190 students go to a school bake sale. 95 buy a chocolate

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

190 students go to a school bake sale. 95 buy a chocolate

by AAPL » Wed Dec 05, 2018 5:23 am

Timer

00:00

Your Answer

Global Stats

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.

Quote

Source: Beat The GMAT — Problem Solving | Wed Dec 05, 2018 5:23 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Wed Dec 05, 2018 1:50 pm

Hi All,

We're told that 190 students go to a school bake sale. Of those students, 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and AT LEAST 12 buy both. We're asked for the LEAST number of students who could have bought NEITHER type of cookie. This question is a variation on a standard Overlapping Sets question (although there is a 'twist'; AT LEAST 12 students bought both types of cookie), but we can still use the Overlapping Sets Formula:

Total = (1st group) + (2nd group) - (Both) + (Neither)

Based on the given information, the equation would look like this:

190 = (95) + (75) - (AT LEAST 12) + (Neither)
190 = 170 - (AT LEAST 12) + (Neither)
20 = (Neither) - (AT LEAST 12)

To minimize the "neither group", we have to make the "both" group as SMALL as possible. In this case, that would be exactly 12 people...

20 + 12 = Neither
32 = Neither

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Quote

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Wed Dec 05, 2018 6:07 pm

AAPL wrote: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

Excellent opportunity for the Venn diagram (aka overlapping sets)!

$$? = {\left( R \right)_{\min }}$$
$$R = 190 - \left( {95 + 75 - {\rm{both}}} \right) = 20 + {\rm{both}}$$
$${\rm{both}} \ge 12\,\,\,\left( {{\rm{given}}} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 32$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Mar 22, 2019 8:23 am

AAPL wrote: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.

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]