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25 Mar 2023, 01:02
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
64% (02:37) correct
36%
(02:46)
wrong
based on 408
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A certain language school offers courses in English, Hindi, and German. Last year, 1500 students enrolled in the school. Each student took at least one language course. 900 students enrolled in English, 750 enrolled in German, and 500 students enrolled in Hindi language courses. 75 students enrolled in both Hindi and English language courses only, 150 students enrolled in both German and English language courses only, and 175 students enrolled in both Hindi and German language courses only. How many students enrolled in all three language courses?
(A) 50
(B) 75
(C) 125
(D) 175
(E) 250
(A) 50
(B) 75
(C) 125
(D) 175
(E) 250
25 Mar 2023, 02:34
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ChandlerBong
Number of people taking only one course = \(E_1\)
Number of people taking exact two courses = \(E_2\)
Number of people taking exact three courses = \(E_3\)
Quote:
\(E_1 + E_2 + E_3 = 1500\) -- (1)
Quote:
\(E_1 + 2E_2 + 3E_3 = 900 + 750 + 500 = 2150\) -- (2)
Quote:
\(E_2 = 75 + 150 + 175 = 400\)
Substituting the value of \(E_2\) in equation (1) and equation (2) we get
\(E_1 + E_3 = 1100\) -- (4)
\(E_1 + 3E_3 = 1350\) -- (5)
Substracting (4) from (5)
\(2E_3 = 250 \)
\(E_3 = 125\)
Option C
14 Apr 2023, 13:08
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gmatophobia
Can you go into detail around your substituting the value of \(E_2\) in equation (1) and equation (2) and would you mind also referencing \(E_1 + 2E_2 + 3E_3 . Is that referencing either of the advanced overlapping sets formulas stated by Bunuel 's post here? --> https://gmatclub.com/forum/advanced-ove ... 44260.html
If not, please help me to understand the steps you're taking with these formulas.
Thanks and I appreciate your input!
Can you go into detail around your substituting the value of \(E_2\) in equation (1) and equation (2) and would you mind also referencing \(E_1 + 2E_2 + 3E_3 . Is that referencing either of the advanced overlapping sets formulas stated by Bunuel 's post here? --> https://gmatclub.com/forum/advanced-ove ... 44260.html
If not, please help me to understand the steps you're taking with these formulas.
Thanks and I appreciate your input!
