This is a sample GRE question. The answer claims that we cannot make an inference due to insufficient information.
Compare the following quantities:
Of the 25 people in Fran’s apartment building, there are 9 residents who use the roof only for tanning and 8 residents who use the roof only for gardening. The roof is only used by tanners and gardeners.
Quantity A: The ratio of people who use the roof to total residents
Quantity B: 17:25
In this question, we do not know if there is any overlap between tanners and gardeners. How many, if any, residents do both activities? Since we don’t know, the relationship cannot be determined from the information given.
Given that this question specifies only, how can the answer imply that there may be an overlap? E.g. If I use the roof for tanning and gardening then I do not use the the roof only for tanning.
Thoughts?
We know that there are 9 people who only garden and 8 who only tan; that leaves 8 who might do both or might do neither. If all 8 of the leftover do neither, then the ratio is indeed 17:25 - but if all 8 do both, then the ratio is 25:25. Or if four of them do neither and four do both, the ratio is 21:25. As a matter of fact, for any integer $n$ between $17$ and $25$ inclusive we can come up with a scenario in which the ratio is $n$:25.