If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 4.
II. x is an integer multiple of 3
III. x is an integer multiple of 6
Choose the correct choice from the following choices
A) a) I only  B) b) II only  C) c) I and II only  D) d) I and III only  E) e)II and III only
The answer should be D i.e. X will be an integer and multiple of 3 and 6.   Let us take example n, n+1, n+2 as 3 three consecutive positive integers.   In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12   Hence in a product of 3 consecutive integers, the product is always divisible by 3.   Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.   Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even   Answer e)II and III only
<result>E</result>
If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 4.
II. x is an integer multiple of 3
III. x is an integer multiple of 6