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30 Jan 2024, 07:11
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E
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Difficulty:
25%
(medium)
Question Stats:
82% (01:57) correct
18%
(02:27)
wrong
based on 443
sessions
History
Date
Time
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All 15 members of a foreign language club speak one or more of three languages-Spanish, French, and German. If 1/3 of the members speak Spanish, 2/5 of the members speak French, 2/3 of the members speak German, and 1 member speaks all three of the languages, how many members speak exactly two of the languages?
A. 0
B. 1
C. 2
D. 3
E. 4
2024-01-30_18-08-01.png [ 48.2 KiB | Viewed 7893 times ]
A. 0
B. 1
C. 2
D. 3
E. 4
Attachment:
2024-01-30_18-08-01.png [ 48.2 KiB | Viewed 7893 times ]
30 Jan 2024, 07:28
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guddo
- 1/3 of the members speak Spanish, means 1/3 * 15 = 5 members speak Spanish
- 2/5 of the members speak French, means 2/5 * 15 = 6 members speak French
- 2/3 of the members speak German, means 2/3 * 15 = 10 members speak German
Adding these gives 5 + 6 + 10 = 21 members. However, the member who speaks all three languages is counted thrice, in each of the groups above, so we subtract 2 to count this member just once, resulting in 21 - 2 = 19 members.
The surplus of 4 members must be those who speak exactly two of the languages and thus are included twice in the count. Subtracting these once again so that those members are counted only once gives the total of 15.
Answer: E.
For a direct solution using formulas, check the following topics: ADVANCED OVERLAPPING SETS PROBLEMS
10 Mar 2025, 02:24
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guddo
Total = 15
All speak atleast 1 language
Spanish = (1/3)*15 = 5
French = (2/5)*15 = 6
German = (2/3)*15 = 10
Speak all = 1
Total = F+S+G-(two language speakers)-2*(three language speakers)
15 = 5+6+10 - (two language speakers) - 2*1
(two language speakers) = 4
Answer: Option E
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