Types of representation of data
Data can be represented in a multitude of ways, including tables and different charts. We will look at the different representations of data in this section.
1) The Bar family
A bar chart or bar graph is a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. Bar charts are used for plotting discrete (or 'discontinuous') data which has discrete values and is not continuous
1a) Simple Bar graph
Look at the example below. The Y-axis denotes the points scored by Teams A, B & C over the years 2003-2006. For eg, Team A scores 25 points in the year 2004.
1b) Cumulative/Stacked Bar Graph
The stacked bar graph is a graph that is used to compare the parts to the whole. The bars in a stacked bar graph are divided into categories. Each bar represents a total.
In the example below, in the year 2005, team A scores 20% of the available points, team B scores 20% of the points, and Team C scores 60% of the points.
2) The Line family
A line chart or line graph is a type of graph, which displays information as a series of data points connected by straight line segments. It is a basic type of chart common in many fields. It is an extension of a scatter graph (see Figure 5 below), and is created by connecting a series of points that represent individual measurements with line segments. A line chart is often used to visualize a trend in data over intervals of time – a time series – thus the line is often drawn chronologically.
2a) Scatter Graph
A scatter plot or scatter graph is a type of mathematical diagram using Cartesian co-ordinates to display values for two variables for a set of data. The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis
Each point in the graph below shows the profit and turnover data for a company. Each company belongs to one of the three food commodity industries-Jowar, Bajra and Ragi.
2b) Simple Line Graph
In the example below, it can be seen that Team A scores 10 points in 2003, 25 points in 2004, 20 points in 2005 and 50 points in 2006
2c) Stacked Line Graph/ Band Diagram
A stacked line graph or a Band Diagram is a line chart in which lines do not overlap because they are cumulative at each point. A stacked line chart displays series as a set of points connected by a line. Values are represented on the y-axis and categories are displayed on the x-axis. You can read it similar to a stacked bar graph
In the example below, Team A scores 10 points in 2003, Team B scores (30-10) 20 points in 2003 and Team C scores (60-20-10) 30 points in 2003.
The same data, for clearer understanding, is represented in a stacked bar graph as follows
2d) Cumulative Line Graph
To read a cumulative line chart, the values are “Accumulated” or “Added on” to those of the previous data point in the chart. Look at the example below. In the first quarter, both Primary and Secondary education comprise 10% of the budget allocation. In the second quarter, the budget allocation for Primary Education becomes 20% (30-10) and the budget allocation for Secondary Education becomes 10% (40-30)
3) The pie family
A pie chart (or a circle graph) is a circular chart divided into sectors, illustrating proportion. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents. Together, the sectors create a full disk. The pie chart is perhaps the most ubiquitous statistical chart in the business world and the mass media. Pie charts can be an effective way of displaying information in some cases, in particular if the intent is to compare the size of a slice with the whole pie, rather than comparing the slices among them
A chart with one or more sectors separated from the rest of the disk is known as an exploded pie chart. This effect is used to either highlight a sector, or to highlight smaller segments of the chart with small proportion.
3b) Doughnut Chart:
A doughnut chart (also spelled donut) is functionally identical to a pie chart, with the exception of a blank center and the ability to support multiple statistics as one. There are 2 types of doughnut charts, doughnut and exploded doughnut.
IMPROVE YOUR CALCULATION PROWESS
The Importance of Reciprocal Percentages and Fractions
In the DI section, the CAT tests your ability to interpret and understand questions based on facts and figures. It also tests your calculation speed; as if you can minimize your calculation, you will be able to increase your attempts in the paper
Let’s take an example:
Suppose you have to calculate 5.26% of 760 as a sub-step of the a DI calculation. For instance,
Tips To Remember Some Values
The value of the reciprocal percentage (RP) for 6 is exactly half that for 3 (half of 33.33 = 16.66)
The Reciprocal for 8 is exactly half of 4 (half of 25 = 12.5)
Seven is easy to remember: 7 into 2 (14), followed by 14 into 2 (28), which makes it 14.28
9 is one-third of 3 (33.33 divided by 3 = 11.11)
Note to students
This booklet contains 10 practice tests based on questions from Data Interpretation & Logical Reasoning.
PRACTICE EXERCISES IN DATA INTERPRETATION & LOGICAL REASONING- SET 1
DI & LR 01
No of questions- 14 Time: 30 mins
DIRECTIONS for questions 1 to 5: Answer the questions on the basis of the data given below.
No of questions- 14 Time: 30 mins
DIRECTIONS for questions 1 to 5: Answer the questions on the basis of the data given below.
Note: Some of the values are missing in the tables.
1) Which team was ranked third in Group A after the first round?
a)Australia b) England c)South Africa d) New Zealand
2) Which team was ranked fourth in Group B after the first round?
- a) Pakistan b) Zimbabwe c)Sri Lanka d) Bangladesh
3) How many matches in the first round resulted in a draw?
- a) 6 b) 7 c) 12 d) 14
4) Which of the following teams did not lose a single match in the tournament?
- a) South Africa b) England c) New Zealand d) Bangladesh
5) Which of the following teams was the runner-up in the tournament?
- a) England b) Bangladesh c) India d) None of these
DIRECTION for question 6 to 9: Answer the questions on the basis of the data given below.In US a survey was done for 100 Congressmen. The scores of the 100 Congressmen in three fields: Honesty, Accessibility, Efficiency are tabulated below in Table A, B and C respectively. A score is given in the first column, and the second column gives the number of congressmen who have secured less than that score. For example, in Table A the second entry indicates that 18 Congressmen have scored less than 1 in the Honesty. Similarly, Tables B and C provide data in a similar format. The ‘Overall Score’ for a Congressman is equal to the sum of his/her scores in the three individual fields. The scores in the three fields can have only integer values and the maximum score in any field is 10.
Assume that, if the Congressmen are arranged in descending order of their scores in the Honesty Field, their scores in the Accessibility and Efficiency fields are also in same order.
6) What is the ‘Overall Score’ of the Congressmen who stood first in the test?
- a) 27 b) 28 c) 29 d) Cannot be determined
7) Which of the following statements is false?
- a) Only one Congressman scored 1 mark in each of the three fields
- b) No Congressman got an overall score of 30.
- c) Only one Congressman scored more than 7 marks in each of the three fields.
