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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:
25%
(medium)
Question Stats:
83% (01:59) correct
17%
(02:42)
wrong
based on 48
sessions
History
Date
Time
Result
Not Attempted Yet
Language - Number of students
Arabic - 18
English - 16
French - 14
The table above shows the number of students at Adam Zachary High School who are proficient in Arabic, English and French. Three students know all these three languages, five students know Arabic and English only, six students know Arabic and French only and four students know English and French only. How many different students are there in the school?
A - 25
B - 26
C - 27
D - 28
E - 29
Arabic - 18
English - 16
French - 14
The table above shows the number of students at Adam Zachary High School who are proficient in Arabic, English and French. Three students know all these three languages, five students know Arabic and English only, six students know Arabic and French only and four students know English and French only. How many different students are there in the school?
A - 25
B - 26
C - 27
D - 28
E - 29
11 Jan 2022, 07:30
Kudos
Bookmarks
ALL= 18+16+14-(6+3+5+3+4+3) + 3 = 27
11 Jan 2022, 08:41
Kudos
Bookmarks
bacca2323
I approached the question slightly differently from the earlier poster but arrived at the same answer. Of course, there is only one way for a student to be proficient in all three languages. There are three ways (from 3C2) for a student to be proficient in two languages, and the problem tells us exactly how many students fit each of these combinations. Thus, we only need to figure out the duplicates and subtract to find the number of single-language-proficient students:
18 + 16 + 14 = 48
3 students * 3 languages = 9
5 students * 2 languages = 10
6 students * 2 languages = 12
4 students * 2 languages = 8
(Note that all students taking two languages could be combined upfront, as in, (5 + 6 + 4) * 2. The numbers will be the same.)
9 + 10 + 12 + 8 = 39
48 - 39 = 9 more students who must take a single language
9 (single language) + 15 (two languages) + 3 (three languages) = 27 students
The answer must be (C).
- Andrew
