**I. Directions for questions 1 to 5:** These questions are based on the following diagram.

Circle A represents even numbers from 2 to 50.

Circle B represents odd numbers from 2 to 50.

Circle C, represents prime numbers from 2 to 50.

1. How many elements are there in set A only?

a. 25 b. 24 c. 23 d. 22

2. How many elements are there in set B only?

a. 14 b. 25 c. 10 d. 13

3. How many elements are there in B n C?

a. 14 b. 11 c. 24 d. 13

4. How many elements are there in A U C?

a. 0 b. 1 c. 2 d. 3

5. How many elements are there in C’ (complement of C)?

a. 35 b. 25 c. 34 d. 14

**II. Directions for questions 6 to 10: **Read the following data and then answer the questions that follow.

In a class, there are 60 students. For every 8 students learning Judo there are 4 students who learn Karate. For every 14 students learning Judo there are 7 students who learn both Judo and Karate and 7 students learning none.

6. How many students learn only Karate?

a. 20 b. 30 c. 0 d. 40

7. How many students learn only Judo?

a. 20 b. 40 c. 0 d. 14

8. How many students learn both Karate and Judo?

a. 0 b. 10 c. 60 d. 20

9. If the students who learn both Judo and Karate stop learning Judo, then what percentage of the total number of students learn Judo?

a. 50% b. 33 1/3% c. 40% d. 55%

10. If 50% of those learning only Karate stop learning Karate and start learning Judo, then what is the ratio of the number of students learning Judo to those learning Karate?

a. 3 : 1 b. 2 : 1 c. 4 : 1 d. Cannot be determined

**Answer & Explanations**

I.

Number of even numbers from 2 to 50 are 25.

Number of odd numbers from 2 to 50 are 24.

Number of prime numbers from 2 to 50 are 15.

1. Number of elements in set A only = 24

i.e, the even numbers which are not primes. Choice (2).

2. There are 10 elements in only set B, i.e, there are 10 odd numbers which are not primes.

Choice (3).

3. There are 14 elements in B n C i.e, there are 14 odd prime numbers. Choice (1).

4. There is only one element in A n C i.e, 2 is the only even prime number. Choice (2).

5. Number of elements in C’ = the elements which do not belong to the set C. There are

(24 + 10) = 34 such numbers i.e, numbers are non primes. Choice (3).

II. From the given data, we get the following diagram.

Taken = 60 students

J : K = 8 : 4 = 2 : 1

J : Both : None = 14 : 7 : 7 = 2 : 1 : 1 @ 2x, x, x (After removing the ratio)

=> x + x + x = 3x = 60

= x = 20

Hence

1. x = 20 students learn only Judo.

2. None learn only Karate.

3. x = 20 students learn both.

6. None learn only Karate. Choice (3)

7. 20 students learn only Judo. Choice (1)

8. 20 students learn both. Choice (4)

9. 20 students learn both Judo and Karate. If they stop learning Judo then only 20 students would

learn Judo. The total number of students is 60.

Percentage of class learning only Judo = 20/60 x 100

= 33 1/3%. Choice (2)

10. Since none learn only Karate, so the given statement does not make any sense. The number of

students learning Judo therefore remains the same.

2x = 2 x 20 = 40 students learn Judo.

Ratio : 40 : 20 = 2 : 1. Choice (2)

**Directions for Questions 1 to 2**: These Questions are based on the following table.

POPULATION OF FOUR METRO CITIES AT THE BEGINNING OF THE YEAR 1990

1. If Bombay were to become the most populous city at the end of the year, what is the least number of people who must shift to Bombay during the year, given that, every year 1% of its population shifts to other cities (Assume that the population of other metro does not change)?

a. 6

b. 1,04,64,301

c. 1,05,706

d. 1,05,705

2. If the most populous city has 40% female population, and the least has 35% female population, then the difference between male population of these two cities is closest to

a. 60 lakh

b. 57 lakh

c. 17.9 lakh

d. 56 lakh

**Directions for questions 3 and 4**: These questions are based on the graph given below, which shows the number of deaths due to fire accidents in the summer of 1992.