- d) 8 Congressmen scored 6 marks in each of the three fields.
8) What is the number of Congressmen who scored more than 4 marks in each of the three fields?
- a) 10 b) 20 c) 30 d) Cannot be determined
9) The number of Congressmen who definitely scored 0 marks in each of the three fields is:
- a) 18 b) 25 c) 31 d) None of these
Questions 6 to 10: Answer the questions based on the information given below
At the Kovalam beach, a popular tourist attraction and commercial spot, there was a survey conducted on the type of vehicles being parked at the beach common parking lot over a period of 5 years (April 2000 to March 2005)
The pie chart gives the distribution of the type of vehicles being parked. The table below gives the parking rates for different vehicles. Assume that the charges are on a per day basis and no vehicle is parked for more than 24 hours
VEHICLES | PARKING FEE (Rs) |
2 wheelers | 10 |
3 wheelers | 20 |
Cars | 30 |
Vans | 40 |
Trucks | 50 |
Others | 0 |
The following bar graph gives the percentage breakup of vehicles that were parked in the lot each year from 2000 to 2005. (Year starts from April and ends in March next year)-read the graph from left to right
DIRECTIONS for questions 11 to 14: Answer the questions on the basis of the data given below. In a college the performance of a student is judged by his overall performance in five tests in a semester. In each test the students are given grades A+, A, B, C, D each containing points 10, 7, 4, 1, 0 respectively. The GPA of a student is equal to the average of the points obtained in the five tests. The points obtained by a batch of fifteen students in these 5 tests are given below.
Name | Test 1 | Test 2 | Test 3 | Test 4 | Test 5 | GPA |
Manish | C | B | 4.4 | |||
Alok | D | A | 3.6 | |||
Vijay | D | C | 4.2 | |||
Ravi | C | A | 4.6 | |||
Raj | A | A+ | 3.8 | |||
Mohit | C | A | A+ | 5.2 | ||
Sagar | C | B | A+ | 6.4 | ||
Rakesh | C | A | 5 | |||
Shekhar | B | A | 8.2 | |||
Pankaj | D | D | 2.2 | |||
Akshay | D | A+ | 6.2 | |||
Paresh | B | A+ | 5.6 | |||
Salman | C | A | 5.6 | |||
Vinod | B | A+ | 7 | |||
Neeraj | A+ | 3.2 |
It is also known that the grade scored by a student in a test are never less than the grade obtained in the previous test, e.g., the grade scored in Test 5 will be greater than or equal to the grade scored in Test 4.
11) How many students definitely scored A+ in Test 5?
a) 10 b) 12 c) 13 d) 14
12) The number of candidates who got A+ grade in at least two out of the five tests is:
- a) not more than 5 b) not more than 6
- c) not more than 7 d) None of these
13) Which of the following statements cannot be true?
- a) Only two students secured the same grade in three consecutive tests.
- b) Exactly five students did not get D grade in any of the tests.
- c) The average score of the fifteen students in Test 2 is equal to 2.
- d) The average score of the fifteen students in Test 3 is equal to 5.
14) It is known that Ravi and Akshay secured equal grades in Test 3. So, which of the following statements is definitely true?
- a) Everyone except Alok and Ravi got A+ grade in Test 5.
- b) Exactly eight students got C grade in Test 2.
- c) Exactly 6 students got less than A grade in Test 3.
- d) None of these.
Questions 1 to 5: Answer the questions based on the information given below
Six players, Kramnik, Topalov, ,Shirov, Leko, Polgar and Anand participate in a chess tournament. In the first round each player plays one match against every other player. The winning player is awarded 3 points and the losing player gets 1 point. In case of a draw each player is awarded 2 points. The player with the highest number of points enters the final. The semifinal is played between the next two players. The winner of the semifinal enters the final. The winner of the finals is declared the champion. There can be no draws in the final and the semifinal. The results of all the matches played by the players at the end of the tournament are given below.
1) Who is the champion?
- a) Kramnik b) Topalov c) Leko d)Anand
2) The semifinal is played between players
- a) Kramnik and Topalov b) Topalov and Polgar
- c) Kramnik and Anand d) Polgar and Anand
3) Find the points of the semifinalists before the semifinal
- a) 9,10 b) 10,10 c)10,11 d)11,11
4) Which two players played the final?
- a) Kramnik and Topalov b) Topalov and Leko
- c) Kramnik and Anand d)Topalov and Anand
5) Which of the following is/are true?
The top three rankings at the end of the tournament are the same as those at the end of the first round.
Anand won the maximum number of matches in the first round.
Kramnik has the highest number of points at the end of first round .
- a) I only b) II only c) III only d) I, II and III
Directions for Question 6 to 10: Answer the questions on the basis of the information given below.
The following table provides information about the marks obtained by 30 students in three different sections namely QA, LRDI and VA in MOCK Test 10. The total marks obtained by the students in MOCK Test 10 are the sum of the marks obtained by the student in the mentioned three sections. It also provides information about the center at which the student is enrolled. The students belong to either one of the five centers namely I, II, III, IV and V. Each student is enrolled at only one center. Each student is given only one rank from 1 to 30 based on the marks obtained by him/her in the MOCK Test 10. This rank is called ‘overall rank’. A student A (assume) is given a numerically lesser rank than the other student B (assume) if the total marks obtained by A is greater than the total marks obtained by B. If the total marks obtained by A is same as that by B, then the student having obtained more marks in VA section is given a numerically lesser rank. If marks obtained by two students in VA section are also same, then the student having obtained more marks in LRDI section is given a numerically lesser rank.
