# DILR Miscellaneous

Welcome to Quantifiers’ DILR Miscellaneous section! Here, we provide an extensive question bank with detailed answers and video explanations for various topics within Data Interpretation and Logical Reasoning (DILR).

## Unlock the Power of DILR Mastery

In our commitment to CAT exam excellence, Quantifiers presents a comprehensive collection of practice questions and thorough video explanations covering a wide array of DILR topics. While excluding specific categories, this section encompasses an assortment of challenging problems to refine your problem-solving skills and enhance your overall DILR proficiency.

Quantifiers’ DILR Miscellaneous section is designed to augment your CAT exam preparation by providing ample practice material and insightful explanations. Strengthen your foundation, refine your strategies, and excel in the DILR section with our comprehensive question bank and video explanations.

## Practice Questions for CAT with Solutions

### 1. CAT - Distribution Set

Sahil wanted to purchase a bike and went to take test drive of Pulsar, KTM, Ninja, Bullet and Apache, he took 5 parameters to test the bike, namely, pick-up, engine power, ABS, turbo and torque. He ranked the models on five parameters pick-up, Engine power, ABS, Turbo and Torque. In each parameter, he ranked the five models from 1 to 5 such that a better model was given a numerically lower rank as compared to a worse model. No two models received the same rank in any parameter.

The following information is known about the ranks of each model in each parameter:

1. Each model was ranked third in at least one parameter and exactly two models were not ranked first in any parameter.
2. Apache was ranked fourth in Engine power, while KTM was ranked second in two parameters.
3. No model received the same rank in more than two parameters, while Bullet did not receive the same rank in any two parameters.
4. Bullet was ranked worse than Ninja in all the parameters except Turbo, while KTM was ranked better than Ninja in pick-up.
5. Ninja was ranked better in Engine power than at least three models, while KTM was ranked neither first nor last in Torque.
6. Apache, which was ranked fifth in Turbo, was ranked better than Ninja and KTM in pick-up and in ABS but was not ranked first in either of the two parameters.

Q1. Which bike was ranked second in engine power?

Q2. Which bike was ranked 3rd in pick-up?

Q3. How many bikes were better than KTM in engine power?

KTM

KTM

1

### 2. CAT - Entry Exit Type Set

Seven friends – Abhishek, Ashish, Somil, Avinash, Lokpriya, Inshia and Mohit – decided to study together on a day starting from morning until evening at a park. On a particular day, their plan failed as no one was able to come on time and all left the park before 12 noon. They arrived at 7:30am, 9 am, 8:20 am, 8am, 9:50 am, 8:15 am and 7:45am respectively. But they all left on some different time at 10 am, 10:30 am, 10:50 am, 11 am, 11:05 am, 11:05 am and 11:20, not necessarily in the same order. Further, it is known that:

1. Everyone studied for more than one hour.
2. Mohit spent the maximum time and Lokpriya spent the least time at the park.
3. Ashish was not the first person to leave the park and difference between the time spent by Ashish and Inshia in the park was 40 minutes.
4. The difference between the time spent by Somil and Abhishek in the park was 20 minutes.
Q1. If Lokpriya was not the last person to leave the park, then who could be the two persons leaving together at 11:05 am?
1. Lokpriya and Ashish
2. Mohit and Abhishek
3. Somil and Avinash
4. Lokpriya and Mohit
Q2. If Avinash spent 2 hrs and 50 minutes in the park, then at what time did Somil left?
1. 10:30 am
2. 10:00 am
3. 11:05 am
4. 11:20 am
Q3. If Mohit has spent less than 3.5 hours, then at what time did Lokpriya leave?
1. 11:00 am
2. 10:50 am
3. 11:20 am
4. 11:05 am
Q4. What is the difference between the time spent by Mohit and the time spent by Inshia?
1. 50 Minutes
2. 35 minutes
3. 20 Minutes
4. CBD

a. Lokpriya and Ashish

a. 10:30 am

c. 11:20 am

d. CBD

### 3. CAT - Currency Exchange Rates

The base exchange rate of a currency X with respect to a currency Y is the number of  units of currency Y which is equivalent in value to one unit of currency X. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates.