3. The average number of deaths per day during the given period is

a. 22.04

b. 22.5

c. 23.09

d. 21.08

4. Out of the total deaths from 30^{th} March to 8^{th} May, if 22% occurred in place X and 10% of them are because of cigarettes, then the number of fire accidents for the given period in place X because of cigarettes is approximately.

a. 19

b. 20

c. 22

d. 23

**Directions for questions 5 to 7**: These questions are based on the following bar diagram.

5. The average production for the last three years when compared with the average production for the first three years has dropped by

a.5%

b.3%

c.9%

d.7%

6. If Left over = Production – Consumption, then the year in which there is the least left over as a percentage of production is

a.1995

b.1992

c.1991

d.1993

7. Which of the following statements is true?

a. There is a steady increase in production from 1991 to 1995.

b. The consumption is increasing and decreasing in alternate years.

c. The steepest increase in production immediately follows the steepest fall in consumption.

d. None of the above.

**Directions for questions 8 to 10:** These questions are based on the following bar diagrams.

**Note:**

1. The players in the Commercial Vehicle Segment are Ashok-Leyland, Telco, Bajaj Tempo and DCM-Toyota.

2. The players in the Passenger Car Segment are Hind Motors, Maruti and Premier Auto.

8. What was the percentage increase in the sales of commercial vehicles over the one year period mentioned?

a.25%

b.16%

c. 33 1/3%

d. 22 6/7%

9. If Bajaj Tempo had a 10% share of the commercial vehicles market and sold its vehicles at 10% less than the list price, what were its sales (in rupees) in 1993-94, if the list price of its vehicles was Rs.10,000?

a.13572 crore

b.167.25 lakh

c.135.72 crore

d.167.25 crore

10. Which of the following is true of the percentage increase in the sales of passenger cars for the given period?

a. It was higher than the percentage increase in the production of cars for the given period.

b. It was lower than the percentage increase in the production of cars for the given period.

c. It was equal to the percentage increase in the production of cars for the given period.

d. Insufficient information to decide.

**Answers & Explanations:**

1. Exp: 1% shift = 105700

Also, Calcutta is 5 more than Bombay initially, so a minimum of 105706

people should come to Bombay for it to become the most populous city.

2. Exp: 10570005 x 0.6 – 7000000 x 0.65 =

6 3 4 2 0 0 3

4 5 5 0 0 0 0

——————-

1 7 9 2 0 0 3

3. Exp: 970/44 = Total deaths/Total days = 22.04.

4. Exp: 850 x 0.22 x 0.1 = 19.

5. Reqd. %

Required % = 386/7330 x 100 = 5.26%

lesser by 5.26%≈ 5% Choice(1)

6. By observation it is the least in 1995. Choice(1)

7. By observation, only statement three is true. Choice(3)

8. Percentage increase 3.02/12.06 *100= 25 Choice(1).

9. Sales of Bajaj Temp 1993-94

1.508 x 10^{5} x 9000 = Rs.135.72 crores. Choice(3).

10. The % increase of sales of cars = 4.59/16.48 *100n≈ 27.5%

This is lower than the % increase in production of cars which is 28.57%.

Choice(2).

I.Study the following line graph and answer the questions

Exports from Three Companies Over the Years (in Rs. Crore)

1. For which of the following pairs of years the total exports from the three Companies

together are equal?

a) 1995 and 1998 b) 1996 and 1998 c) 1997 and 1998 d)1995 and 1996

2. Average annual exports during the given period for Company Y is approximately what

percent of the average annual exports for Company Z?

a) 87.12% b) 89.64% c) 91.21% d)93.33%

3. In which year was the difference between the exports from Companies X and Y the

minimum?

a)1994 b)1995 c)1996 d)1999

4. What was the difference between the average exports of the three Companies in 1993

and the average exports in 1998?