NAME | Gender | Center | QA | LRDI | VA | NAME | Gender | Center | QA | LRDI | VA |
Dennis | M | IV | 9 | 10 | 21 | Sagarika | F | I | 7 | 11 | 23 |
Preeti | F | V | 8 | 12 | 16 | Manish | M | IV | 19 | 10 | 15 |
Anurag | M | IV | 6 | 9 | 23 | Nitya | F | V | 13 | 6 | 14 |
Pronab | M | IV | 13 | 8 | 29 | Aditi | F | III | 11 | 8 | 19 |
Abishek | M | III | 14 | 7 | 31 | Avni | F | II | 21 | 21 | 4 |
Shefali | F | II | 11 | 8 | 17 | Anshul | M | I | 5 | 20 | 14 |
Reema | F | I | 5 | 16 | 6 | Sachin | M | II | 22 | 6 | 6 |
Rahul | M | V | 21 | 13 | 19 | Nidhi | F | III | 7 | 9 | 17 |
Rohit | M | IV | 11 | 11 | 22 | Saurav | M | III | 4 | 8 | 31 |
Jeevika | F | III | 7 | 19 | 23 | Anya | M | IV | 16 | 17 | 10 |
Sharanya | F | II | 16 | 4 | 22 | Gaurav | M | V | 10 | 5 | 7 |
Arjun | M | V | 19 | 5 | 29 | Sunil | F | IV | 9 | 19 | 9 |
Akshay | M | V | 3 | 13 | 31 | Deepali | F | V | 1 | 13 | 14 |
Vidya | F | III | 4 | 21 | 30 | Salim | M | III | 21 | 15 | 11 |
Tarun | M | I | 2 | 17 | 35 | Sanjay | M | II | 18 | 11 | 9 |
6) Find the rank of Nidhi.
a) 24 b) 25 c) 26 d) 27 e) none of these
7) How many male students got more marks in VA than the marks obtained by Deepali in VA but less marks in QA than the marks obtained by Avni in QA?
a) 12 b) 11 c) 10 d) 9 e) 8
8) Find the number of female students who obtained more total marks than at most five female students and more total marks than at least two male students.
a) 1 b) 2 c) 3 d) 4 e) none of these
9) If the criterion for ranking the students is followed by each center to rank the students enrolled there, then find the difference between‘ overall rank’ and the ‘center rank’ of Rohit. (Overall rank is the rank when all the 30 students are taken into consideration and ‘center rank’ is the rank when only the students of that particular center is taken into consideration.)
a) 13 b) 12 c) 11 d) 9 e) 6
10) From which center, the maximum possible number of students obtained a total of at least 40 marks and at most a total of 54 marks?
a) IV b) III c) V d) Both IV and V e) Both III & I
Directions for questions 1 to 5
Mr. Andrews Music academy is a leading house of Music education in India. It provides music classes in Violin, Guitar, Harmonica, Piano and the Accordion. The following two charts give the composition of his students over certain periods of time.
In the July of 2005, the number of students learning Violin was 7.23% of those learning violin from April 2005 to March 2006. Also, it is known that Mr. Andrews Music academy had 527000 students from April 2005 to March 2006, considering enrolments for all the instruments.
1) In July 2005, total number of students learning music was what percent of students learning music under Mr. Andrews from April 2005 to March 2006.
a) 7.23% b) 7.68% c) 8.01% d) 6.89% e) Cannot be determined
2) What is the approximate number of students learning Accordion in July 2005.
a) 405 b) 685 c) 527 d) 490 e) Cannot be determined
3) Which two instruments had the same ratio of the number of students in July 2005 to number of students in April 2005 to march 2006?
a) Violin, Harmonica
b) Accordion, Harmonica
c) Violin, Piano
d) Piano, Accordion
e) Cannot be determined
4) A total of 155500 students were enrolled from April 2005 to July 2005. What percent of students enrolled in a year, from April 2005 to march 2006, actually enrolled in the first quarter of the year?
a) 10% b) 22% c) 39% d) 50% e) None of these
5) For which instrument was the ratio of no of enrolments in July 2005 to enrolments from April 2005 to March 2006 the maximum?
a) Violin b) Guitar c) Harmonica d) Piano e) Accordion
Questions 6 to 10: Answer the questions based on the information given below
Gautam is preparing for a Common Entrance Exam (CEE) to get into his dream college for MBA. In his first Mock CEE, he scores 50 marks out of 100 in each of the four sections VA, QA, Reasoning and RC. Resolving to fare better, he burns the midnight lamp for the next 15 days after which he takes his second mock CEE. He also aims to score 20% more in Reasoning, 28% more in QA,44% more in VA and 12% more in RC In the second Mock CEE. Here the maximum marks are 25 for each section. The results are announced after 3 days and he observes that he has scored exactly what he has expected in two sections whereas he has exceeded his expectations in the other two sections. In one of those two sections, the percentage increase in marks was thrice that he aimed at and in the other section he scored 10 marks more than what he expected. After realizing that he could achieve his goal, he sat tight and set higher targets for the next Mock CEE.
6) What could the maximum percentage growth in marks in a single section be?
a) 50% b) 66.66% (c) 100% (d) 92% e) 60%
7) What is the maximum possible percentage growth in Gautam’s marks in Mock CEE 2 over Mock CEE 1?
a) 25% b) 50% c) 60% d) 70% e) none of these
8) If the overall percentage increase in marks in Mock CEE 2 is 52%, then how much does in score in RC in Mock CEE 2?
a) 0% b) 36% c) 60% d) 42% e) 50%
9) If Gautam had scored 5 marks more in each section than he had aimed at, then what would be his percentage growth in marks?
a) 52% b) 62% c) 64% d) 66% e) 72%
10) What could the minimum percentage growth in total marks in the two MOCK CEEs be?
a) 21% b) 22% c) 30% d) 24% e) 15%
Questions 11 to 13: Answer the questions based on the information given below
Eight years ago, Yellow was half as old as Green will be when Green is one year older than Blue will be at the time when Yellow will be five times as old as Blue will be 2 years from now. Ten years from now Blue will be twice as old as Green was when Yellow was nine times as old as Blue.
When Blue was one year old, Yellow was three years older than Blue will be when Green is three times as old as Yellow was six years before the time when Green was half as old as Blue will be when Yellow will be ten years older than Yellow was when Green was 1/3 rd as old as Blue will be when Yellow will be three times as old as she was when Green was born.
11) How old is Blue?
a) 4 b) 6 c) 2 d) none of these
12) How old will Green be 10 years from now?
a) 17 b) 8 c) 18 d) None of these
13) How old would have Yellow been 6 years ago?
a) 15 b) 8 c) 9 d) None of these
Questions 14 to 16 Answer the questions based on the information given below
When the records were finally retrieved, the management, out of sheer exuberance, decided to reward the staff as follows. If any of the staff had named all 5 in the right order he would get Rs 10000 as cash prize. If the staff names “n” out of all 5 years correctly, he will get (n+1) thousand as cash. It was found that each staff won a different amount of money
Direction for questions 6 to 8: Answer the questions based on the following information.
