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# CAT Past Year Question Paper - 2007 CAT Notes | EduRev

## CAT Mock Test Series 2020

Created by: Bakliwal Institute

## CAT : CAT Past Year Question Paper - 2007 CAT Notes | EduRev

``` Page 1

1. Consider the set S = {2, 3, 4, ……, 2n + 1}, where ‘n’ is a positive integer larger than 2007. Define
X as the average of the odd integers in S and Y as the average of the even integers in S. What is the
value of  X – Y?
(1) 0 (2) 1 (3)
1
n
2
(4)
n1
2n
+
(5) 2008
2. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years.
Three years later, one member died at the age of 60 years and a child was born during the same
year. After another three years, one more member died, again at 60, and a child was born during the
same year. The current average age of this eight-member joint family is nearest to
(1) 23 years (2) 22 years (3) 21 years (4) 25 years (5) 24 years
3. A function ƒ(x) satisfies ƒ(1) = 3600 and ƒ(1) + ƒ(2) + ... + ƒ(n) = n
2
f(n), for all positive integers
n  > 1. What is the value of ƒ(9)?
(1) 80 (2) 240 (3) 200 (4) 100 (5) 120
4. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and
50 Misos. In how many ways can you pay a bill of 107 Misos?
(1) 17 (2) 16 (3) 18 (4) 15 (5) 19
5. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja.
giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise,
Shailaja noticed that she was left with exactly three times as much as the amount on the cheque.
Which of the following is a valid statement about the cheque amount?
(1) Over Rupees 13 but less than Rupees 14
(2) Over Rupees 7 but less than Rupees 8
(3) Over Rupees 22 but less than Rupees 23
(4) Over Rupees 18 but less than Rupees 19
(5) Over Rupees 4 but less than Rupees 5



	
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

1. Consider the set S = {2, 3, 4, ……, 2n + 1}, where ‘n’ is a positive integer larger than 2007. Define
X as the average of the odd integers in S and Y as the average of the even integers in S. What is the
value of  X – Y?
(1) 0 (2) 1 (3)
1
n
2
(4)
n1
2n
+
(5) 2008
2. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years.
Three years later, one member died at the age of 60 years and a child was born during the same
year. After another three years, one more member died, again at 60, and a child was born during the
same year. The current average age of this eight-member joint family is nearest to
(1) 23 years (2) 22 years (3) 21 years (4) 25 years (5) 24 years
3. A function ƒ(x) satisfies ƒ(1) = 3600 and ƒ(1) + ƒ(2) + ... + ƒ(n) = n
2
f(n), for all positive integers
n  > 1. What is the value of ƒ(9)?
(1) 80 (2) 240 (3) 200 (4) 100 (5) 120
4. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and
50 Misos. In how many ways can you pay a bill of 107 Misos?
(1) 17 (2) 16 (3) 18 (4) 15 (5) 19
5. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja.
giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise,
Shailaja noticed that she was left with exactly three times as much as the amount on the cheque.
Which of the following is a valid statement about the cheque amount?
(1) Over Rupees 13 but less than Rupees 14
(2) Over Rupees 7 but less than Rupees 8
(3) Over Rupees 22 but less than Rupees 23
(4) Over Rupees 18 but less than Rupees 19
(5) Over Rupees 4 but less than Rupees 5



	
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.
6. How many pairs of positive integers m, n satisfy
14 1
mn 12
+= , where, ‘n’ is an odd integer less than
60?
(1) 6 (2) 4 (3) 7 (4) 5 (5) 3
Directions for Questions 7 to 10: Each question is followed by two statements A and B. Indicate your
response based on the following directives.
Mark (1) if the questions can be answered using A alone but not using B alone.
Mark (2) if the question can be answered using B alone but not using A alone.
Mark (3) if the question can be answered using A and B together, but not using either A or B alone.
Mark (4) if the question cannot be answered even using A and B together.
7. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II,
each with 50 students. The average weight,
I
W , of Section I is smaller than the average weight
II
W ,
of the Section II. If the heaviest student say Deepak, of section II is moved to Section I, and the
lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the
two sections are switched, i.e., the average weight of Section I becomes
II
W and that of Section II
becomes
I
W . What is the weight of Poonam?
A:
II I
W –W1.0 = .
B: Moving Deepak from Section II to I (without any move I to II) makes the average weights of the
two sections equal.
8. ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in
order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical
tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the
tank capacity adequate to met ABC’s requirements?
A: The inner diameter of the tank is at least 8 meters.
B: The tank weights 30,000 kg when empty, and is made of a material with density of
3 gm/cc.