a)Rs.15.33crores b)Rs.18.67crores c) Rs.20crores d)Rs.22.17crores

5. In how many of the given years, were the exports from Company Z more than the

average annual exports over the given years?

a)2 b)3 c)4 d) 5

II. The following line chart shows the sale of hardware by the Indian computer Industry between the years 1991-96, within the country and outside in crores of rupees. Study the data given in the chart and answer the questions that follow :

1. What was the difference on sale of hardware between domestic and exports in 1993-

94?

a) Rs.1000 crores b) Rs.500 crores c) Rs.1200 crores d) Rs.700 crores

2. In which of the following years was the percentage increase in sale of hardware in

domestic sector maximum over the preceding years ?

a) 1992-93 b) 1993-94 c) 1994-95 d) 1995-96

3. What was the difference between the total hardware sale in exports sector in 1992-93

and 1993-94 together and that of domestic sector in 1993-94?

a) Rs.300 crores b)Rs.200 crores c) Rs.400 crores d) Rs.150 crores

4. Approximately what was the percentage increase in sale in domestic sector from 1994-

95 to 1995-96?

a)35 b)25 c)40 d)20

5. What was the difference in the average sale between the domestic and export sectors?

a) Rs.900 crores b) Rs.1380 crores c) 1560 crores d) Rs.600 crores

**Answer & Explanations**

I.1. Option D

Explanation:

Total exports of the three Companies X, Y and Z together, during various years are:

In 1993 = Rs. (30 + 80 + 60) crores = Rs. 170 crores.

In 1994 = Rs. (60 + 40 + 90) crores = Rs. 190 crores

In 1995 = Rs. (40 + 60 + 120) crores = Rs. 220 crores

In 1996 = Rs. (70 + 60 + 90) crores = Rs. 220 crores.

In 1997 = Rs. (100 + 80 + 60) crores = Rs. 240 crores.

In 1998 = Rs. (50 + 100 + 80) crores = Rs. 230 crores.

In 1999 = Rs. (120 + 140 + 100) crores = Rs. 360 crores.

Clearly, the total exports of the three Companies X, Y and Z together are same during

the years 1995 and 1996.

2. Option: D

Explanation:

From the graph it is clear that

1.The amount of exports of Company X (in crore Rs.) in the years 1993, 1994, 1995,

1996, 1997, 1998 and 1999 are 30, 60, 40, 70, 100, 50 and 120 respectively.

2.The amount of exports of Company Y (in crore Rs.) in the years 1993, 1994, 1995,

1996, 1997, 1998 and 1999 are 80, 40, 60, 60, 80, 100 and 140 respectively.

3.The amount of exports of Company Z (in crore Rs.) in the years 1993, 1994, 1995,

1996, 1997, 1998 and 1999 are 60, 90,, 120, 90, 60, 80 and 100 respectively.

Average annual exports (in Rs.crore) of Company Y during the given period

= 1/7 * (80 + 40 + 60 + 60 + 80 + 100 + 140) = 560/7 = 80

Average annual exports (in Rs. crore) of Company Z during the given period

1/7 * (60+90+120+60+80+100) = 600/7

:. Required percentage 80/(600/7)*100 % = 93.33%.

3. Option C

Explanation:

The difference between the exports from the Companies X and Y during the various

years are:

In 1993 = Rs. (80 – 30) crores = Rs. 50 crores.

In 1994 = Rs. (60 – 40) crores = Rs. 20 crores.

In 1995 = Rs. (60 – 40) crores = Rs. 20 crores.

In 1996 = Rs. (70 – 60) crores = Rs. 10 crores.

In 1997 = Rs. (100 – 80) crores = Rs. 20 crores.

In 1998 = Rs. (100 – 50) crores = Rs. 50 crores.

In 1999 = Rs. (140 – 120) crores = Rs. 20 crores.

Clearly, the difference is minimum in the year 1996.

4. Answer: Option C

Explanation:

Average exports of the three Companies X, Y and Z in 1993 = (30+80+60)/3 = 170/3

crores.

Average exports of the three Companies X, Y and Z in 1998 =(50+100+80)/3 = 230/3.

