CAT Past Year Question Paper - 2006 | Additional Study Material for CAT PDF Download

 Page 1


Directions for questions 1 to 5: Answer the questions on the basis of the information given below:
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:
1. A team must include exactly one among P, R, and S.
2. A team must include either M or Q, but not both.
3. If a team includes K, then it must also include L, and vice versa.
4. If a team includes one among S, U, and W, then it must also include the other two.
5. L and N cannot be members of the same team.
6. 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.
1. Who cannot be a member of a team of size 3?
(1) L (2) M (3) N (4) P (5) Q
2. Who can be a member of a team of size 5?
(1) K (2) L (3) M (4) P (5) R
3. What would be the size of the largest possible team?
(1) 8 (2) 7 (3) 6 (4) 5 (5) Cannot be determined
4. What could be the size of a team that includes K?
(1) 2 or 3 (2) 2 or 4 (3) 3 or 4 (4) Only 2 (5) Only 4
5. In how many ways a team can be constituted so that the team includes N?
(1) 2 (2) 3 (3) 4 (4) 5 (5) 6

	



Instructions:
1. The Test Paper contains 75 questions. The duration of the test is 150 minutes.
2. The paper is divided into three sections. Section-I: 25 Q:, Section-II: 25 Q:, Section-III: 25 Q.
3. Wrong answers carry negative marks. There is only one correct answer for each question.
Page 2


Directions for questions 1 to 5: Answer the questions on the basis of the information given below:
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:
1. A team must include exactly one among P, R, and S.
2. A team must include either M or Q, but not both.
3. If a team includes K, then it must also include L, and vice versa.
4. If a team includes one among S, U, and W, then it must also include the other two.
5. L and N cannot be members of the same team.
6. 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.
1. Who cannot be a member of a team of size 3?
(1) L (2) M (3) N (4) P (5) Q
2. Who can be a member of a team of size 5?
(1) K (2) L (3) M (4) P (5) R
3. What would be the size of the largest possible team?
(1) 8 (2) 7 (3) 6 (4) 5 (5) Cannot be determined
4. What could be the size of a team that includes K?
(1) 2 or 3 (2) 2 or 4 (3) 3 or 4 (4) Only 2 (5) Only 4
5. In how many ways a team can be constituted so that the team includes N?
(1) 2 (2) 3 (3) 4 (4) 5 (5) 6

	



Instructions:
1. The Test Paper contains 75 questions. The duration of the test is 150 minutes.
2. The paper is divided into three sections. Section-I: 25 Q:, Section-II: 25 Q:, Section-III: 25 Q.
3. Wrong answers carry negative marks. There is only one correct answer for each question.
Directions for questions 6 to 10: Answer questions on the basis of the information given below:
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. (Dipan's score in English Paper II has been intentionally removed in the
table.)
PCB Group 
Social 
Science 
Group 
Vernacular 
Group 
English Group Name of the 
student 
Phy. Chem. Bio. 
Mathematics 
Group 
Hist. Geo. Paper I Paper II Paper I Paper II 
Final 
Score 
Ayesha (G) 98 96 97 98 95 93 94 96 96 98 96.2 
Ram (B) 97 99 95 97 95 96 94 94 96 98 96.1 
Dipan (B) 98 98 98 95 96 95 96 94 96 ?? 96.0 
Sagnik (B) 97 98 99 96 96 98 94 97 92 94 95.9 
Sanjiv (B) 95 96 97 98 97 96 92 93 95 96 95.7 
Shreya (G) 96 89 85 100 97 98 94 95 96 95 95.5 
Joseph (B) 90 94 98 100 94 97 90 92 94 95 95 
Agni (B) 96 99 96 99 95 96 82 93 92 93 94.3 
Pritam (B) 98 98 95 98 83 95 90 93 94 94 93.9 
Tirna (G) 96 98 97 99 85 94 92 91 87 96 93.7 
Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl.
6. How much did Dipan get in English Paper II?
(1) 94 (2) 96.5 (3) 97 (4) 98 (5) 99
7. Among the top ten students, how many boys scored at least 95 in at least one paper from each of
the groups?
(1) 1 (2) 2 (3) 3 (4) 4 (5) 5
8. 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:
(1) Pritam, Joseph, Tirna, Agni (2) Joseph, Tirna, Agni, Pritam
(3) Pritam, Agni, Tirna, Joseph (4) Joseph, Tirna, Pritam, Agni
(5) Pritam, Tirna, Agni, Joseph
Page 3


