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Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is

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Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is [#permalink]

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New post 04 Sep 2017, 02:05
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Is a positive integer x divisible by 12?

1) x is divisible by 8
2) x is divisible by 6

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Re: Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is [#permalink]

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New post 04 Sep 2017, 09:46
MathRevolution wrote:
Is a positive integer x divisible by 12?

1) x is divisible by 8
2) x is divisible by 6


Q : Is X divisible by \(12 (2^2*3)\)?

#1. X is divisible by 8
- X can be 24 -> divisible by 12.
- X can be 32 -> NOT divisible by 12.
NOT SUFFICIENT.

#2. X is divisible by 6
- X can be 12 -> divisible by 12.
- X can be 18 -> NOT divisible by 12.
NOT SUFFICIENT.

Combine #1 & #2
- X must divisible by LCM of 8&6 = 24.
- Since 24 is multiple of 12, so X must divisible by 12.
SUFFICIENT.
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Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is [#permalink]

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New post 04 Sep 2017, 10:09
Is a positive integer x divisible by \(12(2^2 * 3)\)?

From the information given in Statement 1
If x is divisible by \(8(2^3)\), 8 is not divisble by 12 but 24 is (Insufficient)
From the information given in Statement 2
If x is divisible by \(6(2*3)\), 8 is not divisble by 6 but 24 is (Insufficient)

However, on combining the information available in both the statements,
it is the clear the positive number x is definitely divisible by 12 as it is a multiple of \(24(2^3 * 3)\) (Option C)
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Re: Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is [#permalink]

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New post 04 Sep 2017, 10:55
My answer is C. We need both statements together to have a definite answer.

X is a positive int. Means x greater than 0 and is an interger.
12= 2*2*3.

Statement 1- x is divisible by 8.
This implies that x has a minimum of 2*2*2.
But it does not say anything about the factor 3.
So, not sufficient.

Statement 2- x is divisible by 6.
That is x has a minimum of 2*3.
This does not say anything about the another 2.

Thus, not sufficient.

Now statement 1 + 2-
X is factor of 8 and 6.
Thus, x has minimum of 2^4 and 3 as factors.
This sufficiently proves that x is divisible by 12, and gives us a definite answer.

Hence, answer is C.


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Re: Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is [#permalink]

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New post 06 Sep 2017, 01:28
=>1) Since 8 is not a multiple of 12, this is not sufficient.

2) Since 6 is not a multiple of 12, this is not sufficient.

1) & 2) Since lcm(8,6) = 24 is a multiple of 12, these are sufficient.

Ans: C
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Re: Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is   [#permalink] 06 Sep 2017, 01:28
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