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Number Properties

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Source: — Data Sufficiency |
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by GmatKiss » Tue Oct 04, 2011 8:23 am
1) x can be 3,6,9.....333,336,339 and so on!

if you solve , not all (x)(x + 2)(x + 4) will be divisible by 12 - Not- sufficient

2) x must be even and it can be 2,4,6,8... and so on!

if you solve , all (x)(x + 2)(x + 4) will be divisible by 12 - sufficient

IMO:B
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by sl750 » Tue Oct 04, 2011 9:53 am
We have a consecutive sequence of 3 numbers having a difference of 2 between every successive number

Statement 1

x^2+2x is a multiple of 3 or 3 is a factor of x(x+2). From this we don't know whether x+4 will have two factors of 2. For example, x=1, x(x+2)(x+4) is not divisible by 12. For x=4, x(x+2)(x+4) is divisible by 12. Not sufficient

Statement 2
3x is a multiple of 2 or 2 is a factor of 3x, this makes x an even number. So the sequence, x(x+2)(x+4) will be a consecutive sequence of even numbers. For a consecutive sequence of three numbers we are sure to have one factor of 3, since this sequence is also an even sequence we have two factors of 2 as well. Example x=2, 2*4*6 has a factor of 3 and 4. Divisible. For x=6, 6*8*12 is divisible by 12. Sufficient
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