GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
At Lexington High School, each student studies at least one
[#permalink]
05 Aug 2018, 15:01
05 Aug 2018, 15:01
2
Expert Reply
3
Bookmarks
00:00
Question Stats:
91% (01:21) correct
8% (01:46) wrong based on 73 sessions
Hide Show timer Statistics
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
[#permalink]
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
[#permalink]
23 Aug 2018, 07:48
23 Aug 2018, 07:48
1
Expert Reply
1
Bookmarks
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.