A currency exchange outlet uses the local currency L to buy and sell three international currencies A, B, and C, but does not exchange one international currency directly with another. The base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. The buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates, and their selling exchange rates are 10% above their corresponding base exchange rates.

The following facts are known about the outlet on a particular day:
1. The amount of L used by the outlet to buy C equals the amount of L it received by selling C.
2. The amounts of L used by the outlet to buy A and B are in the ratio 5:3.
3. The amounts of L the outlet received from the sales of A and B are in the ratio 5:9.
4. The outlet received 88000 units of L by selling A during the day.
5. The outlet started the day with some amount of L, 2500 units of A, 4800 units of B, and 48000 units of C.
6. The outlet ended the day with some amount of L, 3300 units of A, 4800 units of B,and 51000 units of C.

Q1. How many units of currency A did the outlet buy on that day? [TITA]

Q2. How many units of currency C did the outlet sell on that day?
1. 3000
2. 22000
3. 6000
4. 19000

Q3. What was the base exchange rate of currency B with respect to currency L on that day? [TITA]

Q4. What was the buying exchange rate of currency C with respect to currency L on that day?
1. 1.10
2. 0.95
3. 2.20
4. 1.90

1200

d. 19000

240

d. 1.90

### 4. CAT - Sitting Arrangement

In a competition, six pairs of chairs were arranged in such a way that one chair in each pair faces south and the other faces north, with the backs of every pair of chairs tied together. Thus any person sitting in a north facing chair cannot see any of the persons sitting in the south facing chairs and vice versa. The pairs of chairs were numbered from 1 to 6, from west to east, such that, both the chairs (i.e., the north facing chair and the south facing chairs) at the west end are numbered 1 and so on, till both the chairs at the east end are numbered 6.Six men – A through F – along with their wives – P through U – not necessarily in the same order, participated in the competition. All the men sat in the chairs that were facing north and all the women sat in the chairs facing south. Each of the men was provided with a paper on which he was asked to write the number of the chair on which his spouse was sitting. The following are the replies by each of them: A – 4, B – 4, C – 5, D – 6, E – 1 and F –3.

Further, it is known that

1. none of the men wrote the same number as that of the chair he was sitting in.
2.  exactly three men guessed the chair numbers of their wives correctly.
3.  P is sitting three places to the right of Q, who is the wife of C
4.  R, the wife of A, is to the right of P and left of S.
5.  exactly three persons were sitting in the same numbered chairs as their wives.
Q1. If F is sitting behind B’s wife, then B must be sitting behind
1. E’s wife
2. D’s wife
3. F’s wife
4. CBD

Q2. Who among the following did not sit in the same numbered chair as her husband?

1. S
2. R
3. P
4. More than one of the above
Q3. Which of the following statements is definitely true?
1. T is the wife of F
2. T is the wife of D
3. S is the wife of E
4. P is the wife of E
Q4. If T is sitting in an even numbered chair, who among the following is sitting in the same numbered chair as D?
1. Q
2. T
3. U
4. S

a. E's wife

d. More than one of the above

c. S is the wife of E

c. U

### 5. CAT - Binary Logic

Harsha went to a village to buy a fruit orchard. He inquired of three persons A, B, and C, who are the only persons working on a farm, about the prices of a Mango orchard, an Orange orchard and a Guava orchard. It is known that the prices of the three orchards are distinct. Each of the three persons gave three statements in reply to Harsha’s enquiry. Two of the three persons are alternators, who always alternate between truth and lie, in any order, while the third person is either a truth teller, who always tells the truth, or a liar, who always lies. The following are the statements made by each of the persons:

