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190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 12...

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by AAPL » Thu Nov 19, 2020 5:15 am
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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

OA D
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Re: 190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 1

by Scott@TargetTestPrep » Mon Nov 30, 2020 9:25 am
AAPL wrote: ↑
Thu Nov 19, 2020 5:15 am
 Princeton Review

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

OA D
Solution:

We can use the equation:

#total = #chocolate chip + #peanut butter - #both + #neither

#neither = #total - #chocolate chip - #peanut butter + #both

As we can see from the equation, keeping everything else constant, the number of students who purchase neither kind of cookie decreases as the number of students who purchase both kinds decreases. Therefore, to minimize #neither, we should minimize #both:

190 = 95 + 75 - 12 + neither

190 = 158 + neither

32 = neither

Answer: D

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