How many integers are there such that v<n<w?
(1) v and w are positive integers?
How is it even possible that v<w when v-w=4?
The question stem seems to ask how many integral triplets exists which are bound by v<n<w?
Whereas the intent is to ask how many integral values of n
exist such that v<n<w ?
Only if we are interested in finding the no. of integral values n can take then we can get the answer
by combining 1&2 (as Bunnel stated)
But if we are interested in finding integers then obeying 1&2 we can take any natural no. as v and accordingly our w will get fixed and then we can choose any 3 no.s between w and v to get n.So infinite no. of triplets can be formed.
@Bunnel: I would be thankful if you clarify