Question

Kara did a survey to determine to study the types of pets that students in her school had. She surveyed 300 students and found that 40% of them had cats, 12% had both cats and dogs, and 45%

didn't have either. How many of the students that Kara surveyed had dogs?
1) 61
2) 71
3) 81
4) 91​

Answer 1

(C)81

Explanation:

Total Number of Students =300

Percentage who had cats, n(C) = 40%

Percentage who had both cats and dogs ,
`n(C \cap D)` = 12%

Percentage who had neither cats nor dogs,
`n(C \cup D)'` =45%

Now:

Universal Set,
`U = n(C)+n(D)-n(C \cap D)+n(C \cup D)'`

`100 = 40 + n(D)-12+45\\n(D)=100-73\\$Percentage of those who own dogs =27\%`

Therefore:

Number of Students who had dogs

=27% of 300

=81