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

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

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New post 17 Oct 2018, 01:17
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A
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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  [#permalink]

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New post 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:
Image

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
Image

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

So, there are 8 students taking BOTH French and Spanish

Answer: B

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

To learn more about the Double Matrix Method, watch this video:

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

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New post 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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New post 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.

The best answer is 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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New post 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

Answer: 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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New post 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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New post 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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New post 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
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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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In a group of 50 students, 31 are taking French, 17 are taking Spanish

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