The bar graph below shows the foreign investments broken up into FDI (Foreign Direct Investment) and FII (Foreign Institutional Investment) in five countries Brazil, Russia, India, China and Indonesia as a percentage of their GDP. Observe the graph and answer the questions that follow.
6) If the difference between the FDIs of Brazil and Indonesia is $ 8.34 billions, then what is the difference in their FIIs?
a) $ 5.56 b b) $ 8.34 b c) $ 12.51 b d) Cannot be determined
7) If the FDI in china is 18 times of that in India, than by how many times of India’s GDP is the FII in China greater than that in India
Directions for Qs. 9 to 13: Refer to the following information and answer following questions.
Milind received a large order for stitching designer formal shirts for women from Jasmine and Aakruti boutiques .He has two cutters who will cut the fabric, five tailors who will do the stitching, and two assistants to stitch the buttons and button holes. Each of these nine persons will work for exactly 10 hours a day. Each of the Jasmine shirts requires 20 min. for cutting the fabric, one hour for stitching, and 15 min. for stitching buttons and button holes for the shirts, whereas the Aakruti shirt requires 30 min., 1 hour, and 30 min. respectively for these activities.
9) What is the maximum number of Aakruti shirts that Milind can complete in a day?
a) 50 b) 20 c) 40 d) 30
10) On particular day, Milind decided to complete 20 Aakruti shirts. How many Jasmine shirts can he complete on that day?
a) 30 b) 40 c) 20 d) 0
11) If Milind decides to complete 30 Aakruti shirts only and no other on a particular day, how many total man-hours will be idle?
a) 20 b) 30 c) 5 d) 25
12) If he hires one more assistant, what is the maximum number of Jasmine shirts that he can complete in a day?
a) 40 b) 50 c) 60 d) 30
13) Milind has the option to hire one more employee of any category. Which category should he hire to get maximum increase in production capacity, assuming that he needs to stitch only Jasmine shirts on that day?
a) Tailor b) Cutter c) Assistant d) Cannot be determined
Questions 1 to 5:- Answer the questions based on the information given below
4 friends; Karan, Lavanya, Mariam, and Nargis are playing a game called “Lose It” wherein the loser doubles the money of each of the other players. They played 4 times and each friend lost one game in the alphabetical order. Each friend has Rs 96 at the end of the last game.
1) Who had same amounts at the end of the second game?
a) Mariam, Nargis b) Karan, Nargis c) Karan, Lavanya d) none of these
2) How much money did Mariam have initially?
- a) 25 b) 54 c) 122 d) none of these
3) Who had the minimum deviation from the opening amount?
a) Karan b) Lavanya c) Mariam d) Nargis
4) What was the amount left with Karan at the end of the second round?
a) 6 b) 12 c) 18 d) 24
5) Who had the maximum profit by the end of the 4th round?
a) Karan b) Lavanya c) Mariam d) Nargis
Questions 6 to 10:- Answer the questions based on the information given below
The International Kabbadi League (IKL) was formed last month to give a boost to the game at international standards. It had a tournament, where 2 teams played some matches. Each team comprised of 7 players each. The listings of the 2 teams X and Y were lost, but certain details regarding the players were available. A, B, C, D, E, F, G, H, I, J, K, L, M and N are the players.
D and E were in Team X, K and G were in team Y.
H and B were in the same team, but not in the team in which F was.
The sum of the scores of members of Team Y was not greater than 115.
The table containing the details of the players and their scores is below
A | B | C | D | E | F | G | H | I | J | K | L | M | N |
28 | 12 | 29 | 10 | 9 | 11 | 13 | 14 | 22 | 28 | 16 | 20 | 18 | 15 |
6) Which of these players was definitely in Team Y?
a) L b) M c) N d) None of these
7) If the score for team Y was less than 110, what could be the score of team X?
a) 135 b) 137 c) 139 d) cannot be determined
8) Which of these players could not be in team Y, if the score of Y was 115?
a) A b) L c) M d) N
9) Which of these players was definitely in team X, if the score of Y was 112?
a) I b) L c) M d) N
10) Which of these players are definitely in Team X?
a) F b) H c) B d) None of these
Questions 11 to 15: Answer the questions based on the information given below
The given figure shows the production and consumption of Ragi in India over a period of 5 years.
11) If surplus ragi available each year was exported, what % of the ragi produced between the years ’97-98 and ’00-01 was exported?
a) 4.57 b) 7.31 c) 6.27 d) none of these
12) Between the years ’96-97 and ‘00-01, the following can be said about the cumulative production and consumption of ragi
a) Cumulative production of ragi exceeded that of consumption by 18 lac tones
b) Cumulative consumption of ragi was 89% of the cumulative consumption of ragi during this period.
c) Cumulative production of ragi exceeded cumulative production of ragi by 4.7% during this period.
d) Consumption of ragi never exceeded the production of ragi during this period.
13) Which of the following statements are true?
I) The YOY rate of growth of production of ragi has been greater than the YOY rate of growth of consumption of ragi during the period 97-98 to 00-01
II) The CAGR rate of growth of production of ragi has been greater than the CAGR rate of growth of consumption of ragi during the period 97-98 to 00-01
III) The amount of ragi exported in a given year was greater than the previous year during all the years in the period 97-98 to 00-01
a) I only b) I and II only c) III only d) II only
14) What was the % rate of growth in production of ragi between the period 99-00 and 00-01?
- a) 4.05% b) 5.71% c) 1.67% d)10%
15) Which of the following years witnessed a two-digit rate of growth in production of ragi?
- I) 97-98 II) 99-00 III) 00-01
- a) I only b) I and II c) I and III d) None of these
Direction for question 1 to 5: Questions are based on the following data.
P, Q, R, S, T, U, and V are seven students whose pet dogs are standing in a row. The pets are numbered 1 to 7 from left to right.
Neither P’s pet nor U’s pet are at the ends of the row.
R’s pet is to the right of S’s pet.
T and Q’s pets are adjacent to each other.
V’s pet is among the three middle pets in the row.
Q’s pet is not adjacent to R’s pet but it is one of the two pets between R’s and V’s pets.
