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In a group of 50 students, 31 are taking French, 17 are taking Spanish
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17 Oct 2022, 05:41
17 Oct 2022, 05:41
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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
(A) 4
(B) 8
(C) 12
(D) 14
(E) 16
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GRE Math Essentials (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: In a group of 50 students, 31 are taking French, 17 are taking Spanish
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17 Oct 2022, 21:40
17 Oct 2022, 21:40
1
Expert Reply
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.
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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Joined: 10 Apr 2015
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Re: In a group of 50 students, 31 are taking French, 17 are taking Spanish
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18 Oct 2022, 07:10
18 Oct 2022, 07:10
1
Carcass 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
(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
Answer: B
This question type is VERY COMMON on the GRE, so be sure to master the technique.
To learn more about the Double Matrix Method, watch this video:
