LR - Selection & Distribution - Previous Year CAT/MBA Questions
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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”.
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).
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).
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
Answer: Option B
Text Explanation :
The probability of winning in the international competition is very less (5%). So the students selected for it should have a greater chance of scoring cent percent.
Option (1) is eliminated because 4 & 11 score cent percent just once.
In option (2), the combined number of times cent percent is scored is 15 + 12 + 20 = 47
In option (3), the combined number of times cent percent is scored is 7 + 10 + 6 = 23
In option (4), 2 of the members score cent percent less number of times. Combined cent percent is 2 + 20 + 5 = 27
In option (5), the combined number of times cent percent is scored is 7 + 8 + 1 = 16
Hence, option (b).
Workspace:
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
Answer: Option D
Text Explanation :
The probability of winning in the district level competition is high (95%).
So Ms. Banerjee needs to select students who have high averages.
The number of times the students score cent percent is not important.
Students 4 & 11 have high an average of 70 and they score cent percent just once.
So option (1) is eliminated as it has student 14 who has scored cent percent 20 times.
Similarly, option (3) is also eliminated. In options (2) and (4), we select option (4) as the correct option because both students 1 & 13 have the same average but student 13 scores cent percent just twice.
Hence, option (d).
Workspace:
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
Answer: Option D
Text Explanation :
A student selected for international competition cannot be selected for national competition. So, students 2, 8 and 14 cannot be a part of national team. The probability of winning in the national competition is 10%. So, here the stress should be on the number of times cent percent is scored.
Also, the students with higher averages are preferred.
Option (1) has students having high averages but lesser cent percent scores.
Option (2) has students having lower average scores like 60.
Option (3) has all the students having an average score of 60.
Option (4) has students having higher averages of 65 and 70. Also, their combined cent percent scores is very high, 8 + 10 + 7 = 25.
Hence, option (d).
Workspace:
Lionel and Ronaldo had a discussion on the ages of Jose’s sons. Ronaldo made following statements about Jose’s sons:
- Jose has three sons.
- The sum of the ages of Jose’s sons is 13.
- The product of the ages of the sons is the same as the age of Lionel.
- Jose’s eldest son, Zizou weighs 32 kilos.
- The sum of the ages of the younger sons of Jose is 4.
- Jose has fathered a twin.
- Jose is not the father of a triplet.
- The LCM of the ages of Jose’s sons is more than the sum of their ages.
Which of the following combination gives information sufficient to determine the ages of Jose’s sons?
- (a)
i, ii, iii and iv
- (b)
i, ii, iv and vi
- (c)
i, ii, iii and v
- (d)
i, ii, v and vii
- (e)
i, ii, v and vi
Answer: Option E
Text Explanation :
Consider each option separately,
Consider option A:
In this case, we don’t know the Lionel’s age.
Hence, the only conclusion can be derived is;
Jose has 3 sons and sum of their age is 13.
Consider option B:
In this case also, we only know that Jose has 3 sons and sum of their ages is 13 and two of them are twin.
But it still doesn’t provide adequate information to calculate age of each son.
Consider option C:
As, age of Lionel is not known, we only know that the sum of ages of Jose’s three son is 13 out of which sum of the age of the younger two brother is 4.
By this we can calculate age of the Jose’s eldest son, but we cannot age of the remaining two children.
Consider option D:
In this case, statement 7 is redundant, as by statement 2 only we can guess that Jose is not the father of a triplet.
Hence this statement doesn’t provide adequate information to guess the ages of all the three children.
Consider option E:
By, i, ii and iii, we can conclude that the age of the Jose’s eldest son is 9 and sum of the other two children is 4.
Now, by statement vi, Jose has fathered twins, we can easily conclude that the younger two children are twins.
Hence, their ages are 2 and 2 respectively.
Hence, E is sufficient to answer.
Hence, option (e).
Workspace:
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