# CAT Data Interpretation Previous Year Question Paper of 2007

## CAT Sample Papers 2007 for Data Interpretation

1. The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10 n, on the nth 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 nth 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

2. A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at

x = 0 is 1. What is the value of f(x) at x = 10?

(1) –119

(2) –159

(3) –110

(4) -180

(5) -105

3. 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

Directions for Questions 4 and 5:

Let S be the set of all pairs (i, j) where 1 ≤ i ≤ j < n and n ≥ 4. 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.

4. For general n, how many enemies will each member of S have?

(1) n – 3

(2)

(3) 2n – 7

(4)

(5)

5. 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) 2n – 6

(3)

(4) n – 2

(5)

Directions for Questions 6 and 7:

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%

6. The maximum guaranteed return to Shabnam is

(1) 0.25%

(2) 0.10%

(3) 0.20%

(4) 0.15%

(5) 0.30%

7. What strategy will maximize the guaranteed return to Shabnam?

(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 8 and 9:

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 a.m. A 3:00 p.m.

A 4:00 p.m. B 8: p.m.

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.

8. 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

9. What is the plane’s cruising speed in km per hour?

(1) 700

(2) 550

(3) 600

(4) 500

(5) Cannot be determined

10. 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

11. In a tournament, there are n teams T1 , T2 ....., T with n > 5. Each team consists of k

players, k > 3. The following pairs of teams have one player in common:

T1 & T2 , T2 & T3 ,......, Tn − 1 & Tn , and Tn & T1.

No other pair of teams has any player in common. How many players are

(1) n(k – 1)

(2) k(n – 1)

(3) n(k – 2)

(4) k(k – 2)

(5) (n – 1)(k – 1)

Directions for Questions 12 and 13:

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 + cx2, 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 66.66%.

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.

12. How many units should Mr. David produce daily?

(1) 130

(2) 100

(3) 70

(4) 150

(5) Cannot be determined

13. 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

Directions for Questions 14 and 15:

Let a1 = p and b1 = q, where p and q are positive quantities.

Define:

an = pbn − 1 bn = qbn − 1, for even n > 1

and an = pan − 1 bn = qan − 1, for odd n > 1.

15. If p = 1/3 and q = 2/3, then what is the smallest odd n such that an + bn < 0.01?

(1) 7

(2) 13

(3) 11

(4) 9

(5) 15

Directions for Questions 16 through 19:

Each question is followed by two statements A and B. Answer each question using the

following instructions.

Mark (1) if the question can be answered by using statement A alone but not by using

statement B alone.

Mark (2) if the question can be answered by using statement B alone but not by using

statement A alone.

Mark (3) if the question can be answered by using both the statements together but not by

using either of the statements alone.

Mark (4) if the question cannot be answered on the basis of the two statements.

16. 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, WI, of Section I is

smaller than the average weight, WII, of 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 WII and that of Section II

becomes WI. What is the weight of Poonam?

A. WII – WI = 1.0

B. Moving Deepak from Section II to I (without any move from I to II) makes the

average weights of the two sections equal.

17. Consider integers x, y and z. What is the minimum possible value of x2 + y2 + z 2 ?

A. x + y + z = 89

B. Among x, y, z two are equal.

18. Rahim plans to draw a square JKLM with a 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.

19. 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 meet ABC’s requirements?

A. The inner diameter of the tank is at least 8 meters.

B. The tank weighs 30,000 kg when empty, and is made of a material with density

of 3 gm/cc.

20. 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

21. How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an

odd integer less than 60?

(1) 6

(2) 4

(3) 7

(4) 5

(5) 3

22. 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

23. Consider the set S = {2, 3, 4, ...., 2n + l}, 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) n/2

(4) n+1/2n

(5) 2008

24. 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

25. A function f(x) satisfies f (1) = 3600, and f(l) + f(2) + ... + f(n) = n2 f(n), for all

positive integers n>1. What is the value of f(9) ?