1) Whose among the following can be pet no.2?
a) T b) P c) Q d) S
2) Which pet belongs to U?
a) no.2 b) no. 3 c) no. 4 d) Cannot be determined
3) If it is known that S’s pet is U’s pet’s immediate neighbor, then whose pet is to the immediate right of P’s pet?
a) U b) V c) S d) R
4) Among the following, whose pet is nearest to S’s pet?
a) R b) V c) U d) T
5) Among the following, whose pet is farthest from R’s pet?
a)S b) P c) U d)Cannot be determined
Directions for questions 6 to 9: Answer these questions based on the following data.
Nine cities – A through I – one connected with two way roads, which are between A & B; A & D; B & C; B & E; C & F; D & E; D & G; E & H; E & F; F & I; G & H and H & I. each road is 10 km in length.
6) If a person wants to go from A to I, by travelling through the least number of cities, then how many ways are available to him?
a) 4 b) 6 c) 8 d) None of these
7) If a person wants to visit all the towns, each being visited exactly once, and if he wants to start at A, then how many ways are available to him?
a) 6 b) 8 c)10 d) None of these
8) In how many ways can a man reach D, starting from A such that the person does not visit the same city twice?
a) 5 b) 9 c) 7 d) None of these
9) What is the longest possible distance to reach D, starting from A? Assume that no city can be visited twice.
a) 60 km b) 70 km c)80 km d)None of these
Directions for question 10 to 14: Answer These questions based on the following data.
Each of five people – A, B, C, D, and E – owns a house each in different cities among Bangalore, Madras, Jaipur, Delhi, and Bombay, and the colours of these houses are black, green, blue, white, and red, not necessarily in that order. No two houses are of the same colour. It is also known that:
A’s house is not black and it is not in Madras.
B’s house is green and it is not in Jaipur.
E’s house is not white and it is not in Bombay.
C’s house is in Madras and it is not blue in colour.
D’s house is not red and it is in Delhi.
Questions 5 to 9:- Answer the questions based on the information given below In the annual Gulab Jamun(G) eating competition, it was conceded that beyond a particular number of Gulab Jamuns, higher weightage needs to be given, as it was unanimously agreed that the difficulty level increases with the number of Gulab Jamuns consumed. The competition was divided into stages & the points were rewarded as given aboveAlso ( + = x, - = +, x=/ and / = - )
Questions 10 to 14: Answer the questions based on the information given below
In her annual college fest, Disha visits a 7 up 7 down stall to make a fast buck. She plays 5 times in the game. She manages to win in all the even-numbered games wherein she invests the entire amount she has with her at that point of time and makes 2 times that amount. However, in the odd-numbered games, she invests 1/5th the amount she has with her and loses it entirely. Finally, she has Rs. 1024 left with her with which she proceeds to the food stalls with great celerity
10) How much money did Disha win in all?
a) 500 b) 534 c) 564 d) 524 e) 584
11) How much money did Disha have in the beginning of game 2?
a) 500 b) 400 c) 450 d) 550 e) None of these
12) How much money did she invest in the 5th game?
a) 450 b) 350 c) 250 d) 280 e) None of these
13) How much money did she win in game 4?
a) 640 b)650 c) 660 d) 670 e) 680
14) What is the highest amount she has invested in any round of the game?
a) 640 b) 560 c) 450 d) 550 e) 550
Directions for questions 5 to 9: Answer the questions are based on the data given below:
Study the table below and answer the following question:
TABLE 1: IMPORT, (WEIGHT %)
TABLE 2: EXPORT, (WEIGHT %)
5) The three commodities which had highest export growth rate in the year 2004-05 as compared to the previous year, arranged in descending order of growth rates are:
- a) petroleum products, ores and minerals, engineering goods
- b) ores and minerals, gems and jewellery, chemicals and related products
- c) gems and jewellery, chemicals and related products, agri and allied products
- d) ores and minerals, chemicals and related products, agri and allied products
6) In the year 2005-06 the commodity which witnessed maximum growth in exports (in Indian Rupees) as compared to the year 2004-05 is:
- a) petroleum products b) project goods
- c) ores& minerals d) None of these
7) In the two-year period from 2004-05 to 2005-06, the average growth in import (in Indian Rupees) of which commodity to India was maximum?
- a) bulk imports b) pearls, precious and semi-precious stones
- c) machinery d) project goods
8) Percentage growth of trade imbalance (exports less imports) in dollar terms in the year 2005-06 as compared to the previous year was:
a) 39.77 % b) 41.85 % c) 91.24 % d) 95.98 %
9) Given that the weight (%) of Petroleum crude and products in the total imports of India is 26.70, 27.87, and 30.87 in the years 2003-04,2004-05, and 2005-06 respectively. What is the ratio of yearly difference in the export of Petroleum Products and import of Petroleum crude and products, in dollar terms, in the year 2005-06 versus 2004-05?
a) 1.36 b) 1.38 c) 1.46 d) 1.48
Directions for Questions 10 to 12: Answer the questions on the basis of the information given below.
The first chart provides information about five PC manufacturers namely Compaq-HP, HCL, Acer, Zenith and Sony. It shows the selling price per PC and the cost price per PC for each of these mentioned manufacturers.
The second chart provides information about the annual sales for each PC manufacturer for a given year. It also provides information about the sales tax rate as a percentage of the selling price for each manufacturer
Additional information given:
Profit = Selling Price – Cost Price – Sales Tax
Revenue = (Selling Price per PC) × (Number of PC’s sold)
Questions 13 to 15: Answer the questions based on the information given below
Arnab was keen to make his money work for him, and being a prudent financial analyst, he decided to distribute his earnings in various avenues. Following is the distribution of his earnings over the years from 94-95 to 99-00. Note that, higher proportion in equities and equity options indicate a better equity market and a higher proportion in debt and government bonds indicate a better debt market.
Directions for questions 6 to 10: Answer the questions on the basis of the data given below
Chingfisher Airlines is recruiting candidates in the year 2010-2011 for its three sectors;
Air Staff(Levels A1,A2,A3), Ground Staff(Levels G1,G2,G3,G4) and Engineers(Levels E1,E2,E3).
The number of candidates interviewed by only Ground Staff, which was same as the number of candidates interviewed by both Ground Staff and Air Staff but not Engineering sector was thrice of those interviewed by only Engineering sector.
The number of candidates interviewed by all three sectors, which was less than the number of candidates interviewed by only Ground Staff, was one more than those interviewed by the Air Staff and Engineering Sectors.
