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

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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4720
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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190 students go to a school bake sale. 95 buy a chocolate ch [#permalink] New post 30 Dec 2017, 13:29
Expert's post
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Question Stats:

100% (00:45) correct 0% (00:00) wrong based on 2 sessions
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

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Question: 6
Page: 560

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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4720
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1622 [0], given: 385

CAT Tests
Re: 190 students go to a school bake sale. 95 buy a chocolate ch [#permalink] New post 03 Jan 2018, 16:48
Expert's post
Explanation

Substitute the given values into the groups equation: Total = Group 1 + Group 2 − Both + Neither. So 190 = 95 + 75 – 12 + N. N = 32.

If you pick a number larger than 12 to represent the number of students who buy both cookies, the number that buy neither cookie also increases.

The question asks for the least number that bought neither cookie, so the answer is choice D.
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Re: 190 students go to a school bake sale. 95 buy a chocolate ch [#permalink] New post 05 Jun 2018, 09:06
Expert's post
sandy 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


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 decreases as the number of students who purchase both kind 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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Re: 190 students go to a school bake sale. 95 buy a chocolate ch   [#permalink] 05 Jun 2018, 09:06
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190 students go to a school bake sale. 95 buy a chocolate ch

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