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Is 12 a factor of the positive integer n?

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Is 12 a factor of the positive integer n? [#permalink]

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New post 08 Nov 2017, 00:02
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Is 12 a factor of the positive integer n? [#permalink]

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New post 08 Nov 2017, 00:07
Bunuel wrote:
Is 12 a factor of the positive integer n?

(1) n is a factor of 36.

(2) 3 is a factor of n.


(1) if n is a factor of 36 n can be 1, 2, 3, 4, 9, 12 , 18, 24, 36...not sufficient

(2) n can take 3, 6, 9, 12, 18, 21 24, 36.....not sufficient

on combining n can take 12, 18, 24, 36..not sufficient

E
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Last edited by Luckisnoexcuse on 08 Nov 2017, 22:56, edited 1 time in total.

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Re: Is 12 a factor of the positive integer n? [#permalink]

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New post 08 Nov 2017, 13:29
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Luckisnoexcuse wrote:
Bunuel wrote:
Is 12 a factor of the positive integer n?

(1) n is a factor of 36.

(2) 3 is a factor of n.


(1) if n is a factor of 36 n can be 1, 2, 3, 4, 9, 12 , 18, 24, 36...not sufficient

(2) n can take 3, 6, 9, 12, 18, 21 24, 36.....not sufficient

on combining n can take 18, 24, 36..not sufficient

E


Hi Luckisnoexcuse,

Just one small observation/correction in your explanation. Although it should not affect your answer.

on combining n can take 12, 18, 24, 36..not sufficient

You missed to include 12 upon combining.
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Re: Is 12 a factor of the positive integer n? [#permalink]

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New post 08 Nov 2017, 22:10
Bunuel wrote:
Is 12 a factor of the positive integer n?

(1) n is a factor of 36.

(2) 3 is a factor of n.


Is 12 a factor of n--> does n have 2^2 *3 ?

1.n is a factor of 36
36= 2^2 * 3^2
Not sufficient since n can be 1 , multiple of 2 or 3 or can be 12 or a multiple of 12

2. 3 is a factor of n
Not sufficient as if n might have 2^2 also

Combining 1 and 2 , we get
Not sufficient
If n = 12 or its multiple , then Yes
If n = 3 , then No

Answer E
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Re: Is 12 a factor of the positive integer n? [#permalink]

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New post 09 Nov 2017, 17:35
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Bunuel wrote:
Is 12 a factor of the positive integer n?

(1) n is a factor of 36.

(2) 3 is a factor of n.


Target question: Is 12 a factor of the positive integer n?

Statement 1: n is a factor of 36
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 12, in which case 12 IS a factor of n
Case b: n = 6, in which case 12 is NOT a factor of n
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3 is a factor of n
Once again, there are several values of n that satisfy statement 2. Here are two:
Case a: n = 12, in which case 12 IS a factor of n
Case b: n = 6, in which case 12 is NOT a factor of n
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: n = 12, in which case 12 IS a factor of n
Case b: n = 6, in which case 12 is NOT a factor of n
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer:
[Reveal] Spoiler:
E


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Re: Is 12 a factor of the positive integer n? [#permalink]

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New post 12 Nov 2017, 08:41
Bunuel wrote:
Is 12 a factor of the positive integer n?

(1) n is a factor of 36.

(2) 3 is a factor of n.


We need to determine whether n/12 = integer.

Statement One Alone:

n is a factor of 36.

We do not have enough information to answer the question. If n is 1, then n/12 is not an integer; however, if n is 36, then n/12 is an integer. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

3 is a factor or n.

We do not have enough information to answer the question. If n is 3, then n/12 is not an integer; however, if n is 36, then n/12 is an integer. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

We still do not have enough information to answer the question. If n is 3, then n/12 is not an integer; however, if n is 36, then n/12 is an integer.

Answer: E
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Re: Is 12 a factor of the positive integer n?   [#permalink] 12 Nov 2017, 08:41
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