The number of candidates interviewed by the sector Air Staff was one less than twice the number of candidates interviewed by all three sectors. Ground Staff and Engineering sector but not Air Staff sector interviewed two more than thrice the number of candidates that only the Ground Staff sector interviewed.
The number of candidates interviewed for A1 was 2 more than half the number of candidates interviewed for A2 and the number of candidates interviewed for A2 was 3 more than the number of candidates interviewed for A3.
Candidates interviewed for G2 was 1.5 times the number of candidates that were interviewed for A2. For G1, 2 candidates less than G2 were interviewed. For G3, 2 candidates more than G4 were interviewed and for G4, one candidate more than A2 was interviewed.
An equal number of candidates were interviewed for E1 and E2 and for E3, one candidate more than E1 was interviewed. For A1 interview, the number was half the number of candidates interviewed by E2,
Ground Staff sector recruited 41 candidates in all, which was 50% of the number of interviews they totally conducted.
6) How many candidates were interviewed for Ground Staff?
a) 10 b) 15 c) 17 d) 16 e) none of these
7) How many candidates at a minimum recruited for the four Levels in Ground Staff were also interviewed by Engineering sector but not the Air Staff sector?
a) 7 b) 6 c) 8 d) 10 e) 9
8) Find the number of candidates interviewed for E2 as a percentage of those interviewed for A2 and G2?
a) 100% b) 66% c) 50% d) 82% e) none of these
9) Find the difference between the number of candidates interviewed by only the ground Staff sector and only the Air Staff sector?
a) 3 b) 6 c) 5 d) 4 e) 2
10) Find the sum of number of candidates interviewed for G1 and the number of candidates interviewed by Engineers?
a) 80 b) 83 c) 75 d) 80 e) none of these
DI & LR 01
Solutions for questions 1 to 5
The number of matches played by each team in the first round is 4 and the team earned 5, 2 or 0
points from each match. The only way in which the teams can score
17 is 3 wins and 1 draw;
12 is 2 wins, 1 draw and 1 loss;
11 is 1 win and 3 draws;
7 is 1 win, 1 draw and 2 losses and 0 is 4 losses.
Now, we can fit these values in the table for Group A after the first round as follows:
Team | W | D | L | Total Points |
Australia | 1 | 1 | 2 | 7 |
England | 2 | 1 | 1 | 12 |
S Africa | 3 | 1 | 0 | 17 |
W Indies | 0 | 0 | 4 | 0 |
N Zealand | 1 | 3 | 0 | 11 |
Similarly, we can complete the table for Group B after the first round:
Team | W | D | L | Total Points |
Pakistan | 0 | 3 | 1 | 6 |
India | 4 | 0 | 0 | 20 |
Sri Lanka | 1 | 1 | 2 | 7 |
Zimbabwe | 0 | 2 | 2 | 4 |
Bangladesh | 1 | 2 | 1 | 9 |
At the end of round 2, the table looks like this.
WIN | DRAW | LOST | |
INDIA | 2 | 1 | 0 |
SA | 0 | 1 | 2 |
ENGLAND | 0 | 3 | 0 |
BANGLADESH | 1 | 1 | 1 |
1) (d) -New Zealand
2) (a) - Pakistan
3) (b)
4) Only New Zealand does not lose any match in the entire tournament (c)
5) From statement (iii), we know that Bangladesh scored 9 points in first round and is the runner-up in the tournament with 7 points in the second round. Hence,(b).
Solutions for questions 6 to 9
Consider Table B:
100 Congressmen scored less than 10, i.e., no one scored 10 marks
99 Congressmen scored less than 9, i.e., exactly one scored 9 or more. Since, no one scored 10, exactly one Congressman scored 9. 97 Congressmen scored less than 8, i.e., number of Congressmen who scored 8 = 99-97 = 2, and so on.
Thus, using all the tables, we get the exact number of Congressmen who scored from 0 to 10 marks in each of the three fields, which is tabulated below.
The table also gives the cumulative number of the Congressmen in the descending order of their scores
Honesty | Accessibility | Efficiency | ||||
Score | No. | C.NO. | NO. | C.NO. | NO. | C.NO. |
0 | 18 | 100 | 25 | 100 | 31 | 100 |
1 | 14 | 82 | 15 | 75 | 19 | 69 |
2 | 16 | 68 | 10 | 60 | 10 | 50 |
3 | 2 | 52 | 15 | 50 | 10 | 40 |
4 | 20 | 50 | 10 | 35 | 10 | 30 |
5 | 18 | 30 | 13 | 25 | 12 | 20 |
6 | 7 | 12 | 5 | 12 | 4 | 8 |
7 | 2 | 5 | 4 | 7 | 3 | 4 |
8 | 1 | 3 | 2 | 3 | 1 | 1 |
9 | 1 | 2 | 1 | 1 | 0 | 0 |
10 | 1 | 1 | 0 | 0 | 0 | 0 |
C.NO.=>Cumulative Number
It is given that the order, when the Congressmen are arranged in the descending order of their scores in the Honesty field, is the same as that when they are arranged in the descending order of their scores in the Accessibility as well as Efficiency fields.
6) The Congressman who stood first must be the highest scorer in all the fields.
∴ The ‘Overall Score’ of the Congressman who stood first = 10 + 9 + 8 = 27. Hence, (a).
7) From the table, we can see that the first 68 Congressmen scored at least 2 marks in the Honesty field and the first 69 Congressmen scored at least 1 mark in the Efficiency field. Thus, there is exactly one Congressman who scored 1 mark in each of the three fields. Thus, statement (1) is true.
The maximum overall score for a congressman is 27 as mentioned in the question above and hence, statement (2) is also true.
The number of Congressmen who scored more than 7 marks in the Honesty, Accessibility and Efficiency fields is 3, 3 and 1 respectively. Thus, statement (3) is also true.
The maximum number of Congressmen who scored 6 marks in any field is 7; hence, statement (4) is not true. Hence, (d)
8) The number of Congressmen who scored more than 4 (i.e., 5 or more) in the Honesty, Accessibility and Efficiency fields is 30, 25 and 20 respectively. As 20 is the least number, this is the answer. 20 Congressmen definitely scored more than 4 marks in each of the three fields.
9) The number of Congressmen who scored 0 in the Honesty, Accessibility and Efficiency fields is 18, 25 and 31 respectively. As 18 is the least number, 18 Congressmen definitely scored 0 in all the three fields.
