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Reasoning CAT

Data Interpretation & Reasoning CAT 2006

Directions for Questions 1 to 5: Use following data to answer:

In a Class X Board examination, ten papers are distributed over five Groups – PCB, Mathematics, Social Science, Vernacular and English. Each of the ten papers is evaluated out of 100. The final score of a student is calculated in the following manner. First, the Group Scores are obtained by averaging marks in the papers within the Group. The final score is the simple average of the Group Scores. The data for the top ten students are presented below.

1. How much did Dipan get in English Paper II?

A. 94

B. 96.5

C. 97

D. 98

E. 99

2. Students who obtained Group Scores of at least 95 in every group are eligible to apply for a prize. Among those who are eligible, the student obtaining the highest Group Score in Social Science Group is awarded this prize. The prize was awarded to:

A. Shreya

B. Ram

C. Ayesha

D. Dipan

E. None from the top ten

3. Among the top ten students, how many boys scored at least 95 in at least one paper from each of the groups?

A. 1

B. 2

C. 3

D. 4

E. 5

4. Each of the ten students was allowed to improve his/her score in exactly one paper of choice with the objective of maximizing his/her final score. Everyone scored 100 in the paper in which he or she chose to improve. After that, the topper among the ten students was:

A. Ram

B. Agni

C. Pritam

D. Ayesha

E. Dipan

5. Had Joseph, Agni, Pritam and Tirna each obtained Group Score of 100 in the Social Science Group, then their standing in decreasing order of final score would be:

A. Pritam, Joseph, Tirna, Agni

B. Joseph, Tirna, Agni, Pritam

C. Pritam, Agni, Tirna, Jospeh

D. Joseph, Tirna, Pritam, Agni

E. Pritam, Tirna, Agni, Joseph

Directions for Questions 6 to 10

Mathematicians are assigned a number called Erdös number, (named after the famous mathematician, Paul Erdös). Only Paul Erdös himself has an Erdös number of zero. Any mathematician who has written a research paper with Erdös has an Erdös number of 1. For other mathematicians, the calculation of his/her Erdös number is illustrated below: Suppose that a mathematician X has co-authored papers with several other mathematicians. From among them, mathematician Y has the smallest Erdös number. Let the Erdös number of Y be y. Then X has an Erdös number of y + 1. Hence any mathematician with no co-authorship chain connected to Erdös has an Erdös number of infinity.

In a seven day long mini-conference organized in memory of Paul Erdös, a close group of eight mathematicians, call them A, B, C, D, E, F, G and H, discussed some research problems. At the beginning of the conference, A was the only participant who had an infinite Erdös number. Nobody had an Erdös number less than that of F.

On the third day of the conference F co-authored a paper jointly with A and C. This reduced the average Erdös number of the group of eight mathematicians to 3. The Erdös numbers of B, D, E, G and H remained unchanged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Erdös number of the group of eight to as low as 3.

At the end of the third day, five members of this group had identical Erdös numbers while the other three had Erdös numbers distinct from each other.

On the fifth day, E co-authored a paper with F which reduced the group‘s average Erdös number by 0.5. The Erdös numbers of the remaining six were unchanged with the writing of this paper.

No other paper was written during the conference.

6. The person having the largest Erdös number at the end of the conference must have had Erdös number (at that time):

A. 5

B. 7

C. 9

D. 14

E. 15

7. How many participants in the conference did not change their Erdös number during the conference?

A. 2

B. 3

C. 4

D. 5

E. Cannot be determined

8. The Erdös number of C at the end of the conference was:

A. 1

B. 2

C. 3

D. 4

E. 5

9. The Erdös number of E at the beginning of the conference was:

A. 2

B. 5

C. 6

D. 7

E. 8

10. How many participants had the same Erdös number at the beginning of the conference?

A. 2

B. 3

C. 4

D. 5

E. Cannot be determined

Directions for Questions 11 to 15

Two traders, Chetan and Michael, were involved in the buying and selling of MCS shares over five trading days. At the beginning of the first day, the MCS share was priced at Rs. 100, while at the end of the fifth day it was priced at Rs. 110. At the end of each day, the MCS share price either went up by Rs. 10, or else, it came down by Rs. 10. Both Chetan and Michael took buying and selling decisions at the end of each trading day.

