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Is n divisible by 12?

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Source: — Data Sufficiency |
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by kvcpk » Sun Aug 01, 2010 5:29 am
The Jock wrote:Is n divisible by 12?
1. n/6 is an integer.
2. n/4 is an integer.

I thought both statements are sufficient.
Please help me.
1. n/6 is an integer.
let n= 6
6/6 = 1 is integer.
6 is not divisible by 12
let n= 12
12/6 =2 is an integer
12 is divisible by 12
INSUFF
2. n/4 is an integer.
let n= 4
4/4 = 1 is integer.
4 is not divisible by 12
let n= 12
12/4 = 3 is an integer.
12 is divisible by 12
INSUFF

Combining:
n/6 is integer inplies n is multiple of 6
n/4 is an integer means n is multiple of 4
Hence n should be a multiple of LCM(6,4) = 12
SUFF

pick C
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by outreach » Sun Aug 01, 2010 5:42 am
C shd be correct
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by selango » Sun Aug 01, 2010 7:38 am
stmt1,

n/6 is an integer.

n=6a

n/12 is an integer if only a is even.

Insuff

stmt2,

n/4 is an integer.

n=4a

n/12 is an integer if only a is multiple of 3

Insuff

Combining 1 and 2,

n=6a,n=4a

LCM(4,6)=12

n=12a

Suff

Pick C
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