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# In a group of 50 students, 31 are taking French, 17 are taking Spanish

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Re: In a group of 50 students, 31 are taking French, 17 are taking Spanish [#permalink]
Bunuel wrote:
In a group of 50 students, 31 are taking French, 17 are taking Spanish, and 10 are taking neither French nor Spanish. How many students are taking both French and Spanish?

A. 4
B. 8
C. 12
D. 14
E. 16

Total : 50

Neither = 10

Students taking either france or spanish = 40.

Total = france + spanish - both + neither

50 = 31 + 17 - both + 10

Both = 58 - 50

Both = 8.

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Re: In a group of 50 students, 31 are taking French, 17 are taking Spanish [#permalink]
Bunuel wrote:
In a group of 50 students, 31 are taking French, 17 are taking Spanish, and 10 are taking neither French nor Spanish. How many students are taking both French and Spanish?

A. 4
B. 8
C. 12
D. 14
E. 16

We can use the equation:

Total = French + Spanish - both + neither

50 = 31 + 17 - both + 10

50 = 58 - both

Both = 8

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Re: In a group of 50 students, 31 are taking French, 17 are taking Spanish [#permalink]
Let the no. of students taking both French and Spanish = x
31-x +17-x +x+10 =50
x=8
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Re: In a group of 50 students, 31 are taking French, 17 are taking Spanish [#permalink]
Bunuel wrote:
In a group of 50 students, 31 are taking French, 17 are taking Spanish, and 10 are taking neither French nor Spanish. How many students are taking both French and Spanish?

A. 4
B. 8
C. 12
D. 14
E. 16

10 are taking neither French nor Spanish = 50 - 40 , ie 10 Speak French and Spanish

Now, We know French = 31 & Spanish = 17

Thus, we have 40 = 31 + 17 - Both French and Spanish

Or, Both French and Spanish = 48 - 40 => 8, Answer must be (B)
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Re: In a group of 50 students, 31 are taking French, 17 are taking Spanish [#permalink]
We know 10 take neither French (F) nor Spanish (S).

So F only + S only + both = 40...(i)

(F Only + both) + (S only + both) = 31 + 17...(ii)

(ii) - (i) = 8
Re: In a group of 50 students, 31 are taking French, 17 are taking Spanish [#permalink]
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