BTGmoderatorDC wrote:190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 12 buy both. What is the least number of students who could have bought neither type of cookie?
A. 10
B. 24
C. 30
D. 32
E. 45
Total = Group 1 + Group 2 - Both + Neither
Here:
Total = 190.
Group 1 = 95 who buy chocolate chip.
Group 2 = 75 who buy peanut butter.
Plugging these values into the equation above, we get:
190 = 95 + 75 - Both + Neither
20 + Both = Neither
Neither = 20 + Both.
To minimize the value of Neither, we must minimize the value of Both.
Since the least possible number who buy both types of cookies = 12, we get:
Least possible number who buy neither = 20 + 12 = 32.
The correct answer is
D.
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