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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
62% (01:34) correct
38%
(02:14)
wrong
based on 99
sessions
History
Date
Time
Result
Not Attempted Yet
In a group of 150, 70 speak English, 90 speak German, and 60 speak French. If 40 speak English and German, 30 speak French and German, 25 speak English and French, and 5 speak all the three, how many speak exactly two of the three languages?
A. 50
B. 60
C. 70
D. 80
E. 90
A. 50
B. 60
C. 70
D. 80
E. 90
26 Feb 2026, 04:24
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First, we calculate how many people speak at least one language.
Total Individual counts: 70 + 90 + 60 = 220
Minus the pairs: 40 + 30 + 25 = 95
Plus the three-language speakers: 5
Calculation: 220 - 95 + 5 = 130
(This 130 is the number of people who speak at least one language. The remaining 20 people out of the 150 speak none.)
Union = (Sum of Individuals) - (Exactly 2) - 2 × (All 3)
Union: 130
Sum of Individuals: 220
2 × (All 3): 2 × 5 = 10
The Equation:
130 = 220 - (Exactly 2) - 10
130 = 210 - (Exactly 2)
Exactly 2 = 210 - 130
Exactly 2 = 80
Total Individual counts: 70 + 90 + 60 = 220
Minus the pairs: 40 + 30 + 25 = 95
Plus the three-language speakers: 5
Calculation: 220 - 95 + 5 = 130
(This 130 is the number of people who speak at least one language. The remaining 20 people out of the 150 speak none.)
Union = (Sum of Individuals) - (Exactly 2) - 2 × (All 3)
Union: 130
Sum of Individuals: 220
2 × (All 3): 2 × 5 = 10
The Equation:
130 = 220 - (Exactly 2) - 10
130 = 210 - (Exactly 2)
Exactly 2 = 210 - 130
Exactly 2 = 80
Updated on: 26 Feb 2026, 08:57
Originally posted by gmatftw777 on 26 Feb 2026, 04:26.
Last edited by gmatftw777 on 26 Feb 2026, 08:57, edited 1 time in total.
Last edited by gmatftw777 on 26 Feb 2026, 08:57, edited 1 time in total.
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English & German only: 40-5= 35
German & French only: 30-5= 25
English & French only: 25-5= 20
Total (Exactly two): 35+25+20= 80 (D)
German & French only: 30-5= 25
English & French only: 25-5= 20
Total (Exactly two): 35+25+20= 80 (D)
