  [#permalink]

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14 Dec 2015, 06:06
Bunuel wrote:
Is 4 + n/6 an integer?

(1) n is a multiple of 3.
(2) n divided by 6 has a remainder of 0.

Solution:

Is 4 + n/6 an integer?--> is n/6 is an integer?---> is n multiple of 6?

Statement 1) n is a multiple of 3.

n = 3 , 6 or 9--> 3 is not a multiple of 6 , but 6 is.

Hence Insufficient.

Statement 2) n divided by 6 has a remainder of 0.

Clearly n is a multiple of 6.

Hence Sufficient.

Ans B.
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Joined: 12 Sep 2015
Posts: 2996
Re: Is 4 + n/6 an integer?  [#permalink]

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20 Apr 2018, 07:33
1
Top Contributor
Bunuel wrote:
Is 4 + n/6 an integer?

(1) n is a multiple of 3.
(2) n divided by 6 has a remainder of 0.

Target question: Is 4 + n/6 an integer?

This is a good candidate for rephrasing the target question (see video below).

If 4 is an integer, then 4 + n/6 will be an integer if and only if n/6 is an integer. Moreover, n/6 will be an integer if and only if n is divisible by 6. So, we can REPHRASE the target question as....

REPHRASED target question: Is n divisible by 6?

Statement 1: n is a multiple of 3
There are several values of n that satisfy this condition. Here are two values that yield conflicting answers to the REPHRASED target question :
Case a: n = 3, in which case n is NOT divisible by 6
Case b: n = 6, in which case n IS divisible by 6
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n divided by 6 has a remainder of 0
If n is divided 6 leaves remainder 0, then n is definitely divisible by 6.
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

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Re: Is 4 + n/6 an integer? &nbs [#permalink] 20 Apr 2018, 07:33
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