A
1. The cost per acre, in Rs. lakh, of each of the orchards is a prime number less than ten.
2. B always lies.
3. The Mango orchard is the costliest among the three.
B
1. The Guava orchard is the cheapest among the three.
2. No person working on this farm always speaks the truth.
3. The cost per acre, in Rs.lakh, is an even number for one of the orchards.
C
1. The Guava orchard is the costliest orchard.
2. A always lies.
3. The Mango orchard is cheaper than the Orange orchard.
Q1. Who among the following is not an alternator?
1. A
2. B
3. C
4. CBD
Q2. What is the cost per acre (in Rs. lakh) of the Orange orchard?
Q3. Which is the costliest orchard among the three?
1. Orange
2. Mango
3. Guava
4. CBD

c. C

3

b. Mango

### 6. CAT - Investment Families Set

The investment portfolios of certain business families included mutual funds of two categories: Equity and Debt. To take care of the flip side of the market, these business families had come out with a proposal to create a contingency fund, the funding of which would be done by each business family on a monthly basis through withdrawals from the mutual funds that these families had. It was decided that the withdrawal from each Equity fund would be either Rs. 1,000 or Rs. 2,000 every month, the amount remaining the same for every Equity fund for that month; and that from each Debt fund would be Rs. 2,000 or Rs. 3,000 every month, the amount remaining the same for every Debt fund for that month. This would hold good for all the business families. The collection details of various business families are as shown in the table :

Further details on collection as observed for first five months were as given below:
Rs. 2,000 was withdrawn from every fund of every Business family for exactly two months, which were necessarily different for each family. For each of the remaining three months, within any business family, the amount withdrawn from one Debt fund did not equal the amount withdrawn from one Equity fund. Moreover, the combination of amounts withdrawn was not repeated; i.e. if B1 had withdrawn Rs. 2,000 from Equity Funds and Rs. 3,000 from Debt Funds in the month of January, then B1 cannot withdraw the same combination of Rs. 2,000 from Equity and Rs. 3,000 from Debt in any other month.
B1 withdrew Rs. 2,000 from every fund in the 1st and 2nd month.
B2 withdrew Rs. 2,000 from every fund in the 2nd and 3rd month.
B6 withdrew Rs. 2,000 from every fund in the 2nd and 4th month.

Q1. What was the number of mutual funds that were held by Business family B4?
1. 7
2. 4
3. 5
4. CBD
Q2. What was the total amount withdrawn by B3 (in Rs.’000) in the last two months?
Q3. What was the maximum amount withdrawn by B1 (in Rs.’000) in any of the given months?
1. 13
2. 17
3. 10
4. CBD
Q4. What was the amount withdrawn by B1 (in Rs.’000) in April of the given period?
1. 10
2. 13
3. 9
4. CBD

c. 5

18,000

a. 13

d. CBD

### 7. CAT - Binary Logic

3 friends A, B, C have made 3 statements about 3 shapes drawn on the black board of their classroom.  It is known that 1 of them is a liar, 1 is a truth teller and 1 speaks a random mixture of truth and lies (called alternator).

A: 2 of them are circles B is a liar. C is a liar.

B: 2 of them are squares A is not a truth teller. I am not a liar.

C: At least 2 of them have 4 sides each. B is the truth teller.

1 of the shapes is a circle.

Q1. Which of the following can be the list of 3 shapes?
1. Square Circle Rectangle
2. 2 Squares, 1 Oval
3. 2 Squares, 1 Circle
4. None of these
Q2. C’s three statements in the same order (1 −> 2 −> 3) are:
1. Truth −> Truth −> Truth
2. Truth −> Lie −> Lie
3. Lie −> Lie −> Lie
4. Truth −> Truth −> Lie
Q3. Who is the truth teller?
1. A
2. B
3. C
4. Cannot be determined
Q4. A fourth person – D – makes 3 statements, as given below. What kind of a person is he?
1. A is not the alternator.
2. All three figures are quadrilaterals.
3. At most one of C’s statements is true.