Solutions for questions 10 to 14
10)Total number of bugs = 14 + 12 + 10 + 6 + 2 + (a +b) = 44 + 4 = 48. Hence, (a).
11) We need not check for statement II, as we have already deduced it. We need to calculate the values of a and b to find the exact number of bugs involved in each solution.
12 + 6 + 2 + a =21
Thus, we can calculate the exact number of bugs involved in each solution using either statement I or statement III. Hence, (b).
12) The six bugs involved in all the three solutions are to be withdrawn from exactly one solution. Let the number of bugs withdrawn from the Edusoft solution, Financo solution and Elevate solution be x, x – 2 and x – 4 respectively.
Therefore, the number of bugs involved in the Edusoft solution = 24 – x = 20, the number of bugs involved in the Financo solution = 21 – (x-2) = 19, and the number of bugs involved in the Elevate solution.
= 21 – (x - 4) = 21.
Thus, the number of bugs involved in the Edusoft solution = 24 – x = 20, the number of bugs involved in the Elevate solution is 21. Hence, statement (1) is false. The number of bugs involved in the Financo solution is 1 less than that involved in the Edusoft solution. Thus, statement (2) is also false.
The number of bugs involved in the Edusoft solution is 20. Thus, statement (3) is true. Hence, (c).
13) From the previous reasoning, the answer can be marked as option d, as all other options can be true
14) The number of bugs involved in the three solutions after withdrawal are 20, 19 and 21. These numbers being consecutive can be made equal by adding a minimum of 3 new bugs. Hence, (a).
DI & LR 02
Solutions for questions 1 to 5
1) The answer is fastest obtained by the process of elimination. Let’s take for example, that 360 is the total, then Saurav will score 54 runs, this implies that the number of 4’s he scores will not be an integral number which is not integral. Similarly, the other options can be eliminated. 400 will be the total score
2) Once the total score is obtained as 400 the score table will look as follows.
PLAYER | SCORE |
Saurav | 60 |
Sehwag | 40 |
Sachin | 160 |
Rahul | 80 |
Others | 60 |
PLAYER | No of 6’s |
Saurav | 1 |
Sehwag | 3 |
Sachin | 4 |
Rahul | 2 |
Others | 4 |
Total= 14
5) Out of 11 players, 4 are top-scorers🡪 means that 7 players together can score a maximum of 39 each. Score left to distribute among 7 players= 60, can be distributed among 2 players, hence 7-2=5 will the max no. of players who will not score any runs
Solutions for questions 6 to 10
6)Option (d)
All vehicles other than others pay a parking fee
2 wheelers= 14% of 200000= 28000
3 wheelers= 17% of 50000=8500
Cars= 18% of 150000=27000
Vans= 16% of 75000=12000
Trucks 19% of 55000=10450
Total= 85950
7) Option (d)
Calculate the parking fee for each of the years using the same logic as above
Year 2005
(16% of 200000) × 10 + (14% of 50000) × 20 + (13% of 150000) × 30 + (15% of 75000) × 40 + (20% of 55000) × 50 = 2045000
Year 2002
(15% of 200000) × 10 + (16% of 50000) × 20 + (15% of 150000) × 30 + (17% of 75000) × 40 + (18% of 55000) × 50=2140000
Year 2001
(15% of 200000) × 10 + (16% of 50000) × 20 + (19% of 150000) × 30 + (17% of 75000) × 40 + (15% of 55000) × 50=2237500
Year 2003
(14% of 200000) × 10 + (17% of 50000) × 20 + (18% of 150000) × 30 + (16% of 75000) × 40 + (19% of 55000) × 50= 2262500
Hence answer=2003
8) 1) Parking fee collected by trucks can be calculated as = 55000 x 50=2750000
2) Parking fee collected by 2 wheelers can be calculated as= 200000 x 10 = 2000000
Percentage difference in fee collected from trucks different from the parking fee collected by 2 wheelers =
9)Amount contributed by trucks in the total fee collected in 2003 can be calculated as
Fee collected by trucks in 2003 = (19% of 55000)*50 = 522500
Total fee collected in 2003 (refer the 1st question of this caselet) =2262500
10) Option (b)
2 wheelers = (16 % of 200000)*10 = 320000
3 wheelers = (14 % of 50000)*20 = 140000
total =460000
total parking fee in 2005 (refer the 2ND question of this caselet) = 2045000
Percentage contribution of 2 wheelers and 3 wheelers to the parking fee in 2005 =
Solutions for questions 11 to 14
We can calculate the total points scored by each candidate in all the tests together using the formula,
Total points = GPA x 5.
Ravi’s score in tests 2, 3 and 5 = 23 – 1 – 7 = 15
From the conditions given in the data, Ravi scored 1, 4, 10 or 1, 7, 7 or 4, 4 7 in tests 2, 3 and 5 respectively.
Calculating, in a similar manner, we get that Pankaj scored 0, 1, 10 or 0, 4, 7 in tests 3, 4 and 5 respectively.
Also, Akshay scored 1, 10, 10 or 4, 7, 10 in tests 2, 3 and 5 respectively.
Continuing this way, we get the table below.
11) Out of 15 candidates, except Alok, Ravi and Pankaj, all the others scored 10 points or A+ grade in test 5. Hence, (b).
12) Vijay, Sagar, Shekhar, Akshay, Salman, and Vinod i.e. 6 candidates got A+ in at least two of the five tests. Paresh may or may not have scored 10 points in at least two out of the five tests. Hence, (c).
13) Shekhar scored A+ in tests 3, 4, and 5 and Pankaj scored D grade in tests 1, 2 and 3. Ravi may or may not have scored the same grades in three consecutive tests. Thus option (1) may or may not be true.
Ravi, Mohit, Sagar, Shakhar, and Vinod did not score D grade in any of the tests.
Thus, Option (b) is also true.
The average score of the 15 candidates in tests 2 is
Thus, Option (c) can be true.
The total score of all the 15 candidates in Test 3, except Ravi, Akshay and Paresh, is 56. Considering all the possibilities of the points scored by these three in Test 5, none of them add up to 19. Thus the average of 5 cannot be achieved.
Thus option (4) cannot be true. Hence, (d).
