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

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Math Expert
Joined: 02 Sep 2009
Posts: 59730
In a group of 50 students, 31 are taking French, 17 are taking Spanish  [#permalink]

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17 Oct 2018, 01:17
00:00

Difficulty:

5% (low)

Question Stats:

94% (01:00) correct 6% (00:51) wrong based on 110 sessions

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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

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

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Updated on: 17 Oct 2018, 07:59
Top Contributor
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

Let's use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- taking French or not taking French
- taking Spanish or not taking Spanish

From our given information, we can set up our matrix as follows:

Since there are 50 students altogether, we know that, if 31 are taking French then 19 are NOT taking French
And, if 17 are taking Spanish then 33 are NOT taking Spanish

When we fill in the rest of the matrix we get:

So, there are 8 students taking BOTH French and Spanish

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

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Originally posted by GMATPrepNow on 17 Oct 2018, 07:05.
Last edited by GMATPrepNow on 17 Oct 2018, 07:59, edited 1 time in total.
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Posts: 211
Re: In a group of 50 students, 31 are taking French, 17 are taking Spanish  [#permalink]

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17 Oct 2018, 07:18
F+S - F&S + None = 50

F + S - F&S = 40
F&S = 31+17-40 = 8
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Re: In a group of 50 students, 31 are taking French, 17 are taking Spanish  [#permalink]

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17 Oct 2018, 13:28
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]

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18 Oct 2018, 18:14
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]

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03 Nov 2019, 00:48
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]

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03 Nov 2019, 06:48
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]

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03 Nov 2019, 07:47
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] 03 Nov 2019, 07:47
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