Directions for questions 1 to 5: Answer the questions on the basis of the information given below:
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:
1. A team must include exactly one among P, R, and S.
2. A team must include either M or Q, but not both.
3. If a team includes K, then it must also include L, and vice versa.
4. If a team includes one among S, U, and W, then it must also include the other two.
5. L and N cannot be members of the same team.
6. 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.
1. Who cannot be a member of a team of size 3?
(1) L (2) M (3) N (4) P (5) Q
2. Who can be a member of a team of size 5?
(1) K (2) L (3) M (4) P (5) R
3. What would be the size of the largest possible team?
(1) 8 (2) 7 (3) 6 (4) 5 (5) Cannot be determined
4. What could be the size of a team that includes K?
(1) 2 or 3 (2) 2 or 4 (3) 3 or 4 (4) Only 2 (5) Only 4
5. In how many ways a team can be constituted so that the team includes N?
(1) 2 (2) 3 (3) 4 (4) 5 (5) 6

	



Instructions:
1. The Test Paper contains 75 questions. The duration of the test is 150 minutes.
2. The paper is divided into three sections. Section-I: 25 Q:, Section-II: 25 Q:, Section-III: 25 Q.
3. Wrong answers carry negative marks. There is only one correct answer for each question.
Directions for questions 6 to 10: Answer questions on the basis of the information given below:
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. (Dipan's score in English Paper II has been intentionally removed in the
table.)
PCB Group 
Social 
Science 
Group 
Vernacular 
Group 
English Group Name of the 
student 
Phy. Chem. Bio. 
Mathematics 
Group 
Hist. Geo. Paper I Paper II Paper I Paper II 
Final 
Score 
Ayesha (G) 98 96 97 98 95 93 94 96 96 98 96.2 
Ram (B) 97 99 95 97 95 96 94 94 96 98 96.1 
Dipan (B) 98 98 98 95 96 95 96 94 96 ?? 96.0 
Sagnik (B) 97 98 99 96 96 98 94 97 92 94 95.9 
Sanjiv (B) 95 96 97 98 97 96 92 93 95 96 95.7 
Shreya (G) 96 89 85 100 97 98 94 95 96 95 95.5 
Joseph (B) 90 94 98 100 94 97 90 92 94 95 95 
Agni (B) 96 99 96 99 95 96 82 93 92 93 94.3 
Pritam (B) 98 98 95 98 83 95 90 93 94 94 93.9 
Tirna (G) 96 98 97 99 85 94 92 91 87 96 93.7 
Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl.
6. How much did Dipan get in English Paper II?
(1) 94 (2) 96.5 (3) 97 (4) 98 (5) 99
7. Among the top ten students, how many boys scored at least 95 in at least one paper from each of
the groups?
(1) 1 (2) 2 (3) 3 (4) 4 (5) 5
8. 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:
(1) Pritam, Joseph, Tirna, Agni (2) Joseph, Tirna, Agni, Pritam
(3) Pritam, Agni, Tirna, Joseph (4) Joseph, Tirna, Pritam, Agni
(5) Pritam, Tirna, Agni, Joseph
9. 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:
(1) Shreya (2) Ram
(3) Ayesha (4) Dipan
(5) No one from the top ten
10. 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:
(1) Ram (2) Agni (3) Pritam (4) Ayesha (5) Dipan
Directions for questions 11 to 15: Answer the questions on the basis of the information given below:
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 mathema-
ticians, 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.
1 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.
2 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.
3 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.
4 No other paper was written during the conference.
11. How many participants in the conference did not change their Erdös number during the conference?
(1) 2 (2) 3 (3) 4 (4) 5 (5) Cannot be determined
Page 4


Directions for questions 1 to 5: Answer the questions on the basis of the information given below:
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:
1. A team must include exactly one among P, R, and S.
2. A team must include either M or Q, but not both.
3. If a team includes K, then it must also include L, and vice versa.
4. If a team includes one among S, U, and W, then it must also include the other two.
5. L and N cannot be members of the same team.
6. 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.
1. Who cannot be a member of a team of size 3?
(1) L (2) M (3) N (4) P (5) Q
2. Who can be a member of a team of size 5?
(1) K (2) L (3) M (4) P (5) R
3. What would be the size of the largest possible team?
(1) 8 (2) 7 (3) 6 (4) 5 (5) Cannot be determined
4. What could be the size of a team that includes K?
(1) 2 or 3 (2) 2 or 4 (3) 3 or 4 (4) Only 2 (5) Only 4
5. In how many ways a team can be constituted so that the team includes N?
(1) 2 (2) 3 (3) 4 (4) 5 (5) 6

	



