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# Is a positive integer n a multiple of 12

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Math Revolution GMAT Instructor
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Is a positive integer n a multiple of 12  [#permalink]

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13 Mar 2017, 01:17
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Difficulty:

5% (low)

Question Stats:

83% (00:35) correct 17% (00:46) wrong based on 86 sessions

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Is a positive integer n a multiple of 12

1) n is a multiple of 6
2) n is a multiple of 24

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Re: Is a positive integer n a multiple of 12  [#permalink]

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13 Mar 2017, 01:23
1
MathRevolution wrote:
Is a positive integer n a multiple of 12

1) n is a multiple of 6
2) n is a multiple of 24

St I
n is a multiple of 6
n can be 6,12,18,24,.... where 6,18,... are not multiples of 12 ------- Insufficient

St II
n is a multiple of 24
which means n is a multiple of 12*2
n will be of the form 12*2*1, 12*2*2, 12*2*3....
so n will be a multiple of 12 --------- Sufficient

Hence option B is correct
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Re: Is a positive integer n a multiple of 12  [#permalink]

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15 Mar 2017, 01:10
==> In the original condition, there is 1 variable (n) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For remainder questions, you always use direct substitution.
For con 1), n=6 no, n=12 yes, hence not sufficient.
For con 2), n=24,48,…, hence it is always yes and sufficient.

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Re: Is a positive integer n a multiple of 12  [#permalink]

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13 Dec 2017, 06:52
MathRevolution wrote:
Is a positive integer n a multiple of 12

1) n is a multiple of 6
2) n is a multiple of 24

We need to determine whether n/12 = integer.

Statement One Alone:

n is a multiple of 6.

If n = 6, then n/12 is not an integer; however if n = 12, then n/12 is an integer. Statement one is not sufficient to answer the question.

Statement Two Alone:

n is a multiple of 24.

Since n/24 = integer and 12 is a factor of 24, n/12 will always be an integer. Statement two alone is sufficient to answer the question.

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Re: Is a positive integer n a multiple of 12  [#permalink]

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13 Dec 2017, 09:44
MathRevolution wrote:
Is a positive integer n a multiple of 12

1) n is a multiple of 6
2) n is a multiple of 24

Every multiple of a positive integer x, is also a multiple of each of its positive factors (but not vice versa necessarily). Eg, all multiples of 12 (12, 24, 36, 48, 60..) are ALSO multiples of 6 or of 3 or of 4. So, every multiple of 24 will be a multiple of 12 for sure. Second statement is sufficient.

However, every multiple of 6 may or may not be a multiple of 12. Eg, 18 is a multiple of 6 but not of 12, while 36 is a multiple of both. So first statement is not sufficient.

Re: Is a positive integer n a multiple of 12   [#permalink] 13 Dec 2017, 09:44
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