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
coauthored 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
coauthorship chain connected to Erdös has an Erdös number of infinity.
In a seven day long miniconference 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 coauthored 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 coauthorship 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 coauthored 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 oneway 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
SAT (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
E. only 4
22. In how many ways a team can be constituted so that the team
includes N?
A. 2
B. 3
C. 4
D. 5
E. 6
23. What would be the size of the largest possible team?
A. 8
B. 7
C. 6
D. 5
E. Cannot be determined
24. Who can be a member of a team of size 5?
A. K
B. L
C. M
D. P
E. R
25. Who cannot be a member of a team of
size 3?
A. L
B. M
C. N
D. P
E. Q

