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In a group of 50 students, 31 are taking French, 17 are taki
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02 Feb 2020, 03:21
02 Feb 2020, 03:21
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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
Re: In a group of 50 students, 31 are taking French, 17 are taki
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02 Feb 2020, 03:22
02 Feb 2020, 03:22
Two important advanced overlapping rules:
# Total=A+B+C−(sum of 2−group overlaps)+(all three)+Neither.
# Total=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+Neither.
More about Advanced Overlapping Sets Problems
# Total=A+B+C−(sum of 2−group overlaps)+(all three)+Neither.
# Total=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+Neither.
More about Advanced Overlapping Sets Problems
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Re: In a group of 50 students, 31 are taking French, 17 are taki
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02 Feb 2020, 06:43
02 Feb 2020, 06:43
huda 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
To learn more about the Double Matrix Method, watch this video:
