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
Number Properties
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sl750
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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
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