Instructions:
1. The Test Paper contains 75 questions. The duration of the test is 150 minutes.
2. The paper is divided into three sections. Section-I: 25 Q:, Section-II: 25 Q:, Section-III: 25 Q.
3. Wrong answers carry negative marks. There is only one correct answer for each question.
Directions for questions 6 to 10: Answer questions on the basis of the information given below:
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. (Dipan's score in English Paper II has been intentionally removed in the
table.)
PCB Group 
Social 
Science 
Group 
Vernacular 
Group 
English Group Name of the 
student 
Phy. Chem. Bio. 
Mathematics 
Group 
Hist. Geo. Paper I Paper II Paper I Paper II 
Final 
Score 
Ayesha (G) 98 96 97 98 95 93 94 96 96 98 96.2 
Ram (B) 97 99 95 97 95 96 94 94 96 98 96.1 
Dipan (B) 98 98 98 95 96 95 96 94 96 ?? 96.0 
Sagnik (B) 97 98 99 96 96 98 94 97 92 94 95.9 
Sanjiv (B) 95 96 97 98 97 96 92 93 95 96 95.7 
Shreya (G) 96 89 85 100 97 98 94 95 96 95 95.5 
Joseph (B) 90 94 98 100 94 97 90 92 94 95 95 
Agni (B) 96 99 96 99 95 96 82 93 92 93 94.3 
Pritam (B) 98 98 95 98 83 95 90 93 94 94 93.9 
Tirna (G) 96 98 97 99 85 94 92 91 87 96 93.7 
Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl.
6. How much did Dipan get in English Paper II?
(1) 94 (2) 96.5 (3) 97 (4) 98 (5) 99
7. Among the top ten students, how many boys scored at least 95 in at least one paper from each of
the groups?
(1) 1 (2) 2 (3) 3 (4) 4 (5) 5
8. 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:
(1) Pritam, Joseph, Tirna, Agni (2) Joseph, Tirna, Agni, Pritam
(3) Pritam, Agni, Tirna, Joseph (4) Joseph, Tirna, Pritam, Agni
(5) Pritam, Tirna, Agni, Joseph
9. 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:
(1) Shreya (2) Ram
(3) Ayesha (4) Dipan
(5) No one from the top ten
10. 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:
(1) Ram (2) Agni (3) Pritam (4) Ayesha (5) Dipan
Directions for questions 11 to 15: Answer the questions on the basis of the information given below:
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 mathema-
ticians, 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.
1 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.
2 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.
3 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.
4 No other paper was written during the conference.
11. How many participants in the conference did not change their Erdös number during the conference?
(1) 2 (2) 3 (3) 4 (4) 5 (5) Cannot be determined
12. The person having the largest Erdös number at the end of the conference must have had Erdös
number (at that time):
(1) 5 (2) 7 (3) 9 (4) 14 (5) 15
13. How many participants had the same Erdös number at the beginning of the conference?
(1) 2 (2) 3 (3) 4 (4) 5 (5) Cannot be determined
14. The Erdös number of C at the end of the conference was:
(1) 1 (2) 2 (3) 3 (4) 4 (5) 5
15. The Erdös number of E at the beginning of the conference was:
(1) 2 (2) 5 (3) 6 (4) 7 (5) 8
Directions for questions 16 to 20: Answer the questions on the basis of the information given below:
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.
1 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.
2 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.
16. 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?
(1) Rs 90 (2) Rs 100 (3) Rs 110 (4) Rs 120 (5) Rs 130
17. 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?
(1) Rs 90 (2) Rs 100 (3) Rs 110
(4) Rs 120 (5) Not uniquely determinable
18. If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of the
share at the end of day 3?
(1) Rs 90 (2) Rs 100 (3) Rs 110 (4) Rs 120 (5) Rs 130
Page 5


Directions for questions 1 to 5: Answer the questions on the basis of the information given below:
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:
1. A team must include exactly one among P, R, and S.
2. A team must include either M or Q, but not both.
3. If a team includes K, then it must also include L, and vice versa.
4. If a team includes one among S, U, and W, then it must also include the other two.
5. L and N cannot be members of the same team.
6. 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.
1. Who cannot be a member of a team of size 3?
(1) L (2) M (3) N (4) P (5) Q
2. Who can be a member of a team of size 5?
(1) K (2) L (3) M (4) P (5) R
3. What would be the size of the largest possible team?
(1) 8 (2) 7 (3) 6 (4) 5 (5) Cannot be determined
4. What could be the size of a team that includes K?
(1) 2 or 3 (2) 2 or 4 (3) 3 or 4 (4) Only 2 (5) Only 4
5. In how many ways a team can be constituted so that the team includes N?
(1) 2 (2) 3 (3) 4 (4) 5 (5) 6