9. Consider integers x, y, z. What is the minimum possible value of
22 2
xy z ++ ?
A: x + y + z = 89.
B: Among x, y, z two are equal.
10. Rahim plans to draw a square JKLM with point O on the side JK but is not successful. Why is
Rahim unable to draw the square?
A: The length of OM is twice that of OL.
B: The length of OM is 4 cm.
Page 3

1. Consider the set S = {2, 3, 4, ……, 2n + 1}, where ‘n’ is a positive integer larger than 2007. Define
X as the average of the odd integers in S and Y as the average of the even integers in S. What is the
value of  X – Y?
(1) 0 (2) 1 (3)
1
n
2
(4)
n1
2n
+
(5) 2008
2. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years.
Three years later, one member died at the age of 60 years and a child was born during the same
year. After another three years, one more member died, again at 60, and a child was born during the
same year. The current average age of this eight-member joint family is nearest to
(1) 23 years (2) 22 years (3) 21 years (4) 25 years (5) 24 years
3. A function ƒ(x) satisfies ƒ(1) = 3600 and ƒ(1) + ƒ(2) + ... + ƒ(n) = n
2
f(n), for all positive integers
n  > 1. What is the value of ƒ(9)?
(1) 80 (2) 240 (3) 200 (4) 100 (5) 120
4. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and
50 Misos. In how many ways can you pay a bill of 107 Misos?
(1) 17 (2) 16 (3) 18 (4) 15 (5) 19
5. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja.
giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise,
Shailaja noticed that she was left with exactly three times as much as the amount on the cheque.
Which of the following is a valid statement about the cheque amount?
(1) Over Rupees 13 but less than Rupees 14
(2) Over Rupees 7 but less than Rupees 8
(3) Over Rupees 22 but less than Rupees 23
(4) Over Rupees 18 but less than Rupees 19
(5) Over Rupees 4 but less than Rupees 5



	
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.
6. How many pairs of positive integers m, n satisfy
14 1
mn 12
+= , where, ‘n’ is an odd integer less than
60?
(1) 6 (2) 4 (3) 7 (4) 5 (5) 3
Directions for Questions 7 to 10: Each question is followed by two statements A and B. Indicate your
response based on the following directives.
Mark (1) if the questions can be answered using A alone but not using B alone.
Mark (2) if the question can be answered using B alone but not using A alone.
Mark (3) if the question can be answered using A and B together, but not using either A or B alone.
Mark (4) if the question cannot be answered even using A and B together.
7. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II,
each with 50 students. The average weight,
I
W , of Section I is smaller than the average weight
II
W ,
of the Section II. If the heaviest student say Deepak, of section II is moved to Section I, and the
lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the
two sections are switched, i.e., the average weight of Section I becomes
II
W and that of Section II
becomes
I
W . What is the weight of Poonam?
A:
II I
W –W1.0 = .
B: Moving Deepak from Section II to I (without any move I to II) makes the average weights of the
two sections equal.
8. ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in
order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical
tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the
tank capacity adequate to met ABC’s requirements?
A: The inner diameter of the tank is at least 8 meters.
B: The tank weights 30,000 kg when empty, and is made of a material with density of
3 gm/cc.
9. Consider integers x, y, z. What is the minimum possible value of
22 2
xy z ++ ?
A: x + y + z = 89.
B: Among x, y, z two are equal.
10. Rahim plans to draw a square JKLM with point O on the side JK but is not successful. Why is
Rahim unable to draw the square?
A: The length of OM is twice that of OL.
B: The length of OM is 4 cm.
Directions for Questions 11 and 12: Answer the following questions based on the information given
below:
Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the
schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on
the same day.
Departure Arrival
City Time City Time
B 8:00 am A 3:00 pm
A 4:00 pm B 8:00 pm
Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced
by a steady wind blowing from east to west at 50 km per hour.
11. What is the time difference between A and B?
(1) 1 hour and 30 minutes (2) 2 hours (3) 2 hours and 30 minutes
(4) 1 hour (5) Cannot be determined
12. What is the plane’s cruising speed in km per hour?
(1) 700 (2) 550 (3) 600
(4) 500 (5) Cannot be determined.
Directions for Questions 13 and 14: Answer the following questions based on the information given
below:
Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee
maximum returns on her investment. She has three options, each of which can be utilized fully or partially
in conjunction with others.
Option A : Invest in a public sector bank. It promises a return of +0.10%.
Option B : Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of  + 5%
while a fall will entail a return of –3%.
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of  –2.5%,
while a fall will entail a return of +2%.
