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05 Jan 2015, 06:59
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
82% (01:27) correct
18%
(01:32)
wrong
based on 279
sessions
History
Date
Time
Result
Not Attempted Yet
Tough and Tricky questions: Overlapping Sets.
In a group of 100 people, 40 study English and 30 study French. The number of people in the group who study neither language is twice the number of people who study both. How many people in the group study both languages?
A. 10
B. 20
C. 26
D. 30
E. 34
Kudos for a correct solution.
05 Jan 2015, 07:57
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The equation for this question is:
English + French - both + neither = 100
The rationale behind this equation is that by simply adding the students that study English and the students that study French, we double-count the students that study both, as they are part of both groups. We therefore have to subtract them again.
From that follows:
- both + neither = 30
- both + 2*both = 30
This is the information given in the question.
Then we get: both = 30
Answer D.
English + French - both + neither = 100
The rationale behind this equation is that by simply adding the students that study English and the students that study French, we double-count the students that study both, as they are part of both groups. We therefore have to subtract them again.
From that follows:
- both + neither = 30
- both + 2*both = 30
This is the information given in the question.
Then we get: both = 30
Answer D.
05 Jan 2015, 17:33
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Bunuel
Number of people in the group = 100
Number of people study both = x
Number of people who study neither = 2x
total number of people = 100 = (40-x) + (30-x) +2x+x
=> 100 = 70+x
x = 30
Ans D
