I would go with A: 116

whats OA?

let distance be x

1 st person: speed = x/4
25<x/4<45 ............mulitply by 4
100<x<180

2nd peson: speed = x/2
45<x/2<60................multiply by 2
90<x<120

combinig the equations...............

100 < x < 120

leaves two choices, 116 and 118

116 divisible by 4, 118 is not

...........................................

A: between 100 and 180
B: between 90 and 120

Intersection: 100 - 120

I agree that 116 and 118 are only possible answers

but I disagree that 116 is the answer
I would call the question as incorrect
or may be we are missing something

It has not said that speed is an integer value
118 is also divisible by 4 but the ans is not interger

Please tell us the source of this question
think could be some typo

source is the GMAT Math tough problems file....

I believe answer could be 116 as well as 118. Since distance doesnt have to be integers, both the options meet the criteria. Though the source is legit but I am still not able to find a reasoning why one is better than the other.

Agreed that 118 is a valid answer

if I had to choose among 116, 118 - I would have taken 116!

that was the only reason why i went for 116.