List of top Data Interpretation & Logical Reasoning (DILR) Questions

In a Class X Board examination, ten papers are distributed over five Groups: PCB, Mathematics, Social Science, Vernacular, and English. Each paper is evaluated out of \(100\).

The final score of a student is calculated as follows:

1. First, the Group Scores are obtained by averaging marks in the papers within the group.
2. The Final Score is the simple average of the five Group Scores.

The data for the top ten students are given below. (Dipan’s score in English Paper II is missing.)

Note: (B) or (G) indicates whether the student is a boy or girl.

Mathematicians are assigned a number called Erdős number (named after the famous mathematician, Paul Erdős). Only Paul Erdős himself has an Erdős number of \(0\). Any mathematician who has written a research paper with Erdős has an Erdős number of \(1\). For other mathematicians, the calculation of his/her Erdős number is as follows:

Suppose a mathematician \(X\) has co-authored papers with several other mathematicians. From among them, mathematician \(Y\) has the smallest Erdős number. Let the Erdős number of \(Y\) be \(y\). Then \(X\) has an Erdős number of \(y + 1\). Hence, any mathematician with no co-authorship chain connected to Erdős has an Erdős number of \(\infty\).

In a seven-day long mini-conference organized in memory of Paul Erdős, a close group of eight mathematicians, call them \(A, B, C, D, E, F, G,\) and \(H\), discussed some research problems. At the beginning of the conference:

• \(A\) was the only participant with an Erdős number of \(\infty\).
• Nobody had an Erdős number less than that of \(F\).

Event Timeline

Day 3 Event:

• \(F\) co-authored a paper jointly with \(A\) and \(C\).
• This reduced the average Erdős number of the group of eight mathematicians to \(3\).
• The Erdős numbers of \(B, D, E, G, H\) remained unchanged.
• No other co-authorship among any three members would have reduced the average Erdős number of the group to as low as \(3\).

At the end of Day 3:

• Five members of the group had identical Erdős numbers.
• The other three had Erdős numbers distinct from each other.

Day 5 Event:

• \(E\) co-authored a paper with \(F\).
• This reduced the group’s average Erdős number by \(0.5\).
• The Erdős numbers of the other six members were unchanged.

Note: No other paper was written during the conference.

Two traders, Chetan and Michael, were involved in the buying and selling of MCS shares over five trading days. At the beginning of the first day, the MCS share was priced at Rs 100, while at the end of the fifth day it was priced at Rs 110. At the end of each day, the MCS share price either went up by Rs 10, or else, it came down by Rs 10. Both Chetan and Michael took buying and selling decisions at the end of each trading day. The beginning price of MCS share on a given day was the same as the ending price of the previous day. Chetan and Michael started with the same number of shares and amount of cash, and had enough of both.
Below are some additional facts about how Chetan and Michael traded over the five trading days:

The table below presents the revenue (in million rupees) of four firms in three states. These firms, Honest Ltd., Aggressive Ltd., Truthful Ltd. and Profitable Ltd. are disguised in the table as A,B,C and D, in no particular order.

Further, it is known that:

• In the state of MP, Truthful Ltd. has the highest market share.
• Aggressive Ltd.’s aggregate revenue differs from Honest Ltd.’s by Rs. 5 million.

The year is 2089. Beijing, London, New York, and Paris are in contention to host the 2096 Olympics. The eventual winner is determined through several rounds of voting by members of the IOC with each member representing a different city. All the four cities in contention are also represented in IOC.