The beginning price of MCS share on a given day was the same as the ending price of the previous day.

Chetan and Michael started with the same number of shares and amount of cash, and had enough of both. Below are some additional facts about how Chetan and Michael traded over the five trading days.

Each day if the price went up, Chetan sold 10 shares of MCS at the closing price. On the other hand, each day if the price went down, he bought 10 shares at the closing price.

If on any day, the closing price was above Rs. 110, then Michael sold 10 shares of MCS, while if it was below Rs. 90, he bought 10 shares, all at the closing price.

11. If Chetan sold 10 shares of MCS on three consecutive days, while Michael sold 10 shares only once during the five days, what was the price of MCS at the end of day 3?

A. 90

B. 100

C. 110

D. 120

E. 130

12. If Michael ended up with Rs. 100 less cash than Chetan at the end of day 5, what was the difference in the number of shares possessed by Michael and Chetan (at the end of day 5)?

A. Michael had 10 shares less than Chetan

B. Michael had 10 shares more than Chetan

C. Chetan had 10 more shares than Michael

D. Chetan had 20 more hsares than Michael

C. Both had same number of shares

13. If Chetan ended up with Rs. 1300 more cash than Michael at the end of day 5, what was the price of MCS share at the end of day 4?

A. 90

B. 100

C. 110

D.120

E. Cannot be determined

14. What could have been the maximum possible increase in combined cash balance for Michael and Chetan at the end of the fifth day?

A. 3700

B. 4000

C. 4700

D. 5000

E. 6000

15. If Michael ended up with 20 more shares than Chetan at the end of day 5,

what was the price of shares at the end of day three?

A. 90

B. 100

C. 110

D. 120

E. 130

Directions for Questions 16 to 20

A significant amount of traffic flows from point S to point T in the one-way street network shown below. Points A, B, C, and D are junctions in the network, and the arrows mark the direction of traffic flow. The fuel cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the street.

Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling is the minimum. If two or more routes have the same least travel cost, then motorists are indifferent between them. Hence, the traffic gets evenly distributed among all the least cost routes.

The government can control the flow of traffic only by levying appropriate toll at each junction. For example, if a motorist takes the route S-A-T (using junction A alone), then the total cost of travel would be Rs. 14 (i.e. Rs. 9 + Rs. 5) plus the toll charged at junction A.

16. If the government wants to ensure that all motorists travelling from S to T pay the same amount (fuel costs and toll combined) regardless of the route they choose and the street from B to C is under repairs (and hence unusable), then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

A. 2, 5, 3, 2

B. 0, 5, 3, 1

C. 1, 5, 3, 2

D. 2, 3, 5, 1

E. 1, 3, 5, 1

17. If the government wants to ensure that no traffic flows on the street from D to T, while equal amount of traffic flows through junctions A and C, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

A. 1, 5, 3, 3

B. 1, 4, 4, 3

C. 1, 5, 4, 2

D. 0, 5, 2, 3

E. 0, 5, 2, 2

18. If the government wants to ensure that all routes from S to T get the same amount of traffic, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

A. 0, 5, 2, 2

B. 0, 5, 4, 4

C. 1, 5, 3, 3

D. 1, 5, 3, 2

E. 1, 5, 4, 2

19. If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to A, from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

A. 0, 5, 4, 1

B. 0, 5, 2, 2

C. 1, 5, 3, 3

D. 1, 5, 3, 2

E, 0, 4, 3, 2

20. The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70% per cent of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to point T under this policy will be:

A. Rs. 7

B. Rs. 9

C. Rs. 10

D. Rs. 13

E. Rs. 14

Directions for Questions 21 to 25

K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:

A team must include exactly one among P, R, and S.

A team must include either M or Q, but not both.

If a team includes K, then it must also include L, and vice versa.

If a team includes one among S, U, and W, then it must also include the other two

L and N cannot be members of the same team.

L and U cannot be members of the same team.

The size of a team is defined as the number of members in the team.

21. What could be the size of a team that includes K?

A. 2 or 3

B. 2 or 4

C. 3 or 4

D. only 2