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06 Jun 2017, 02:37
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D
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There is a total of 400 students. 310 students participated in A, and 120 students participated in B. What is the number of students that participated in both A and B?
1) 24 students did not participate in either A or B.
2) 66 students participated only in B.
1) 24 students did not participate in either A or B.
2) 66 students participated only in B.
06 Jun 2017, 03:42
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MathRevolution
There is a total of 400 students. 310 students participated in A, and 120 students participated in B. What is the number of students that participated in both A and B?
1) 24 students did not participate in either A or B.
2) 66 students participated only in B.
1) 24 students did not participate in either A or B.
2) 66 students participated only in B.
There is a total of 4 categories
1) Participated in A only
2) Participated in B only
3) Participated in A and B both
4) Participated in None
Statement 1: 24 students did not participate in either A or B.
i e. Total participant = 400-24 = 376
Only B = 376-310=66
i.e. participated in both = 120-66 = 54
SUFFICIENT
Statement 2: 66 students participated only in B.
i.e. participated in both = 120-66 = 54
SUFFICIENT
Answer: option D
08 Jun 2017, 00:52
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==> If you modify the original condition and the question, you get a 2 by 2 as shown in the table below.
6.8.png [ 3.11 KiB | Viewed 1755 times ]
As shown above, from a+b+c+d=400, a+c=310, and a+b=120, there are 4 variables and 3 equations. In order to match the number of variables to the number of equations, there must be 1 more equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), from d=24, you get a=54, so con 1) = con 2), hence it is unique and sufficient.
The answer is D.
Answer: D
Attachment:
6.8.png [ 3.11 KiB | Viewed 1755 times ]
As shown above, from a+b+c+d=400, a+c=310, and a+b=120, there are 4 variables and 3 equations. In order to match the number of variables to the number of equations, there must be 1 more equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), from d=24, you get a=54, so con 1) = con 2), hence it is unique and sufficient.
The answer is D.
Answer: D
