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At Lexington High School, each student studies at least one
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05 Aug 2018, 15:01
05 Aug 2018, 15:01
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Question Stats:
91% (01:21) correct
8% (01:46) wrong based on 70 sessions
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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
(A) 198
(B) 220
(C) 242
(D) 264
(E) 286
Re: At Lexington High School, each student studies at least one
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06 Aug 2018, 02:39
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
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
Re: At Lexington High School, each student studies at least one
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23 Aug 2018, 07:48
23 Aug 2018, 07:48
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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.
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.