(1) 0.25% (2) 0.10% (3) 0.20% (4) 0.15% (5) 0.30%
(1) 100% in option A
(2) 36% in option B and 64% in option C
(3) 64% in option B and 36% in option C
(4) 1/3 in each of the three options
(5) 30% in option A, 32% in option B and 38% in option C
Page 4

1. Consider the set S = {2, 3, 4, ……, 2n + 1}, where ‘n’ is a positive integer larger than 2007. Define
X as the average of the odd integers in S and Y as the average of the even integers in S. What is the
value of  X – Y?
(1) 0 (2) 1 (3)
1
n
2
(4)
n1
2n
+
(5) 2008
2. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years.
Three years later, one member died at the age of 60 years and a child was born during the same
year. After another three years, one more member died, again at 60, and a child was born during the
same year. The current average age of this eight-member joint family is nearest to
(1) 23 years (2) 22 years (3) 21 years (4) 25 years (5) 24 years
3. A function ƒ(x) satisfies ƒ(1) = 3600 and ƒ(1) + ƒ(2) + ... + ƒ(n) = n
2
f(n), for all positive integers
n  > 1. What is the value of ƒ(9)?
(1) 80 (2) 240 (3) 200 (4) 100 (5) 120
4. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and
50 Misos. In how many ways can you pay a bill of 107 Misos?
(1) 17 (2) 16 (3) 18 (4) 15 (5) 19
5. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja.
giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise,
Shailaja noticed that she was left with exactly three times as much as the amount on the cheque.
Which of the following is a valid statement about the cheque amount?
(1) Over Rupees 13 but less than Rupees 14
(2) Over Rupees 7 but less than Rupees 8
(3) Over Rupees 22 but less than Rupees 23
(4) Over Rupees 18 but less than Rupees 19
(5) Over Rupees 4 but less than Rupees 5



	
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.
6. How many pairs of positive integers m, n satisfy
14 1
mn 12
+= , where, ‘n’ is an odd integer less than
60?
(1) 6 (2) 4 (3) 7 (4) 5 (5) 3
Directions for Questions 7 to 10: Each question is followed by two statements A and B. Indicate your
response based on the following directives.
Mark (1) if the questions can be answered using A alone but not using B alone.
Mark (2) if the question can be answered using B alone but not using A alone.
Mark (3) if the question can be answered using A and B together, but not using either A or B alone.
Mark (4) if the question cannot be answered even using A and B together.
7. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II,
each with 50 students. The average weight,
I
W , of Section I is smaller than the average weight
II
W ,
of the Section II. If the heaviest student say Deepak, of section II is moved to Section I, and the
lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the
two sections are switched, i.e., the average weight of Section I becomes
II
W and that of Section II
becomes
I
W . What is the weight of Poonam?
A:
II I
W –W1.0 = .
B: Moving Deepak from Section II to I (without any move I to II) makes the average weights of the
two sections equal.
8. ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in
order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical
tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the
tank capacity adequate to met ABC’s requirements?
A: The inner diameter of the tank is at least 8 meters.
B: The tank weights 30,000 kg when empty, and is made of a material with density of
3 gm/cc.
9. Consider integers x, y, z. What is the minimum possible value of
22 2
xy z ++ ?
A: x + y + z = 89.
B: Among x, y, z two are equal.
10. Rahim plans to draw a square JKLM with point O on the side JK but is not successful. Why is
Rahim unable to draw the square?
A: The length of OM is twice that of OL.
B: The length of OM is 4 cm.
Directions for Questions 11 and 12: Answer the following questions based on the information given
below:
Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the
schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on
the same day.
Departure Arrival
City Time City Time
B 8:00 am A 3:00 pm
A 4:00 pm B 8:00 pm
Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced
by a steady wind blowing from east to west at 50 km per hour.
11. What is the time difference between A and B?
(1) 1 hour and 30 minutes (2) 2 hours (3) 2 hours and 30 minutes
(4) 1 hour (5) Cannot be determined
12. What is the plane’s cruising speed in km per hour?
(1) 700 (2) 550 (3) 600
(4) 500 (5) Cannot be determined.
Directions for Questions 13 and 14: Answer the following questions based on the information given
below:
Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee
maximum returns on her investment. She has three options, each of which can be utilized fully or partially
in conjunction with others.
Option A : Invest in a public sector bank. It promises a return of +0.10%.
Option B : Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of  + 5%
while a fall will entail a return of –3%.
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of  –2.5%,
while a fall will entail a return of +2%.
