Consider the following for the next two (02) items that follow : Collect all the sequences of five consecutive integers such that their product is equal to one of these integers. Let X be the collection of all possible such sequences. Let P be the smallest integer and Q be the largest integer occurring in these sequences. How many such sequences of five consecutive integers are possible ?
- AOne
- BTwo
- CThree
- DFive
Explanation
If none of the five consecutive integers is 0, then |product| ≥ 1·2·3·4·5/... — in fact for |n| ≥ 3 the product's magnitude exceeds |n|+2, so it cannot equal any of the five numbers. Hence the product can equal one of the integers only when it is 0, i.e. when 0 is among the five. That happens for n ∈ {−2,−1,0,1,2}: five sequences. This is option (d).