# DILR Condition BasedSet 3

## Practice Questions for CAT with Solutions

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

Eight students – S1 to S8 – are fighting for supremacy in a college. To prove their supremacy, these eight students compete with each other on one or more of five skills. Two students are said to be in a clash if there is at least one skill where they have equal proficiency. The table below lists the number of clashes for these students.

Q1. How many clashes did S6 have?

Q2. The number of students competing on one skill set is atmost …

Q3. Each skill is given as many points as it has the number of students who have that skill set. If there is exactly one skill set where there was no clash, then the sum total of all the points is ______

Q4. The number of skill sets on which S1 competed is atmost…

4

5

15

2

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

A travel agency operates in India and Nepal only and organizes tours for its customers. The travel agency had to organize trips to Switzerland, France and Italy for 40 of its customers. There were two more Nepalese customers than Indian customers. The packages offered by them included those where only one country, exactly two out of three countries or all three countries could be visited. Each package was taken by at least one traveller.

The following facts were also known:

1. The ratio of the number of Nepalese travelers who selected the package for all three countries and the number of Indians who selected the same package is 1 : 2.
2. 6 people selected both France and Italy, such that atleast one of these did not select Switzerland.
3. The numbers of Indians who selected only Switzerland and only Italy were 20% more and 40% less than the number of Indians who only selected France respectively.
4. The number of Indians who selected both Switzerland and France but not Italy was the same as the number of Nepalese who selected both Switzerland and Italy but not France; and this number was not 0.
5. Less than 10 people selected only Switzerland and their number was 60% of the number of people who selected only France. Among those people who selected exactly one country, maximum people selected only France.
6. 32 people selected exactly one place.
Q1. How many Indians visited only Switzerland as a percentage of the total number of people who visited only France?
1. 60%
2. 50%
3. 40%
4. 30%
Q2. What was the ratio of the number of customers from India who selected Switzerland to the number of customers from Nepal who did not select Switzerland?
1. 2 : 5
2. 9 : 16
3. 9 : 23
4. 2 : 1
Q3. How many Indians as a percentage of the total number of Indian travelers visited at least two countries?
1. 26.3%
2. 23.6%
3. 21%
4. 15.7%
Q4. Considering Indians and Nepalese independently, what is the least number of visitors who selected exactly one country?
1. 2
2. 3
3. 5
4. 6

c. 40%

b. 9 : 16

a. 26.3%

b. 3

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

Ten colleges: COET, COEP, MIT, VIT, CNT, SNT, DNA, ABS, XOT, and ORT were rated on eight parameters: Accessibility, Infrastructure, Resources, Canteen, Industry Interface, Placement, Reputation and Alumni Network. Every college got non-negative integral points on every parameter.
The tables below gives the cumulative points of all the colleges parameter wise and also the cumulative points scored by each college on all the parameters put together. For instance, taking into account the points given to all the colleges, Resources got 25 points in all and VIT got 7 points in all across all parameters.

Q1. If Infrastructure, Resources, Industry Interface and Canteen Facilities are the only parameters on which COET, COEP, MIT, and DNA were rated, then the points scored on Resources by SNT as a percentage of total points scored by SNT cannot be more than
1. 88.75
2. 80.5
3. 86.25
4. 81.25
Q2. If Reputation and Alumni Network were rated in exactly three colleges and no other parameter was rated for in these three colleges, how many colleges were definitely not rated for Reputation?
1. 4
2. 0
3. 2
4. 1
Q3. N parameters were chosen such that their average score for each of the given colleges was the same as well as the largest possible. What is the least number of parameters that cannot be part of N?
1. 4
2. 3
3. 5
4. 2
Q4. The maximum possible colleges got equal points on Resources. What is the least number of points that ORT could have got on Resources, such that it did not have the same points on Resources as anyone else?
1. 0
2. 2
3. 3
4. 1

d. 81.25

d. 1

b. 3

a. 0

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

Maya weight management clinic had height, weight and BMI records for all its patients. It calculated the BMI as the approximate ratio of weight (in kg) to the square of the height (in m). A partially filled spreadsheet with records for seven randomly selected female patients is shown below. No two patients had the same height or weight. Heights (in cm) and weights (in kg) are integral