Difference = (230-170)/3 = 60/3 = 20 crores

5. Option C

Explanation: 1/7 *(60 + 90 + 120 + 90 + 60 + 80 + 100) = 600/7 =85.71 crores

From the analysis of graph the exports of Company Z are more than the average

annual exports of Company Z (i.e., Rs. 85.71 crores) during the years 1994, 1995,

1996 and 1999, i.e., during 4 of the given years.

II. 1. Answer (d)

2. Answer (c)

3. Answer (a)

4. Answer (d)

5. Answer (b)

I.Study the following line graph and answer the questions

Exports from Three Companies Over the Years (in Rs. Crore)

1. For which of the following pairs of years the total exports from the three Companies

together are equal?

a) 1995 and 1998 b) 1996 and 1998 c) 1997 and 1998 d)1995 and 1996

2. Average annual exports during the given period for Company Y is approximately what

percent of the average annual exports for Company Z?

a) 87.12% b) 89.64% c) 91.21% d)93.33%

3. In which year was the difference between the exports from Companies X and Y the

minimum?

a)1994 b)1995 c)1996 d)1999

4. What was the difference between the average exports of the three Companies in 1993

and the average exports in 1998?

a)Rs.15.33crores b)Rs.18.67crores c) Rs.20crores d)Rs.22.17crores

5. In how many of the given years, were the exports from Company Z more than the

average annual exports over the given years?

a)2 b)3 c)4 d) 5

II. The following line chart shows the sale of hardware by the Indian computer Industry between the years 1991-96, within the country and outside in crores of rupees. Study the data given in the chart and answer the questions that follow :

1. What was the difference on sale of hardware between domestic and exports in 1993-

94?

a) Rs.1000 crores b) Rs.500 crores c) Rs.1200 crores d) Rs.700 crores

2. In which of the following years was the percentage increase in sale of hardware in

domestic sector maximum over the preceding years ?

a) 1992-93 b) 1993-94 c) 1994-95 d) 1995-96

3. What was the difference between the total hardware sale in exports sector in 1992-93

and 1993-94 together and that of domestic sector in 1993-94?

a) Rs.300 crores b)Rs.200 crores c) Rs.400 crores d) Rs.150 crores

4. Approximately what was the percentage increase in sale in domestic sector from 1994-

95 to 1995-96?

a)35 b)25 c)40 d)20

5. What was the difference in the average sale between the domestic and export sectors?

a) Rs.900 crores b) Rs.1380 crores c) 1560 crores d) Rs.600 crores

**Answer & Explanations**

I.1. Option D

Explanation:

Total exports of the three Companies X, Y and Z together, during various years are:

In 1993 = Rs. (30 + 80 + 60) crores = Rs. 170 crores.

In 1994 = Rs. (60 + 40 + 90) crores = Rs. 190 crores

In 1995 = Rs. (40 + 60 + 120) crores = Rs. 220 crores

In 1996 = Rs. (70 + 60 + 90) crores = Rs. 220 crores.

In 1997 = Rs. (100 + 80 + 60) crores = Rs. 240 crores.

In 1998 = Rs. (50 + 100 + 80) crores = Rs. 230 crores.

In 1999 = Rs. (120 + 140 + 100) crores = Rs. 360 crores.

Clearly, the total exports of the three Companies X, Y and Z together are same during

the years 1995 and 1996.

2. Option: D

Explanation:

From the graph it is clear that

1.The amount of exports of Company X (in crore Rs.) in the years 1993, 1994, 1995,

1996, 1997, 1998 and 1999 are 30, 60, 40, 70, 100, 50 and 120 respectively.

2.The amount of exports of Company Y (in crore Rs.) in the years 1993, 1994, 1995,

1996, 1997, 1998 and 1999 are 80, 40, 60, 60, 80, 100 and 140 respectively.

3.The amount of exports of Company Z (in crore Rs.) in the years 1993, 1994, 1995,

1996, 1997, 1998 and 1999 are 60, 90,, 120, 90, 60, 80 and 100 respectively.