• In any round of voting, the city receiving the lowest number of votes in that round gets eliminated. The survivor after the last round of voting gets to host the event.
• A member is allowed to cast votes for at most two different cities in all rounds of voting combined. (Hence, a member becomes ineligible to cast a vote in a given round if both the cities (s)he voted for in earlier rounds are out of contention in that round of voting.)
• A member is also ineligible to cast a vote in a round if the city (s)he represents is in contention in that round of voting.
• As long as the member is eligible, (s)he must vote and vote for only one candidate city in any round of voting. The following incomplete table shows the information on cities that received the maximum and minimum votes in different rounds, the number of votes cast in their favour, and the total votes that were cast in those rounds. It is also known that:
• All those who voted for London and Paris in round 1, continued to vote for the same cities in subsequent rounds as long as these cities were in contention. 75% of those who voted for Beijing in round 1, voted for Beijing in round 2 as well.
• Those who voted for New York in round 1, voted either for Beijing or Paris in round 2.
• The difference in votes cast for the two contending cities in the last round was 1.
• 50% of those who voted for Beijing in round 1, voted for Paris in round 3.

Venkat, a stockbroker, invested a part of his money in the stock of four companies --- A, B, C and D. Each of these companies belonged to different industries, viz., Cement, Information Technology (IT), Auto, and Steel, in no particular order. At the time of investment, the price of each stock was Rs.100. Venkat purchased only one stock of each of these companies. He was expecting returns of 20%, 10%, 30%, and 40% from the stock of companies A, B, C and D, respectively. Returns are defined as the change in the value of the stock after one year, expressed as a percentage of the initial value. During the year, two of these companies announced extraordinarily good results. One of these two companies belonged to the Cement or the IT industry, while the other one belonged to either the Steel or the Auto industry. As a result, the returns on the stocks of these two companies were higher than the initially expected returns. For the company belonging to the Cement or the IT industry with extraordinarily good results, the returns were twice that of the initially expected returns. For the company belonging to the Steel or the Auto industry, the returns on announcement of extraordinarily good results were only one and a half times that of the initially expected returns. For the remaining two companies, which did not announce extraordinarily good results, the returns realized during the year were the same as initially expected.

The table below reports the gender, designation and age-group of the employees in an organization. It also provides information on their commitment to projects coming up in the months of January (Jan), February (Feb), March (Mar) and April (Apr), as well as their interest in attending workshops on: Business Opportunities (BO), Communication Skills (CS), and E-Governance (EG).

M=Male, F= Female; Exe=Executive, Mgr=Manager, Dir=Director; Y=Young, I=In-between, O=Old

For each workshop, exactly four employees are to be sent, of which at least two should be Females and at least one should be Young. No employee can be sent to a workshop in which he/she is not interested in. An employee cannot attend the workshop on

• Communication Skills, if he/she is committed to internal projects in the month of January;
• Business Opportunities, if he/she is committed to internal projects in the month of February;
• E-governance, if he/she is committed to internal projects in the month of March.

The table below reports annual statistics related to rice production in select states of India for a particular year.

A management institute was established on January 1, 2000 with 3, 4, 5, and 6 faculty members in the Marketing, Organisational Behaviour (OB), Finance, and Operations Management (OM) areas respectively, to start with. No faculty member retired or joined the institute in the first three months of the year 2000. In the next four years, the institute recruited one faculty member in each of the four areas. All these new faculty members, who joined the institute subsequently over the years, were 25 years old at the time of their joining the institute. All of them joined the institute on April 1. During these four years, one of the faculty members retired at the age of 60. The diagram below gives the area-wise average age (in terms of number of completed years) of faculty members as on April 1 of 2000, 2001, 2002, and 2003.
 

ATP Women's Tournament Seeding

In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed #32) which is designated match No. 1 of first round; the 2nd seeded player plays the 31st seeded player which is designated match No. 2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16th seeded player and the 17th seeded player. In the second round, the winner of match No. 1 of first round plays the winner of match No. 16 of first round and is designated match No. 1 of second round. Similarly, the winner of match No. 2 of first round plays the winner of match No. 15 of first round, and is designated match No. 2 of second round. Thus, for instance, match No. 8 of the second round is to be played between the winner of match No. 8 of first round and the winner of match No. 9 of first round. The same pattern is followed for later rounds as well

Help Distress (HD) - Volunteer Project Information

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects:

• Tsunami Relief (TR) in Tamil Nadu
• Flood Relief (FR) in Maharashtra
• Earthquake Relief (ER) in Gujarat

Each volunteer working with Help Distress has to be involved in at least one relief work project.