As per norms, the clinic classifies patients into four categories based on their BMI:

Underweight – BMI < 18.5

Normal – 18.5 ≤ BMI < 25

Overweight – 25 ≤ BMI < 30

Obese – 30 ≤ BMI

It is also known that:

1. The average weight of the random sample selected is 60 kg.
2. There is atleast one patient from each category and there are more “Normal” patients than the other three categories combined. The “Overweight” person has been asked to reduce exactly 5 kgs of weight to be just counted as “Normal”.
3. Nidhi was also taller than Pooja and shorter than Manisha. Rubina was heavier than Manisha but lighter than Pooja
4. The median height was 1.57 m (for Preeti) while the mean height was between 1.58 and 1.59 m.
5. Asma was 56% heavier than Rubina

Q1. What was Asma’s height (in cm)?

Q2. Kinjal was heavier and taller than how many people?

Q3. By how much did the highest BMI in the normal category exceed the lowest BMI in the normal category?

Q4. What maximum integral weight gain (in kg) would let Rubina be “normal”?

160

5

3.9

18

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

In a laboratory, unit samples of chemicals A, B, C, D, E and F are made by mixing ingredients L, M, N, O and P by weight as shown in the table below:

The cost of each ingredient (in Rs. per mg) is: L – 150; M – 50; N – 125; O – 100; P – 75

A unit sample of chemical ABC represents a new sample formed by mixing a unit sample each of chemicals A, B and C. Similarly, unit samples of chemicals BCD, CDE and DEF are made

Q1. Which of the following chemicals has the highest proportion by weight of ingredient M?
1. ABC
2. BCD
3. CDE
4. DEF
Q2. For which of the following chemicals is the cost of a unit sample the lowest?
1. A
2. B
3. C
4. D
Q3. If a unit sample of each of chemicals A, B, C, D, E and F is mixed together, the proportion of how many ingredients will be more than 20% by weight of the total mixture?
1. 2
2. 3
3. 4
4. 5

c. CDE

d. D

b. 3

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

A cold drink manufacturing company produces 5 different types of cold drinks. The pie-chart given below shows the volume, in percentage, of each type of cold drink produced by that company in the last financial year.

The following information about the company is also known:

In the last financial year the company made a profit of 10 million dollars.

The total volume of cold drinks produced was 1 million litres.

Cold drinks of type C and D together made 45% of the total profit while cold drinks of type B and C together made 35% of the total profit.

The table below gives incomplete information about the profit (in dollars) made per litre for each type of cold drink.

Q1. How much profit (in million dollars) did the cold drink of type E make?

Q2. What volume (in litres) of cold drink of type D was manufactured?

Q3. What is the profit per litre (in dollars) made by the cold drink of type C?

Q4. Considering the total profit made by the company, by how many percent points is the share of profit made by cold drink of type B less than that by cold drink of type C?

1 Million

1.5 Litres

20

5% Less

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

The four faculties at a coaching institute are – Mukesh, Gautam, Vilas and Lakshman. Each of them teaches a different topic and each topic is related to a different course. The topics are – Aptitude, DI and DS, Verbal ability and NLP. The four courses, that these topics are related to are GRE, GMAT, CAT and Soft Skills – not necessarily in that order. Neither Lakshman nor Mukesh teach on any topic related to either CAT or GRE. Neither Aptitude nor DI and DS is related to either Soft Skills or GRE. Lakshman teaches NLP.

Q1. Which of the following additional statements out of the following choices would help you find the correct combination of the name of the faculty, the topics that they teach and the related courses?
1. Neither Gautam nor Vilas delivers a lecture on DI and DS
2. Neither Aptitude nor DI and DS is the topic of Vilas
3. Neither Vilas nor Mukesh teaches Aptitude
4. None of the above
Q2. Which of the following statements can be deduced from the given data?
1. Lakshman deals with the topic related to Soft Skills.
2. Verbal ability is the topic related to GRE.
3. DI and DS is the topic related to GMAT.

