# DILR Condition BasedSet 6

## Practice Questions for CAT with Solutions

### 1. CAT - DILR Condition Based Set 6

In a state, anyone who finished high school is classified as a literate and anyone who did not, is classified as an illiterate. Further, anyone who finished his graduation, i.e., a graduate, would have finished high school; anyone who finished his post-graduation, i.e., a post-graduate, would have finished graduation; any person who finished his doctorate, i.e., a doctor, would have finished post-graduation.

The following table provides for each of five districts – District A through District E – in that state, the percentage of people who are literates, the percentage of the literates who are graduates, the percentage of graduates who are post-graduates, the percentage of post-graduates who are doctors and the number (in “000) of people who are not post-graduates:

Q1. What is the number of illiterates in District D?
Q2. Across the five districts combined, what is the number of people who finished high school but are not graduates?
Q3. How many persons are doctors across the five districts combined?

80

202

107

### 2. CAT - DILR Condition Based Set 6

Mr. Chauhan was murdered in his home and his case was handed over to Mr. Vinod. After investigations, it was found out that the murder happened in the kitchen, bedroom or washroom. The murder weapon could be a knife, an axe or a pistol. The three suspects for the case were Chaman, Hemant and Uday. The following facts were revealed during the case analysis:

The three suspects met Mr. Chauhan in the three places with no two meeting Mr. Chauhan in one place.

Each one of them had only one of the mentioned weapons to possibly murder Mr. Chauhan.

• If the murder happened in the kitchen, then the murder weapon was the pistol.
• If the murderer was Hemant, then Uday met Mr. Chauhan in the kitchen.
• If Chaman was in the bedroom, then the murder happened in the washroom.
• If the murder weapon is the knife, then Mr. Chauhan was murdered in the kitchen.
• If Uday is not the murderer, then the murder weapon is not the pistol.
• If the murder took place in the washroom, then the axe was placed in the kitchen.
• If the murderer is found, then Chaman was in the bedroom.
• If the murder weapon is the axe, then the murderer is Uday.
• If the murder took place in the bedroom, then the murder weapon is the pistol.
• If Hemant and Mr. Chauhan met in kitchen, then Chaman had the knife.

Based on the above information and further analysis; Mr. Vinod found out that Uday was the murderer.

Q1. Where did the murder take place? (0 if CBD)
Q2. What is the murder weapon? (0 if CBD)
Q3. Where did Hemant meet Mr. Chauhan? (0 if CBD)
Q4. Which weapon was placed in the bedroom? (0 if CBD)

Washroom

Pistol

Kitchen

Knife

### 3. CAT - DILR Condition Based Set 6

A company XYZ Ltd. recruited 80 trainees. It was observed that every trainee had

1. exactly one qualification among the following two:
1. B.E.
2. M.Sc.
2. at least one feature among the following two:
1. He is from a reputed college
3. experience in exactly one of the following two domains:
1. Programming
2. Testing
Further it is also known that,
1. 20 trainees who are B.E.s had a good academic record as well as experience in Testing. These trainees form 50% of those with experience in Testing.
2. No trainee with experience in Programming had both the features mentioned in (ii), i.e., being from a good college and having a good academic record.
3. 30 trainees were M.Sc.s, of which 15 had experience in Programming.
4. Of the trainees with experience in Testing, 15 were from a reputed college and they had good academic record.
5. In total, 45 trainees had a good academic record, of which two-thirds were B.E.s and one-third had experience in Programming.
Q1. How many of the trainees are B.E.s with experience in Programming and a good academic record? (0 if CBD)
Q2. How many trainees who are M.Sc.s are from a reputed college but had neither a good academic record nor any experience in Programming? (0 if CBD)
Q3. If 18 B.E.s had a good academic record but are not from a reputed college, how many M.Sc.s are from a reputed college and with a good academic record (0 if CBD)
Q4. How many trainees are B.Es with experience in programming but do not have a good academic record? (0 if CBD)

10

5

3

15

#### 4. CAT - DILR Condition Based Set 6

Five universities – Harvard, MIT, Stanford, NYU and Pennsylvania – offer courses in three different disciplines of Management, viz. Finance, Operations and Marketing. No university offers the same number of courses in any two disciplines and no two universities offer the same number of courses in any discipline. The number of courses offered by any university in any single discipline is at least one and at most five.

