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
190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 12...
This topic has expert replies
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7249
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Solution:AAPL wrote: ↑Thu Nov 19, 2020 5:15 amPrinceton 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
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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews