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19 Dec 2023, 05:27
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B
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Difficulty:
45%
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Question Stats:
77% (02:37) correct
23%
(03:09)
wrong
based on 182
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Each student in St. mary school studies either French, German, or both. There are 140 students who study French and 40% of the students study exactly one of these languages. If 10% of the students study only French, how many students study only German?
A) 20
B) 60
C) 80
D) 180
E) 200
A) 20
B) 60
C) 80
D) 180
E) 200
19 Dec 2023, 10:45
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udit0610
Since there are no students who study neither French nor German (so Neither = 0), we can write:
- {Total} = {Only French} + {Only German} + {Both}
It is given that {Only French} + {Only German} = 40% of the total and {Only French} = 10% of the total. Therefore, {Only German} = 30% of the total.
Furthermore, since 140 students study French, then {Only French} + {Both} = 140.
So, we get:
- {Total} = 140 + {Only German}
{Total} = 140 + 0.3{Total}
{Total} = 200
Hence, {Only German} = 0.3{Total} = 0.3*200 = 60.
Answer: B.
02 May 2025, 15:19
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| French | Not French | Total | |
| German | .6t | 60 | |
| Not German | .1t | 0 | |
| Total | 140 | 60 | 200 |
Each student studies either French, German, or both. In other words, no student falls under neither.
140 students study French
10 percent of total students study only French, not German. Assign the overall total as t.
40 percent of total students study one language so that means that 60 percent of total students study both French and German.
.6t + .1t = 140 but I prefer working with fractions.
6/10t + 1/10t = 140
7/10t = 140
t = 200
We can now subtract 140 from 200 to find out how many students don't speak French.
200 - 140 = 60
No students study neither so 60 - 0 = 60 students who study German but not French.