Given Information:

• A maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project.
• The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.
• 17 volunteers are involved in the TR project.
• The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project alone.
• 10 volunteers involved in the TR project are also involved in at least one more project.

Directions for the following four questions: Answer the questions on the basis of the information given below.

The year was 2006. All six teams in Pool A of World Cup hockey, play each other exactly once.

Each win earns a team three points, a draw earns one point and a loss earns zero points. The two teams with the highest points qualify for the semifinals. In case of a tie, the team with the highest goal difference (Goal For − Goals Against) qualifies.

In the opening match, Spain lost to Germany.

After the second round (after each team played two matches), the pool table looked as shown below.

In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches were drawn. The following are some results from the fourth and fifth round matches

(a) Spain won both the fourth and fifth round matches.

(b) Both Argentina and Germany won their fifth round matches by 3 goals to 0.

(c) Pakistan won both the fourth and fifth round matches by 1 goal to 0.

Directions for the following four questions: Answer the questions on the basis of the information given below.

The data points in the figure above represent monthly income and expenditure data of individual members of the Ahuja family, the Bose family, the Coomar family, and the Dubey family.

The X axis represents Expenditure and the Y axis represents the Income of the individual members.

For these questions, savings is defined as Savings = Income - Expenditure

The straight line in the figure is Linear (Expenditure=Income), from (0, 0) to (3500, 3500).

Data points read from the figure (approximate, to the nearest 50 on each axis):

Directions for the following four questions: Answer the questions on the basis of the information given below.

The Dean’s office recently scanned student results into the central computer system. When their character reading software cannot read something, it leaves the space blank. The scanner output read as follows:

In the grading system, A, B, C, D, and F grades fetch 6, 4, 3, 2, and 0 grade points respectively. The Grade Point Average (GPA) is the arithmetic mean of the grade points obtained in the five subjects. For example Nisha’s GPA is (6 + 2 + 4 + 6 + 0) / 5 = 3.6. Some additional facts are also known about the students’ grades. These are

(i) Vipul obtained the same grade in Marketing as Aparna obtained in Finance and Strategy.

(ii) Fazal obtained the same grade in Strategy as Utkarsh did in Marketing.

(iii) Tara received the same grade in exactly three courses.

Prof. Singh has been tracking the number of visitors to his homepage. His service provider has provided him with the following data on the country of origin of the visitors and the university they belong to: Visitors by Country

Visitors by Country 

Visitors by University 

Purana and Naya are two brands of kitchen mixer-grinders available in the local market. Purana is an old brand that was introduced in 1990, while Naya was introduced in 1997. For both these brands, 20% of the mixer-grinders bought in a particular year are disposed off as junk exactly two years later. It is known that 10 Purana mixer-grinders were disposed off in 1997. The following figures show the number of Purana and Naya mixer-grinders in operation from 1995 to 2000, as at the end of the year.

A study was conducted to ascertain the relative importance that employees in five different countries assigned to five different traits in their Chief Executive Officers. The traits were compassion (C), decisiveness (D), negotiation skills (N), public visibility (P), and vision (V). The level of dissimilarity between two countries is the maximum difference in the ranks allotted by the two countries to any of the five traits. The following table indicates the rank order of the five traits for each country. Country Rank Table
Country Rankings

Coach John sat with the score cards of Indian players from the 3 games in a one-day cricket tournament where the same set of players played for India and all the major batsmen got out. John summarized the batting performance through three diagrams, one for each game. In each diagram, the three outer triangles communicate the number of runs scored by the three top scores from India, where K, R, S, V, and Y represent Kaif, Rahul, Saurav, Virender, and Yuvraj respectively. The middle triangle in each diagram denotes the percentage of the total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game.
John also calculated two batting indices for each player based on his scores in the tournaments:
- The R-index of a batsman is the difference between his highest and lowest scores in the 3 games.
- The M-index is the middle number, if his scores are arranged in a non-increasing order