	



Instructions:
1. The Test Paper contains 75 questions. The duration of the test is 150 minutes.
2. The paper is divided into three sections. Section-I: 25 Q:, Section-II: 25 Q:, Section-III: 25 Q.
3. Wrong answers carry negative marks. There is only one correct answer for each question.
Directions for questions 6 to 10: Answer questions on the basis of the information given below:
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. (Dipan's score in English Paper II has been intentionally removed in the
table.)
PCB Group 
Social 
Science 
Group 
Vernacular 
Group 
English Group Name of the 
student 
Phy. Chem. Bio. 
Mathematics 
Group 
Hist. Geo. Paper I Paper II Paper I Paper II 
Final 
Score 
Ayesha (G) 98 96 97 98 95 93 94 96 96 98 96.2 
Ram (B) 97 99 95 97 95 96 94 94 96 98 96.1 
Dipan (B) 98 98 98 95 96 95 96 94 96 ?? 96.0 
Sagnik (B) 97 98 99 96 96 98 94 97 92 94 95.9 
Sanjiv (B) 95 96 97 98 97 96 92 93 95 96 95.7 
Shreya (G) 96 89 85 100 97 98 94 95 96 95 95.5 
Joseph (B) 90 94 98 100 94 97 90 92 94 95 95 
Agni (B) 96 99 96 99 95 96 82 93 92 93 94.3 
Pritam (B) 98 98 95 98 83 95 90 93 94 94 93.9 
Tirna (G) 96 98 97 99 85 94 92 91 87 96 93.7 
Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl.
6. How much did Dipan get in English Paper II?
(1) 94 (2) 96.5 (3) 97 (4) 98 (5) 99
7. Among the top ten students, how many boys scored at least 95 in at least one paper from each of
the groups?
(1) 1 (2) 2 (3) 3 (4) 4 (5) 5
8. 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:
(1) Pritam, Joseph, Tirna, Agni (2) Joseph, Tirna, Agni, Pritam
(3) Pritam, Agni, Tirna, Joseph (4) Joseph, Tirna, Pritam, Agni
(5) Pritam, Tirna, Agni, Joseph
9. 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:
(1) Shreya (2) Ram
(3) Ayesha (4) Dipan
(5) No one from the top ten
10. 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:
(1) Ram (2) Agni (3) Pritam (4) Ayesha (5) Dipan
Directions for questions 11 to 15: Answer the questions on the basis of the information given below:
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 mathema-
ticians, 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.
1 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.
2 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.
3 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.
4 No other paper was written during the conference.
11. How many participants in the conference did not change their Erdös number during the conference?
(1) 2 (2) 3 (3) 4 (4) 5 (5) Cannot be determined
12. The person having the largest Erdös number at the end of the conference must have had Erdös
number (at that time):
(1) 5 (2) 7 (3) 9 (4) 14 (5) 15
13. How many participants had the same Erdös number at the beginning of the conference?
(1) 2 (2) 3 (3) 4 (4) 5 (5) Cannot be determined
14. The Erdös number of C at the end of the conference was:
(1) 1 (2) 2 (3) 3 (4) 4 (5) 5
15. The Erdös number of E at the beginning of the conference was:
(1) 2 (2) 5 (3) 6 (4) 7 (5) 8
Directions for questions 16 to 20: Answer the questions on the basis of the information given below:
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.
1 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.
2 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.
16. 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?
(1) Rs 90 (2) Rs 100 (3) Rs 110 (4) Rs 120 (5) Rs 130
17. 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?
(1) Rs 90 (2) Rs 100 (3) Rs 110
(4) Rs 120 (5) Not uniquely determinable
18. If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of the
share at the end of day 3?
(1) Rs 90 (2) Rs 100 (3) Rs 110 (4) Rs 120 (5) Rs 130
19. 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)?
(1) Michael had 10 less shares than Chetan.
(2) Michael had 10 more shares than Chetan.
(3) Chetan had 10 more shares than Michael,
(4) Chetan had 20 more shares than Michael.
(5) Both had the same number of shares.
20. What could have been the maximum possible increase in combined cash balance of Chetan and
Michael at the end of the fifth day?
(1) Rs 3700 (2) Rs 4000 (3) Rs 4700 (4) Rs 5000 (5) Rs 6000
Directions for questions 21 to 25: Answer the questions on the basis of the information given below:
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.
A
B S C T
D
95
23 2
71 6
2
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 indiffer-
ent 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.
21. 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:
(1) 1,5,3,3 (2) 1,4,4,3 (3) 1,5,4,2 (4) 0,5,2,3 (5) 0,5,2,2