14) If Ravi and Akshay scored the same points in Test 3, then they must have scored 7 points in that test. From the answer to question 14, exactly three students (i.e., exactly one other than Alok and Ravi) did not score 10 points in Test 5. Thus, Option (a) is false. As the scores of Ravi and Akshay in Test 2 are not known definitely, Option (b) cannot be definitely true. Manish, Alok, Vijay, Raj, Pankaj and Neeraj (i.e., 6 candidates) scored less than 7 points in Test 3. Paresh may or may not have scored less than 7 in Test 3. Thus, Option (c) is not definitely true. Hence, (d).
PLAYER | SCORE |
K | 14 |
T | 9 |
S | 8 |
L | 9 |
P | 11 |
A | 17 |
DI & LR 03
Solutions for questions 1 to 5
Tabulate the total number of points obtained by each person
From the data in the table, it can be clearly inferred that Anand wins the tournament. Also the semi-finalists and the finalist can be deduced as K, P and A. Also, one definite player of the semis is P, and it can also be said that P loses in the semis. Therefore the finals will be played between K and A. The semi finals will be played between P & A. We can directly mark the answers to questions
1)option (d) & 2) option (d)
If A won the tournament, then he will have a score of 14-3=11 before the finals. Notice that K has only one loss, and that loss is the loss in the finals, which implies that K has won all the tournaments before. Before the finals, A’s score will stand at 14, P’s score at 11 (he gains one point after losing the semis) and K’s score will stand at 13, who will be the top scorer and will directly go to the finals. From this, we can clearly say that A will play the semis against P. A’s score then becomes 11+3=14 and P’s score 10+1=11
With this we can answer questions 3) Option (c) 4) Option (c) 5) Option (c)
Only statement 3 is true as K has only one loss, which occurs in the finals
6) (c) Rank of Nidhi is 26.
7) (c) Ten male students namely Saurav, Manish, Tarun, Akshay, Arjun, Rohit, Abishek, Pronab, Anurag and Dennis satisfy the condition given in the question.
8) (b) Two female students namely Preeti and Shefali have obtained more marks than two male students namely Gaurav and Sachin and more marks than four female students namely Reema, Nitya, Nidhi and Deepali.
9) (d) Overall rank of Rohit is 11 and center rank of Rohit is 2. Therefore, the required difference is 11 – 2 = 9.
10) (a) From center IV, five students namely Dennis, Pronab, Rohit, Manish and Anya have obtained at least a total of 40 and at most a total of 54 marks.
DI & LR 04
Solutions for questions 1 to 5
1) (b). 7.68%
3) (b). Accordion, Harmonica
The percentage of number of enrolments for Accordion and Harmonica were same in July 2005 and April 2005-March 2006.
4) (b). 22%
The number of enrolments in the first quarter (April 2005 to June 2005) = 155500 – (7.68% of 527000) = 115000.
Thus the required percentage =
5) (d). Piano
Expected Marks On 100 | |
Reasons | 60 |
QA | 64 |
VA | 72 |
RC | 56 |
Looking at these charts, we find that Piano had the maximum ratio of enrolments in July 2005 compared to from April 2005 to March 2006.
Solutions for questions 6 to 10
Gautam’s marks can be shown as follows
Marks in Mock CEE1 | % GROWTH | EXPECTED MARKS ON 100 | MARKS ON 25 IN Mock CEE2 | |
Reasoning | 50 | 20% | 60 | 15 |
QA | 50 | 28% | 64 | 16 |
VA | 50 | 44% | 72 | 18 |
RC | 50 | 12% | 56 | 14 |
6) For the percentage increase in a single section to be maximum🡪Gautam can score 10 marks more in Reasoning= 15+10=25. The percentage increase will be 100% (from 12.5 to 25)
7) For the percentage increase in marks to be maximum, the increase in marks should also be maximum. This will happen only if he exceeds his expectations in the sections where he was expecting the maximum improvement
He cannot improve his VA percentage 3 times as that will cross 100%. He will improve his QA percentage by 3 times what he expected = 28*3= 84% and he gets 10 marks more than expected in Reasoning
New scores in each section
Reasoning=25; QA=23; VA=18 and RC= 14
Total score on 100= 80. Initial score on 100 = 50
percentage growth = 60%
8) Since the percentage growth is given as 52%> marks = 12.5*1.52*4=76 marks in Mock CEE2
The case will not be the previous case where the maximum growth is expected. This time it will be lesser.
If the percentage growth in his score in Reasoning is thrice that expected and he scores 10 marks more in RC, then his total score can be 78. We are looking for 76 marks
This will happen if the percentage growth in his score in RC is thrice than expected and he scores 10 marks more than expected in Reasoning. He then scores 25+16+18+17=76 marks. Thus, his percentage marks in RC= 12*3= 36%
9)Now we have to increase 4 marks and also the % increase of one of the 4 has to be multiplied by 3 and the other should have a 40 increase in marks.
The only possibility for 40 increase in marks and also a 4 increase in marks is for RC, which makes it a 100% increase in score.
Now, we have to see which subject can a 3 time % increase happen, it can happen only in reasoning and QA. But to maximize we will have to take QA.
Finally | Initial | Increased | 4 marks added = 4% | % ↑ |
Reasoning | 50 | 20% | + 4 | 24% |
QA | 50 | 28 × 3 = 84% | + 4% | 88% |
VA | 50 | 44% | 4% | 48% |
RC | 50 | 12% + 10 marks | 4% | 100% |
260/4 = 65% |
10) Minimum % growth happens when he exceeds his expectations in the subjects where he scored the least marks. REASONING=10 marks increase= 25(15+10).
QA= 16. VA=18 and RC=36% increase=19 Total = 78. percentage increase =23.8% .
Answers for the five questions are Option (c), Option (c), Option (b), Option (d), Option (d)
Solutions for questions 11 to 13
This should be solved either by assumption using answer options or by forming equations. Since none of these is also involved, it’s better to proceed by using equations
11) d 12) c 13) c
Let y1, y2 … be the indefinite years. Let t be the year blue was born, j green and m- yellow. Let y be the current year
Solutions for questions 14 to 16
14) Option (d) To the left of Amita is Binoy and Shama, north east of both is Payal.
15) Option (a) B-S(25) S-AM(40) AM-ARIYA(60) ARIYA-P(90) TOTAL=215
16) North east of Shama- Payal South of Payal- Amita and Ariya
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