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# Is a positive integer x a factor of 12?

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

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09 Mar 2017, 02:39
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Difficulty:

45% (medium)

Question Stats:

62% (01:23) correct 38% (01:37) wrong based on 118 sessions

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Is a positive integer x a factor of 12?

1) 3x is a factor of 48
2) 2x is a factor of 12

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

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09 Mar 2017, 04:06
MathRevolution wrote:
Is a positive integer x a factor of 12?

1) 3x is a factor of 48
2) 2x is a factor of 12

ste 1: x can be 2,4,12,16 not suff

ste 2: x can be only 6,2,3 suff
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Re: Is a positive integer x a factor of 12?  [#permalink]

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09 Mar 2017, 06:05
ST 1: 3x is the factor of 48. x is the factor of 16. x can be 1, 2, 4, 8, 16. Out of these 8 and 16 are not the factor of 12. INSUFFICIENT

St 2: 2x is the factor 12. x is the factor of 6 and all the factor of 6 will factor of 12 as 6 is itself the factor of 12. ANSWER

Option B
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Is a positive integer x a factor of 12?  [#permalink]

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09 Mar 2017, 10:30
Is a positive integer x a factor of 12?

1) 3x is a factor of 48

It mean that 3x is divisible by 48....then 48/3x= 16/x

If x= 2........16/2 =8....then x is factor of 12

If x =8..........16/8=2...then x is NOT factor of 12

Insufficient

2) 2x is a factor of 12

It mean that 2x is divisible by 12....then 12/2x= 6/x

x MUST be factor of 6 which in turn is factor of 12

Sufficient

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

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12 Mar 2017, 18:44
==> In the original condition, there is 1 variable (x) 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), “3x is a factor of 48” becomes “x is a factor of 16”, and x=2 yes but x=8 no, hence it is not sufficient.
For con 2), “2x is a factor of 12” becomes “x is a factor of 6”, hence it is always yes and sufficient.

The answer is B.
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Re: Is a positive integer x a factor of 12?  [#permalink]

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31 Jan 2019, 09:15
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Re: Is a positive integer x a factor of 12?   [#permalink] 31 Jan 2019, 09:15
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