Ms. Banerjee's Mathematics Competition Team Selection
XAT 2014 · Decision Making · Hard · Decision Making
Passage / data set
Read the following case-let and answer the questions that follow:
Ms. Banerjee, class teacher for 12th standard, wants to send teams (based on past performance) of three students each to district, state, national, and international competition in mathematics. Till now, every student of the class has appeared in 100 school level tests. The students had following distribution of marks in the tests, in terms of "average" and "number of times a student scored cent per cent marks".
| Student | Average | Number of times scored cent per cent |
|---|---|---|
| 1 | 70 | 7 |
| 2 | 60 | 15 |
| 3 | 65 | 8 |
| 4 | 70 | 1 |
| 5 | 65 | 6 |
| 6 | 65 | 10 |
| 7 | 65 | 4 |
| 8 | 60 | 12 |
| 9 | 65 | 3 |
| 10 | 60 | 8 |
| 11 | 70 | 1 |
| 12 | 65 | 6 |
| 13 | 70 | 2 |
| 14 | 60 | 20 |
| 15 | 65 | 5 |
Ms. Banerjee has carefully studied chances of her school winning each of the competitions. Based on in-depth calculations, she realized that her school is quite likely to win district level competition but has low chances of winning the international competition. She listed down the following probabilities of wins for different competitions. Prize was highest for international competition and lowest for district level competition (in that order).
| Competition | Probability of win |
|---|---|
| District | 0.95 |
| State | 0.60 |
| National | 0.10 |
| International | 0.05 |
All the students are studying in the school for last twelve years. She wanted to select the best team for all four competitions (Ms. Banerjee had no other information to select students).
Question 1 of 3
Which of three members should form the team for the International competition?
- A.
4, 11, 14
- B.
2, 8, 14
- C.
1, 6, 12
- D.
13, 14, 15
- E.
1, 3, 4
B
Explanation
For international competitions where win probability is low, high peak performers (highest cent per cent scores: 14 with 20, 2 with 15, 8 with 12) are needed to maximize peak performance probability.
Question 2 of 3
Which of the following members should constitute the team for the district level competition?
- A.
4, 11, 14
- B.
1, 4, 11
- C.
4, 5, 6
- D.
4, 11, 13
- E.
Any team can win the competition
D
Explanation
For district competition with very high win probability, consistent top average scorers with low variability should be selected (4, 11, 13 all have high average of 70).
Question 3 of 3
Ms. Banerjee has to select the team for national competition after she has selected the team for international competition. A student selected for international competition cannot be a part of national competition. Which is the best team for the national competition?
- A.
1, 7, 4
- B.
8, 9, 10
- C.
2, 8, 14
- D.
3, 6, 1
- E.
Any of remaining students, as it would not matter
D
Explanation
After excluding 2, 8, 14, the best remaining high cent-per-cent and solid average performers are 6 (10 cent per cents), 3 (8 cent per cents), and 1 (7 cent per cents).
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