1. Liar
2. Alternator
3. Truth Teller
4. CBD

b. 2 Squares, 1 Oval

d. Truth -> Truth -> Lie

b. B

b. Alternator

### 8. CAT - Entry Exit Type

Jay, Aadi, Ram, Chintu, Bheem, Raj, and Seeta often played in a garden in their locality.
One day the guard noticed ten broken flower pots and he suspected it was the work of the seven children. The guard got the following answers when he tried finding out who was present in the garden on that day. He found that three of the children had visited the garden twice that day

1. Jay: When I came, Ram and Aadi were already playing and we three were the first ones to reach the garden on that day. I later left with Ram.
2. Aadi: I went twice to the garden that evening. The first time I went only for a short time and left immediately after Chintu arrived. The second time I arrived, I, Bheem and Raj were the only people chatting for some time. I and Seeta were the last persons to leave the garden.
3. Bheem: I went to meet Chintu while he was playing in the garden. Other than Chintu, only Jay and Ram were present when I reached. I returned along with Raj and Ram.
4. Raj: I went to wish happy birthday to Seeta, but when I reached only Chintu and Bheem were there. Seeta joined us later.
5. Seeta: When I reached the garden, only four of us were there. Bheem and Raj were busy playing badminton. So I went home along with my brother.
6. Ram:  I and Seeta both went twice to the garden. I and Seeta went together the second time to look for her frisbee which she forgot in the garden the first time she went there
Q1. Who is Seeta’s brother?
2. Ram
3. Chintu
4. Jay
Q2. How many people met Raj in the garden?
1. 4
2. 2
3. 5
4. CBD

Q3. Who was the fifth person to enter the garden?

c. Chintu

c. 5

Bheem

### 9. CAT - Binary Logic

Piklu, Chiklu, Dholu and Neelu are four regions of a country called Urbanistan. Only three tribes – Abra, Cabra and Dabra – live in the four regions of this country. The people of Abra tribe tell a lie and a truthful statement alternately, in any order. The people of the Dabra tribe always lie. The people of the Cabra tribe always tell the truth. Akbar, Birbal, Chandragupta and Moreshwar came from different regions of this country. When asked about the region they came from, their replies were:

Akbar : I came from Chiklu. Moreshwar came from Dholu.
Birbal : I came from Dholu. Chandragupta came from Chiklu.
Chandragupta : I came from Piklu. Akbar came from Neelu.
Moreshwar : I came from Chiklu. Birbal came from Piklu.

It is known that exactly one of the four belongs to the Dabra tribe, at least one of them belongs to the Cabra tribe and at least one of them belongs to the Abra tribe.

Q1. Who among the following is a Cabra?

Q2. Who has come from Neelu?

Q3. To which region does Moreshwar belong?

Chandragupta

Akbar

Chiklu

### 10. CAT - Routes & Networks

The diagram shows the racetrack for a certain motor race. There are 8 nodes in the circuit. Each node is identified by a number. There are also roads connecting the various nodes. Each road is identified by a letter. Each road also has an associated time of travel (in minutes) that is a positive integer. This time of travel is the same for a road every time it is traversed. Only one road has a time of travel that is less than 3 minutes.

A race is defined as a journey that starts from node 1 or 2 and ends at node 8 by traversing only the roads shown on the diagram.

The test driver for a particular car company does 5 test races, all of which have different routes. The information collected by him from the five races is summarized in table 1.

Further, it is known that there is an oil spillage at two of the nodes. It is not known which these two nodes are. It is known, however, that there is no oil spillage at nodes 2 and 8. An oil spillage at a node means that a car passing through that node will suffer a 2 minute increase in its total race time

S. No. Route followed Time taken for the journey (in minutes)

1

AFI

11

2 CEG 18

3

AFHDCEG

41

4

DHI

16

5

BECDHI

26

Q1. What is the time taken (in minutes) to travel across road I? Disregard possible delays at node 6.

Q2. Based only on the information given, which of the following could be a node with oil slippage?
1. 1
2. 2
3. 3
4. 4
Q3. Assuming that A = 3 and F = 4, which of the following is definitely a node with oil slippage?
1. 3
2. 4
3. 6
4. 7
Q4. After analyzing the results of the test runs, a racer has to choose the route which takes the second lowest time so as to ensure both speed and safety. Which route will he choose? He assumes that the times required to traverse roads C and E are different.
1. BG
2. AFI
3. CEG
4. DHI

2

c. 3

d. 7

a. BG

### 11. CAT - Routes & Networks

In the city XYZ, P is a water source from where water flows into the tanks – Q, R, S, T and U. The following diagram shows the network of the source and all the five tanks connected with pipes through which water flows.