Further, it is known that,
1. the total number of courses offered at Pennsylvania is six.
2. in Operations, MIT offers two courses and Stanford offers three courses.
3. Harvard offers five courses in Finance, the discipline in which Stanford offers only two courses and MIT offers only one.
Q1. If the total number of courses, in all the disciplines put together, offered by Harvard is 12, then what is the total number of courses, in all the disciplines put together, offered at NYU?
Q2. The maximum number of courses, in all the disciplines put together, can be offered at which of the following universities? (Write 0 if CBD)
Q3. If the difference between the total number of courses, in all the disciplines put together, offered by MIT and Stanford is one, then the difference between the number of courses offered in Marketing at Stanford and Pennsylvania is (Write 0 if CBD)
Q4. Which of the following statements is definitely true?
1. The total number of courses offered at NYU is the same as that offered at Stanford.
2. The total number of courses offered at Harvard is the same as that offered at NYU.
3. MIT offers the second lowest number of courses in all the disciplines put together.
4. Stanford offers the second highest number of courses in all the disciplines put together.

10

0

2

c. MIT offers the second lowest number of courses in all the disciplines put together.

#### 5. CAT - DILR Condition Based Set 6

The table below give some information about the points scored by Arjun in a worldcup, in each of 5 games – Dice, Dance, Dupe, Digit and Dynasty

It is also known that

1. for every successful attempt Arjun gets one point and for every unattempted problem he loses 1/6th of a point and for every failure he loses 1/3rd of a point.
2. Arjun scored a total of 67 points and attempted 125 problems
3. The number of failures of Arjun in “Digit” is 1/6th of his total number of failures and twice his number of failures in “Dance”.
4. Arjun’s net score in “Dance is double than Dupe”
Q1. What is total number of failures of Arjun in competition
Q2. Maximum number of failures of Arjun in any game was ___?
Q3. What is the number of problems attempted by Arjun in any dance competition?
Q4. What is Arjun’s net score in dynasty?

36

12

18

26

#### 6. CAT - DILR Condition Based Set 6

Ramlal, Hotilal and Mohanlal are three call center cab drivers allocated to pick up four customer service representatives (CSRs) from their respective homes and drop them at their office. To ensure that the CSRs do not make the cab wait, the office has a rule. Depending on the driver’s wait time (in minutes), a penalty is levied as shown below.

In the table, m is the extra time beyond 10 minutes that the driver has to wait. For instance, if the driver waits 17 minutes, m = 7.

The table on the side shows travel time to reach a CSR’s house, wait time at a CSR’s house, the total time and penalty collected by each driver on a particular day. All timing values are in minutes while the penalty is in rupees.

Also:

Hotilal collected penalty from only two CSRs and he waited for the same time for both of them.

For one executive, Ramlal waited for the same time as the time that he took to travel to his house.

Hotilal waited for both executives longer than the time he took to drive to their respective houses.

For one executive, Ramlal waited longer than the time he took to drive to his house.

Ramlal did not collect a penalty from one CSR.

Q1. How many minutes did Ramlal wait at CSR 2’s house?
Q2. Ramlal picked CSR 2, left for CSR 3’s house, waited there, picked CSR 3 and then left for CSR 3’s office. He took 14 minutes to reach office after picking CSR 3. How many minutes after picking CSR 2 did Ramlal reach CSR 3’s office?
Q3. For how long did Hotilal wait for CSR 1?(0 if CBD)
Q4. What could be the maximum total time taken by Mohanlal to drop all three CSRs to office?
1. 30 minutes
2. 36 minutes
3. 42 minutes
4. None of these

1 minute

33 minutes

0

d. None of these

#### 7. CAT - DILR Condition Based Set 6

Three children, Rekha, Shankar and Mukesh, were playing the game of Tic-Tac-Toe, on a grid of 3 × 3 squares. Each game was played by all the three children, with the rules slightly modified from the usual, as described below.

Each person has his/her own symbol, referred to as his/her ‘mark’ and in every turn, he/she places the same mark on the grid. The columns are labelled A to C, from left to right, and the rows are numbered 1 to 3, from top to bottom. The position of a mark on the grid is given by the combination of the column and row labels of the square in which it is placed. For example, a mark in position C2 means that the mark is in column C and row 2. The first person to play a game can place his mark on any square in the 3 × 3 grid except B2. In every subsequent turn, each person has to place his/her mark in any empty square, which is not in the same row or column as that of the mark that was placed immediately before his turn not in any diagonal position in any of the four possible directions to that of the mark that was placed immediately before his turn.

For example, if the first person places his/her mark in C2, the second person cannot place his/her mark in any square in column C or any square the 2nd row or in the squares in the diagonal positions to C2, i.e. B1 and B3. The first person to get three of his/her marks in a straight line (horizontally, vertically, or diagonally) in the grid is the winner. The game ends in a tie if all the nine squares are full or if it is not possible to place any other mark in the remaining squares, without having a winner.

A fresh grid is drawn at the beginning of each game.

The marks of the three persons, Rekha, Shankar and Mukesh, are ‘X’, ‘O’ and ‘I’ respectively. It is known that in any game that they played, the first person to play did not place his/her mark in B2.