(1) 80

(2) 240

(3) 200

(4) 100

(5) 120

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 nth 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

2. A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at

x = 0 is 1. What is the value of f(x) at x = 10?

(1) –119

(2) –159

(3) –110

(4) -180

(5) -105

3. 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

Directions for Questions 4 and 5:

Let S be the set of all pairs (i, j) where 1 ≤ i ≤ j < n and n ≥ 4. 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.

4. For general n, how many enemies will each member of S have?

(1) n – 3

(2)

(3) 2n – 7

(4)

(5)

5. 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) 2n – 6

(3)

(4) n – 2

(5)

Directions for Questions 6 and 7:

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%

6. The maximum guaranteed return to Shabnam is

(1) 0.25%

(2) 0.10%

(3) 0.20%

(4) 0.15%

(5) 0.30%

7. What strategy will maximize the guaranteed return to Shabnam?

(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 8 and 9:

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 a.m. A 3:00 p.m.

A 4:00 p.m. B 8: p.m.

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.

8. 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

9. What is the plane’s cruising speed in km per hour?

(1) 700

(2) 550

(3) 600

(4) 500

(5) Cannot be determined

10. 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

11. In a tournament, there are n teams T1 , T2 ....., T with n > 5. Each team consists of k

players, k > 3. The following pairs of teams have one player in common:

T1 & T2 , T2 & T3 ,......, Tn − 1 & Tn , and Tn & T1.

No other pair of teams has any player in common. How many players are

(1) n(k – 1)

(2) k(n – 1)

(3) n(k – 2)

(4) k(k – 2)

(5) (n – 1)(k – 1)

Directions for Questions 12 and 13:

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 + cx2, 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 66.66%.

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.

12. How many units should Mr. David produce daily?

(1) 130

(2) 100

(3) 70

(4) 150

(5) Cannot be determined

13. 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

Directions for Questions 14 and 15:

Let a1 = p and b1 = q, where p and q are positive quantities.

Define:

an = pbn − 1 bn = qbn − 1, for even n > 1

and an = pan − 1 bn = qan − 1, for odd n > 1.

15. If p = 1/3 and q = 2/3, then what is the smallest odd n such that an + bn < 0.01?

(1) 7

(2) 13

(3) 11

(4) 9

(5) 15

Directions for Questions 16 through 19:

Each question is followed by two statements A and B. Answer each question using the

following instructions.

Mark (1) if the question can be answered by using statement A alone but not by using

statement B alone.

Mark (2) if the question can be answered by using statement B alone but not by using

statement A alone.

Mark (3) if the question can be answered by using both the statements together but not by

using either of the statements alone.

Mark (4) if the question cannot be answered on the basis of the two statements.

16. 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, WI, of Section I is

smaller than the average weight, WII, of 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 WII and that of Section II

becomes WI. What is the weight of Poonam?

A. WII – WI = 1.0

B. Moving Deepak from Section II to I (without any move from I to II) makes the

average weights of the two sections equal.

17. Consider integers x, y and z. What is the minimum possible value of x2 + y2 + z 2 ?

A. x + y + z = 89

B. Among x, y, z two are equal.

18. Rahim plans to draw a square JKLM with a 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.

19. 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 meet ABC’s requirements?

A. The inner diameter of the tank is at least 8 meters.

B. The tank weighs 30,000 kg when empty, and is made of a material with density

of 3 gm/cc.

20. 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

21. How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12 where n is an

odd integer less than 60?

(1) 6

(2) 4

(3) 7

(4) 5

(5) 3

22. 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

23. Consider the set S = {2, 3, 4, ...., 2n + l}, 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) n/2

(4) n+1/2n

(5) 2008

24. 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

25. A function f(x) satisfies f (1) = 3600, and f(l) + f(2) + ... + f(n) = n2 f(n), for all

positive integers n>1. What is the value of f(9) ?

(1) 80

(2) 240

(3) 200

(4) 100

(5) 120

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