A race is defined as a journey that starts from node 1 or 2 and ends at node 8 by traversing only the roads shown on the diagram.

The test driver for a particular car company does 5 test races, all of which have different routes. The information collected by him from the five races is summarized in table 1.

Further, it is known that there is an oil spillage at two of the nodes. It is not known which these two nodes are. It is known, however, that there is no oil spillage at nodes 2 and 8. An oil spillage at a node means that a car passing through that node will suffer a 2 minute increase in its total race time

Q1. What is the time taken (in minutes) to travel across road I? Disregard possible delays at node 6.

Q2. Based only on the information given, which of the following could be a node with oil slippage?
1. 1
2. 2
3. 3
4. 4
Q3. Assuming that A = 3 and F = 4, which of the following is definitely a node with oil slippage?
1. 3
2. 4
3. 6
4. 7
Q4. After analyzing the results of the test runs, a racer has to choose the route which takes the second lowest time so as to ensure both speed and safety. Which route will he choose? He assumes that the times required to traverse roads C and E are different.
1. BG
2. AFI
3. CEG
4. DHI

2

c. 3

d. 7

a. BG

### 12. CAT - Data Sufficiency in DILR

There are 5 friends – Akash, Arvind, Amar, Ajay and Arjun. They have among them 10 bikes of capacities 100 cc, 125 cc, 150 cc and 175 cc.

1. None of the five friends has more than two bikes.
2. There are at least two and at the most three bikes of any given capacity.
3. None of the five friends has both bikes of the same capacity. For example, ‘Amar has two 100 cc bikes’ is an invalid combination.
4. The capacities of bikes with any two of the five friends are necessarily different. For example, ‘Amar has a 100 cc bike and a 125 cc bike and Akash also has a 100 cc bike and a 125 cc bike’ is an invalid combination.
5. The sum of the capacities of the bikes with Ajay is the highest.
6. Akash and Arjun do not have any bike of the same capacity.
7. Amar, Arvind and Akash each have one bike of the same capacity.

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.

Choose 2 if the question can be answered by using either of the statements alone.

Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

Q1. Bikes of which capacities does Ajay have?

A. There are three bikes of 100 cc.

B. The common bike mentioned between Amar, Arvind and Akash is of 125 cc.

1)1                       2)2                       3)3                       4)4

Q2. The bike of which capacities does Amar not own?

A. There is an odd number of 100 cc and 125 cc bikes.

B. Arvind and Ajay do not have any of the two same capacity bikes.

1)1                       2)2                       3)3                       4)4

Q3. Which bike do Akash, Arvind and Amar have in common

A. Ajay owns a 125 cc bike.

B. Amar owns one of the three 125 cc bikes.

1)1                       2)2                       3)3                       4)4

Option 1

Option 3

Option 1

### 13. CAT - Team Selection

The coach of the national rugby team wants to form a team of 5, 6 or 7 players for a practice match against the rival team. The following information is known.

1. A is always selected with K and vice versa.
2. If B is selected, then N should not be selected and vice versa.
3. Either of C, D or E, but not more than one of them must be selected in the team.
4. If the team size is 7, one of J or I should be in the team. They are not selected in a team of any other size.
5. If the team size is 6, neither K nor L should be in the team.
6. M is selected only if A and B are selected for the team.
7. There are 15 players (from A to O) in the squad.

Q1. In how many ways can a team of 5 be formed?

Q2. In how many ways can a team of 6 be formed if A is not selected?

Q3. If B and K are not available for selection and a team of 7 is to be formed, who among the following has to be included in the team?

1) N                     2) G                     3) L                      4) None of these

Q4. In a certain tournament, the coach has no restrictions in terms of team size. At least how many players are left out in each team?

138

6

4) None of these

5

Option c

Option a

Option e

Option b