(1) 0.25% (2) 0.10% (3) 0.20% (4) 0.15% (5) 0.30%
(1) 100% in option A
(2) 36% in option B and 64% in option C
(3) 64% in option B and 36% in option C
(4) 1/3 in each of the three options
(5) 30% in option A, 32% in option B and 38% in option C
Directions for Questions 15 and 16: Answer the following questions based on the information given
below:
Let S be the set of all pairs (i, j) where, 1i j n =< =  and n4 = . Any two distinct members of S are called
“friends” if they have one constituent of the pairs in common and “enemies” otherwise. For example, if
n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1, 2) and (2, 3)
are also friends, but (1, 4) and (2, 3) are enemies.
15. For general ‘n’, how many enemies will each member of S have?
(1) n – 3 (2)
()
2
1
n – 3n – 2
2
(3) 2n – 7
(4)
()
2
1
n – 5n 6
2
+
(5)
()
2
1
n – 7n 14
2
+
16. For general ‘n’, consider any two members of S that are friends. How many other members of S will
be common friends of both these members?
(1)
()
2
1
n – 5n 8
2
+
(2) 2n – 6 (3) ()
1
nn – 3
2
(4) n – 2 (5)
()
2
1
n – 7n 16
2
+
17. In a tournament, there are n teams
12 n
T , T ,..., T ,  with n > 5. Each team consists of ‘k’ players,
k > 3. The following pairs of teams have one player in common:
122 3 n–1n n 1
T &T,T &T,...,T &T ,andT &T
No other pair of teams has any player in common. How many players are participating in the
tournament, considering all the ‘n’ teams together?
(1) n(k –1) (2) k(n –1) (3) n(k –2)
(4) k(n – 2) (5) (n – 1)(k – 1)
18. Consider four-digit numbers for which the first two digits are equal and the last two digits are also
equal. How many such numbers are perfect squares?
(1) 3 (2) 2 (3) 4 (4) 0 (5) 1
Page 5

1. Consider the set S = {2, 3, 4, ……, 2n + 1}, where ‘n’ is a positive integer larger than 2007. Define
X as the average of the odd integers in S and Y as the average of the even integers in S. What is the
value of  X – Y?
(1) 0 (2) 1 (3)
1
n
2
(4)
n1
2n
+
(5) 2008
2. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years.
Three years later, one member died at the age of 60 years and a child was born during the same
year. After another three years, one more member died, again at 60, and a child was born during the
same year. The current average age of this eight-member joint family is nearest to
(1) 23 years (2) 22 years (3) 21 years (4) 25 years (5) 24 years
3. A function ƒ(x) satisfies ƒ(1) = 3600 and ƒ(1) + ƒ(2) + ... + ƒ(n) = n
2
f(n), for all positive integers
n  > 1. What is the value of ƒ(9)?
(1) 80 (2) 240 (3) 200 (4) 100 (5) 120
4. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and
50 Misos. In how many ways can you pay a bill of 107 Misos?
(1) 17 (2) 16 (3) 18 (4) 15 (5) 19
5. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja.
giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise,
Shailaja noticed that she was left with exactly three times as much as the amount on the cheque.
Which of the following is a valid statement about the cheque amount?
(1) Over Rupees 13 but less than Rupees 14
(2) Over Rupees 7 but less than Rupees 8
(3) Over Rupees 22 but less than Rupees 23
(4) Over Rupees 18 but less than Rupees 19
(5) Over Rupees 4 but less than Rupees 5



	
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.
6. How many pairs of positive integers m, n satisfy
14 1
mn 12
+= , where, ‘n’ is an odd integer less than
60?
(1) 6 (2) 4 (3) 7 (4) 5 (5) 3
Directions for Questions 7 to 10: Each question is followed by two statements A and B. Indicate your
response based on the following directives.
Mark (1) if the questions can be answered using A alone but not using B alone.
Mark (2) if the question can be answered using B alone but not using A alone.
Mark (3) if the question can be answered using A and B together, but not using either A or B alone.
Mark (4) if the question cannot be answered even using A and B together.
7. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II,
each with 50 students. The average weight,
I
W , of Section I is smaller than the average weight
II
W ,
of the Section II. If the heaviest student say Deepak, of section II is moved to Section I, and the
lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the
two sections are switched, i.e., the average weight of Section I becomes
II
W and that of Section II
becomes
I
W . What is the weight of Poonam?
A:
II I
W –W1.0 = .
B: Moving Deepak from Section II to I (without any move I to II) makes the average weights of the
two sections equal.
8. ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in
order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical
tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the
tank capacity adequate to met ABC’s requirements?
A: The inner diameter of the tank is at least 8 meters.
B: The tank weights 30,000 kg when empty, and is made of a material with density of
3 gm/cc.