1. Only I
2. Only I and II
3. Only III
4. None of these
Q3. it is known that Vilas teaches Verbal ability, then for which of the following courses does Gautam teach?
1. Soft Skills
2. CAT
3. GMAT
4. Cannot be determined
Q4. Which of the following topics is related to GRE course?
1. Aptitude
2. DI and DS
3. Verbal ability
4. Cannot be determined

c. Neither Vilas nor Mukesh teaches Aptitude

b. Only I and II

b. CAT

c. Verbal ability

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

The following Table gives the number of students across six different classes of Pune Modern School in the years 2010 and 2011.

It is also known that:

1. New students join the school only in class V.
2. No student leaves the school before passing out class X.
3. The students who fail in a class in a year will study in the same class next year.

Q1. What was the maximum possible number of students who joined the school in 2011?

Q2. In 2010, which of the following was not a possible pass percentage of class VI?
1. 60%
2. 16%
3. 58.66%
4. More than one of these
Q3. In 2010, if the number of students who passed in class VI was more than the number of students who failed in class IX, then what was the minimum pass percentage of class VIII?
1. 46.66%
2. 48.33%
3. 53.33%
4. None of these
Q4. In 2010, if the pass percentage in class IX was 60%, then what was the pass percentage of class V?
1. 33.33%
2. 67%
3. 58%
4. None of these

76

a. 60%

b. 48.33%

d. None of these

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

A sports drink manufacturing company carries out certain processes while manufacturing each bottle of its product. These processes have been listed in the first column of the table. Some processes can be carried out independently, while others may be dependent on the completion of other processes. The second column of the table lists the processes which must mandatorily be completed before the process mentioned in the first column begins. The third column lists the costs (in Rs.) of carrying out the processes mentioned in the first column to manufacture each bottle of the sports drink. One bottle is said to be manufactured when exactly one of processes E or K is completed. Completion of any process once is sufficient to ensure that all its dependent processes can also be started (provided their respective mandatory processes are also completed). For example: If H is completed once, both A and J can be started, provided C has been completed.

Q1. What is the minimum cost of producing one bottle of the sports drink?
1. Rs. 38
2. Rs. 36
3. Rs. 34
4. None of these
Q2. The time required (in minutes) to complete a process is numerically equal to the cost (in Rs.) to carry out that process. The processes may occur simultaneously, wherever possible. What is the minimum time required to manufacture a bottle of the sports drink?
1. 23 minutes
2. 26 minutes
3. 28 minutes
4. 37 minutes
Q3. Now if the manufacture of one bottle requires the completion of both E and K, what is the minimum time required to make one bottle? (Assume that the time required (in minutes) is numerically equal to twice the cost (in Rs.) to carry out a process.)
1. 49 minutes
2. 46 minutes
3. 34 minutes
4. None of these

d. None of these

a. 23 minutes

d. None of these

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

The table given below shows the answers given by four people, namely Mithun, Rajnikant, Prabhudeva and Naresh in an entrance exam taken by CICIC Bank. The question paper contained four questions, all carrying equal marks and each of them having four answer choices, namely pq, qr, rs and st. The examiner forgot the correct answers to the questions, but he remembers that each one of them got at least one answer correct and that at least one person answered a question correctly. No two people had same total marks in the exam.

Q1. Who got the minimum marks if each correct answer is worth four points and there is no negative marking?
1. Mithun
2. Rajnikant
3. Naresh
4. Cannot be determined
Q2. What is the sum of the minimum and maximum total marks scored by anyone in the examination if each correct answer is worth four points and there is no negative marking?
Q3. If each question carried 3 marks with a negative marking of 33.33%, what was the second lowest marks got by anyone in the examination?
1. 4
2. 8
3. -4
4. Cannot be determined
Q4. What was the answer to question D?
1. pq
2. qr
3. st
4. Data Insufficient

a. Mithun

20

a. 4