MathRevolution wrote:
Is a positive integer n a multiple of 6?
1) n is the product of the 4 consecutive integers
2) n is a multiple of 12
Please reword statement 1 for clarity... anyways nice question OP
Stmnt 1
If N is the product of 4 consecutive integers then it must necessarily be a multiple of 6 - this is one of those things just like how the product of 3 consecutive integers is a multiple of 3
The statement isn't worded correctly but if you start with
1,2,3,4 for example you have 3 and 2 in there and you could go on infinitely - 2,3,4,5 ... etc and it would be a multiple of 6
Suff
Stmnt 2
Yes because
A multiple of 12n= 3 x 2 x 2 x some constant k
A multiple of 6n= 3 x 2 x some constant k
there's enough 3's and 2's in N according to stmnt 2 so
suff
D