9. Consider integers x, y, z. What is the minimum possible value of
22 2
xy z ++ ?
A: x + y + z = 89.
B: Among x, y, z two are equal.
10. Rahim plans to draw a square JKLM with point O on the side JK but is not successful. Why is
Rahim unable to draw the square?
A: The length of OM is twice that of OL.
B: The length of OM is 4 cm.
Directions for Questions 11 and 12: Answer the following questions based on the information given
below:
Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the
schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on
the same day.
Departure Arrival
City Time City Time
B 8:00 am A 3:00 pm
A 4:00 pm B 8:00 pm
Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced
by a steady wind blowing from east to west at 50 km per hour.
11. What is the time difference between A and B?
(1) 1 hour and 30 minutes (2) 2 hours (3) 2 hours and 30 minutes
(4) 1 hour (5) Cannot be determined
12. What is the plane’s cruising speed in km per hour?
(1) 700 (2) 550 (3) 600
(4) 500 (5) Cannot be determined.
Directions for Questions 13 and 14: Answer the following questions based on the information given
below:
Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee
maximum returns on her investment. She has three options, each of which can be utilized fully or partially
in conjunction with others.
Option A : Invest in a public sector bank. It promises a return of +0.10%.
Option B : Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of  + 5%
while a fall will entail a return of –3%.
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of  –2.5%,
while a fall will entail a return of +2%.
(1) 0.25% (2) 0.10% (3) 0.20% (4) 0.15% (5) 0.30%
(1) 100% in option A
(2) 36% in option B and 64% in option C
(3) 64% in option B and 36% in option C
(4) 1/3 in each of the three options
(5) 30% in option A, 32% in option B and 38% in option C
Directions for Questions 15 and 16: Answer the following questions based on the information given
below:
Let S be the set of all pairs (i, j) where, 1i j n =< =  and n4 = . Any two distinct members of S are called
“friends” if they have one constituent of the pairs in common and “enemies” otherwise. For example, if
n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1, 2) and (2, 3)
are also friends, but (1, 4) and (2, 3) are enemies.
15. For general ‘n’, how many enemies will each member of S have?
(1) n – 3 (2)
()
2
1
n – 3n – 2
2
(3) 2n – 7
(4)
()
2
1
n – 5n 6
2
+
(5)
()
2
1
n – 7n 14
2
+
16. For general ‘n’, consider any two members of S that are friends. How many other members of S will
be common friends of both these members?
(1)
()
2
1
n – 5n 8
2
+
(2) 2n – 6 (3) ()
1
nn – 3
2
(4) n – 2 (5)
()
2
1
n – 7n 16
2
+
17. In a tournament, there are n teams
12 n
T , T ,..., T ,  with n > 5. Each team consists of ‘k’ players,
k > 3. The following pairs of teams have one player in common:
122 3 n–1n n 1
T &T,T &T,...,T &T ,andT &T
No other pair of teams has any player in common. How many players are participating in the
tournament, considering all the ‘n’ teams together?
(1) n(k –1) (2) k(n –1) (3) n(k –2)
(4) k(n – 2) (5) (n – 1)(k – 1)
18. Consider four-digit numbers for which the first two digits are equal and the last two digits are also
equal. How many such numbers are perfect squares?
(1) 3 (2) 2 (3) 4 (4) 0 (5) 1
Directions for Questions 19 and 20: Answer the following questions based on the information given
below:
Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of
each unit is Rs. 30. On the other hand, the cost, in rupees, of producing ‘x’ units is 240 + bx + cx
2
, where
‘b’ and ‘c’ are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units
increases the daily production cost by
2
66 %
3
. However, an increase in daily production from 40 to 60
units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and
that Mr. David can sell as much as he can produce. His objective is to maximize the profit.
19. How many units should Mr. David produce daily?
(1) 130 (2) 100 (3) 70
(4) 150 (5) Cannot be determined
20. What is the maximum daily profit, in rupees, that Mr. David can realize from his business?
(1) 620 (2) 920 (3) 840
(4) 760 (5) Cannot be determined
21. The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the n
th
day of 2007
(n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees
per kilogram) is 89 + 0.15n, on the n
th
day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the
prices of these two varieties of tea be equal?
(1) May 21 (2) April 11 (3) May 20
(4) April 10 (5) June 30
22. Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the
same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range
that includes all possible values of the angle AQP in degrees?
(1) Between 0 and 90 (2) Between 0 and 30
(3) Between 0 and 60 (4) Between 0 and 75
(5) Between 0 and 45
23. A quadratic function ƒ(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1.
What is the value ƒ(x) at x = 10?
(1) –119 (2) –159 (3) –110 (4) –180 (5) –105
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