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In a class of 40 students, 12 enrolled for both English and German. 22

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In a class of 40 students, 12 enrolled for both English and German. 22  [#permalink]

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New post 05 Oct 2010, 05:43
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In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?

A. 30
B. 10
C. 18
D. 28
E. 32
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Re: In a class of 40 students, 12 enrolled for both English and German. 22  [#permalink]

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New post 05 Oct 2010, 06:04
pzazz12 wrote:
In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?

A. 30
B. 10
C. 18
D. 28
E. 32


Total=English+German-Both+Neither --> 40=English+22-12+0 --> English=30 --> Only English=English-Both=30-12=18.

Answer: C.
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Re: In a class of 40 students, 12 enrolled for both English and German. 22  [#permalink]

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New post 05 Oct 2010, 07:37
i actually got A: 30

i solved as:

40 = G + E + N - B
40 = 22 + E + 0 - 12
E = 30

whats the OA?
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Re: In a class of 40 students, 12 enrolled for both English and German. 22  [#permalink]

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New post 05 Oct 2010, 07:39
Bunuel wrote:
pzazz12 wrote:
In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?

A. 30
B. 10
C. 18
D. 28
E. 32


Total=English+German-Both+Neither --> 40=English+22-12+0 --> English=30 --> Only English=English-Both=30-12=18.

Answer: C.


Hi Bunuel. Why would you subtract 12 from 30 if 30 already represents the students in one particular group?
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Re: In a class of 40 students, 12 enrolled for both English and German. 22  [#permalink]

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New post 05 Oct 2010, 07:44
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Re: In a class of 40 students, 12 enrolled for both English and German. 22  [#permalink]

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New post 05 Oct 2010, 08:13
Bunuel wrote:
azule45 wrote:
i actually got A: 30

i solved as:

40 = G + E + N - B
40 = 22 + E + 0 - 12
E = 30

whats the OA?


"How many students enrolled for only English and not German" so you should subtract from 30 students who enrolled for English students who enrolled also for German (who enrolled both for English and German): 30-12=18.

Hope it's clear.


ahh, true. i see now. so only 10 students are in German only, 12 both, and 18 in English only; adding to 40. Thanks.
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Re: In a class of 40 students, 12 enrolled for both English and German. 22  [#permalink]

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New post 05 Oct 2010, 08:20
Just a graphical representation of what the question means. It helps to drawn, especially for more complication questions. See attachment.
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Student Eng - German.pdf [10.71 KiB]
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Re: In a class of 40 students, 12 enrolled for both English and German. 22  [#permalink]

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New post 19 Apr 2011, 18:13
40 = 22 + English - 12

English = 30

Only English = 30 - 12 = 18

Answer - C
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Re: In a class of 40 students, 12 enrolled for both English and German. 22  [#permalink]

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New post 19 Apr 2011, 19:02
English but not german = 40- (12+10) = 18

Answer is C.
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Re: In a class of 40 students, 12 enrolled for both English and German. 22  [#permalink]

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New post 12 Sep 2016, 12:40
At least one subject implies Neither = 0

Eng + German + Both = 40
Both = 12
German + Both = 22
German only = 10
English only = 18
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Re: In a class of 40 students, 12 enrolled for both English and German. 22  [#permalink]

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New post 23 Jan 2018, 09:00
pzazz12 wrote:
In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?

A. 30
B. 10
C. 18
D. 28
E. 32


We can use the equation:

Total = Only German + Only English + Both + Neither

Since 22 enrolled in German and 12 enrolled in both, “Only German” is 22 - 12 = 10. Since all the students are enrolled for at least one of the two subjects, “Neither” is 0. So we have:

40 = 10 + E + 12 + 0

18 = E

Answer: C
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Re: In a class of 40 students, 12 enrolled for both English and German. 22   [#permalink] 23 Jan 2018, 09:00
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