Bunuel wrote:
Of a group of 50 households, how many have at least one cat or at least one dog, but not both?
(1) The number of households that have at least one cat and at least one dog is 4.
(2) The number of households that have no cats and no dogs is 14.
We have a group of 50 households and need to determine how many of those households have at least one cat or at least one dog, but not both.
We can use the following formula:
total = # with at least one dog only + # with at least one cat only + # with both + # with neither
50 = # with at least one dog only + # with at least one cat only + # with both + # with neither
So, we need to determine # with at least one dog only + # with at least one cat only
Statement One Alone:
The number of households that have at least one cat and at least one dog is 4.
So, we have:
50 = # with at least one dog only + # with at least one cat only + 4 + # with neither
46 = # with at least one dog only + # with at least one cat only + # with neither
Since we don’t know the # with neither, we can not determine # with at least one dog only + # with at least one cat only. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
The number of households that have no cats and no dogs is 14.
So, we have:
50 = # with at least one dog only + # with at least one cat only + # with both + 14
36 = # with at least one dog only + # with at least one cat only + # with both
Since we don’t know the # with both, we cannot determine # with at least one dog only + # with at least one cat only. Statement two alone is not sufficient to answer the question.
Statements One and Two Together:
Using statements one and two, we have:
50 = # with at least one dog only + # with at least one cat only + 4 + 14
50 = # with at least one dog only + # with at least one cat only + 18
32 = # with at least one dog only + # with at least one cat only
Answer: C
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