Q1. If a total of 34 games were played, how many games ended in a tieti (Write 99 if CBD)

Q2. In one of the games, Rekha, who was the first person to play, ended up winning the game. Which of the following options could represent the grid immediately after she placed her first mark?

1. CBD
Q3. If ‘I’, ‘O’ and ‘X’ were the first three marks to be placed on the grid in that order, then who among the following could not have won that game?
1. Mukesh
2. Rekha
3. Shankar
4. None of the above

Q4. If Mukesh, Shankar and Rekha played a game, taking turns in that order and Mukesh did not win the game, which of the following options could represent the grid immediately after Rekha placed her first mark?

1. more than one

0 tie

Option c

b. Rekha

Option a

#### 8. CAT - DILR Condition Based Set 6

A firm evaluates the performance of five of its employees and their annual increments are based on their performance rankings. The firm gives an increment of 5, 10, 15, 20 and 25 percent, in decreasing order of ranks. Thus, the worst performing person is ranked 5 and gets 5% increment. The top three employees also receive a bonus (in Rs.) of 5000, 3000 and 2000 respectively. The salary of all employees is Rs. 10,000 in the year 2000. In a certain year, no two employees get the same increment. The table shows the sum of percentage increments for all five employees after 3 years and 5 years respectively.

1. Four employees repeated one of their bonus amounts exactly once.
2. Only three employees managed to get the highest increment such that B and E were two of them.
3. All the five employees were ranked third and fifth at least once.
4. All the employees got the same rank exactly twice.
5. C got the least bonus in 2005 and B got no bonus in 2002.
6. Only C and D got the same rank in two consecutive years.
7. E missed out on bonus in two consecutive years
Q1. Who got the highest bonus amongst all
Q2. What was the highest total increment (in Rs.) given to any one at the end of three years?
Q3. How many employees at least doubled their salary (excluding bonus) at the end of 5 years?
Q4. What is the average bonus given out by the company, per employee per year?

D

8000

3

2000

#### 9. CAT - DILR Condition Based Set 6

Crash time indicates the time in which the corresponding activity can be completed at the earliest along with the corresponding cost involved i.e., crash cost. This crash cost for any activity gets proportionately reduced if the duration (crash time) is increased.

For example, if activity B is to be completed in four weeks, then the cost involved would be Rs. 4,000. On the other hand, if this activity is crashed by one week then the additional cost will be Rs. 1,000 and if it is crashed by two weeks and is now completed in two weeks then the corresponding additional cost would be Rs. 2,000 i.e. Activity B can also be completed in 2 weeks at a cost of Rs. 6,000.

Assume that all the dependent activities commence immediately on completion of the activities preceding them.

Given below is a set of inter-related activities required to complete a project undertaken by a contractor.

Q1. If the project is to be completed in 10 weeks, then what would be the minimum cost involved in the project?
Q2. The contractor has bagged the contract on the condition that it would be completed in eight weeks. If a penalty of Rs. 2,500 per week is to be levied for late completion of the project and a bonus of Rs. 1,000 per week is to be awarded to the contractor for early completion of the project, then which of the following conditions would be ideal for the contractor if the only parameter used is the cost involved?
1. Complete the project in 8 weeks.
2. Complete the project in 9 weeks.
3. Complete the project in 11 weeks.
4. Complete the project in 7 weeks.
Q3. Taking the appropriate condition from the previous question, if activity B starts late by 2 weeks, then what would be the minimum cost involved in the project?
Q4. What would be the ratio of the minimum time to maximum time required for the completion of the project? (Events that can be done simultaneously have to be done simultaneously).

24,500

b. Complete the project in 9 weeks

29,000

8/11

#### 10. CAT - DILR Condition Based Set 6

Each of the five friends: Annie, Brenda, Cindy, Dane and Emily had written exactly one of the tests from GMAT, CAT, XAT, SNAP and JMET, not necessarily in that order.
The percentage scores obtained by them in the tests were 50, 45, 40, 35 and 30, not necessarily in that order.
Further, it is known that:

1. Cindy did not write SNAP.
2. Brenda did not write JMET.
3. The percentage score in SNAP was more by 5 points than the test which Emily had written.
4. The percentage score that Annie obtained was more by 10 points when compared to the score in CAT.
5. The percentage score in GMAT was more than the percentage score in the test written by Cindy by 5 points.
6. The percentage score in the test written by Dane was more than the percentage score obtained in XAT by 10 points.

Q1. If Annie had written GMAT, then what was the percentage score obtained in JMET? (Write 0 if CBD)

Q2. Which test did Emily write? Assume data from the previous question. (Write 0 if CBD)

Q3. What percentage of marks did Brenda score in the test she had written? Assume data from the previous question. (0 if CBD)

Q4. At most how many of the following statements can be true?
4. If Annie had written SNAP, then Brenda had scored 30% marks in the test she had written.

45

XAT

35