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At Lexington High School, each student studies at least one

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GMAT Club Legend
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Joined: 07 Jun 2014
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At Lexington High School, each student studies at least one [#permalink] New post 05 Aug 2018, 15:01
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Question Stats:

88% (00:56) correct 11% (02:39) wrong based on 9 sessions
At Lexington High School, each student studies at least one language—Spanish, French, or Latin —and no student studies all three languages. If 100 students study Spanish, 80 study French, 40 study Latin, and 22 study exactly two languages, how many students are there at Lexington High School?

(A) 198
(B) 220
(C) 242
(D) 264
(E) 286
[Reveal] Spoiler: OA

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Re: At Lexington High School, each student studies at least one [#permalink] New post 06 Aug 2018, 02:39
Latin + spanish + French = 100 + 80 + 40 = 220
Since 22 students study exactly 2 subjects. If we reduce these students we get the number of total students without double counting anyone of them.
Hence total students at school = 220 - 22 = 198
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1659 [0], given: 396

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Re: At Lexington High School, each student studies at least one [#permalink] New post 23 Aug 2018, 07:48
Expert's post
Explanation

This overlapping sets question can be solved with the following equation:

Total # of people = Group 1 + Group 2 + Group 3 – (# of people in two groups) – (2)(# of people in all three groups) + (# of people in no groups)

The problem indicates that everyone studies at least one language, so the number of people in no groups is zero. The problem also indicates that nobody studies all three languages, so that value is also zero:

Total # of students = 100 + 80 + 40 – 22 – (2)(0) + 0 = 198.
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Re: At Lexington High School, each student studies at least one   [#permalink] 23 Aug 2018, 07:48
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