Average annual exports (in Rs.crore) of Company Y during the given period

= 1/7 * (80 + 40 + 60 + 60 + 80 + 100 + 140) = 560/7 = 80

Average annual exports (in Rs. crore) of Company Z during the given period

1/7 * (60+90+120+60+80+100) = 600/7

:. Required percentage 80/(600/7)*100 % = 93.33%.

3. Option C

Explanation:

The difference between the exports from the Companies X and Y during the various

years are:

In 1993 = Rs. (80 – 30) crores = Rs. 50 crores.

In 1994 = Rs. (60 – 40) crores = Rs. 20 crores.

In 1995 = Rs. (60 – 40) crores = Rs. 20 crores.

In 1996 = Rs. (70 – 60) crores = Rs. 10 crores.

In 1997 = Rs. (100 – 80) crores = Rs. 20 crores.

In 1998 = Rs. (100 – 50) crores = Rs. 50 crores.

In 1999 = Rs. (140 – 120) crores = Rs. 20 crores.

Clearly, the difference is minimum in the year 1996.

4. Answer: Option C

Explanation:

Average exports of the three Companies X, Y and Z in 1993 = (30+80+60)/3 = 170/3

crores.

Average exports of the three Companies X, Y and Z in 1998 =(50+100+80)/3 = 230/3.

Difference = (230-170)/3 = 60/3 = 20 crores

5. Option C

Explanation: 1/7 *(60 + 90 + 120 + 90 + 60 + 80 + 100) = 600/7 =85.71 crores

From the analysis of graph the exports of Company Z are more than the average

annual exports of Company Z (i.e., Rs. 85.71 crores) during the years 1994, 1995,

1996 and 1999, i.e., during 4 of the given years.

II. 1. Answer (d)

2. Answer (c)

3. Answer (a)

4. Answer (d)

5. Answer (b)

I. Based on the circle graph given below, answer the following questions.

Expenditure for State and Local Governments

1. What type of information is being presented on this graph?

a. Expenditure for education

b. Expenditure for public welfare

c. Expenditure for state and local governments

d. Expenditure for highways

2. If the total spending is $50,000, how much money was spent on highways?

a. $3,500

b. $22,500

c. $ 15,000

d. $ 20,000

3. Approximately how many times the amount spending on highways is spent on education?

a.10

b.3

c.5

d.15

4. Approximately what fraction of the total expenditures are spent on highways and public welfare combined?

a. 2/5

b. 1/5

c.1/2

d. 2/3

5. How much money was spent as other expenses

a. 22,500

b. 15,000

c. 30,000

d. 20,000

II.Study the graph given below and answer the following questions

1. These two activities took up half of the time of the day

a. Entertainment and School

b. Meals and School.

c. Sleep and School

d. Homework and sleep

2.These two activities took up the least amount of time

a. Sleep and School

b. Meals and Homework

c. Sleep and Job

d. School and Entertainment

3. Which of these took up one fourth of the day?

a. Entertainment

b. Sleep

c. Homework

d. Meals

4. What percent of the day does homework take up?

a.2

b.15

c.8

d.25

5. Which of these takes up the same amount of time as meals and entertainment together?

a. Job

b. School

c. Homework

d. Entertainment

**Answer & Explanations**

I.1.(c)

2.(a)

3.(c)

4.(b)

5.(a).

Exp. The graph title is Expenditures for State and Local Governments. The circle is cut into four sectors,

each representing one category of expenditures, with the percentage of the total for each category.

Money spent on highways is $3,500 ( 50,000* 7 /100 ) = 3,500

State and local governments spent approximately five times more on education than on highways ( 34

% ).

Approximately 1/5 of the total is spent on highways and welfare combined.

( 7 * 50,000/100 + 14 * 50, 000/100 = 3,500 + 7, 000 = 10,500 )

45 *50,000/100 = 22,500

II.1.(c)

2.(b)

3.(b)

4.(c)

5.(b)