Official Solution: Bunuel
In a recent neighborhood survey, fewer than 170 households were surveyed regarding pet ownership. Of those, 150 households reported owning a dog, while 95 households reported owning a cat.
In the table, select for
At least one the number of households that own at least one of a dog or a cat, and select for
Both the number of households that own both a dog and a cat that would be jointly consistent with the given information. Make only two selections, one in each column.
Given that 150 households own a dog and 95 own a cat, we have:
At least one = 150 + 95 − Both = 245 − Both.
Thus, we need two options for At least one (245 − Both) and Both, such that their sum is 245.
From the options, two pairs satisfy this condition for (At least one, Both): (170, 75) and (150, 95). However, since fewer than 170 households were surveyed, At least one cannot be 170. Therefore, the only valid pair is
(At least one, Both) = (150, 95).
Correct answer: At least one
"150"Both
"95"