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).
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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.
- Each model was ranked third in at least one parameter and exactly two models were not ranked first in any parameter.
- Apache was ranked fourth in Engine power, while KTM was ranked second in two parameters.
- No model received the same rank in more than two parameters, while Bullet did not receive the same rank in any two parameters.
- Bullet was ranked worse than Ninja in all the parameters except Turbo, while KTM was ranked better than Ninja in pick-up.
- Ninja was ranked better in Engine power than at least three models, while KTM was ranked neither first nor last in Torque.
- 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?
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:
- Everyone studied for more than one hour.
- Mohit spent the maximum time and Lokpriya spent the least time at the park.
- 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.
- The difference between the time spent by Somil and Abhishek in the park was 20 minutes.
- Lokpriya and Ashish
- Mohit and Abhishek
- Somil and Avinash
- Lokpriya and Mohit
- 10:30 am
- 10:00 am
- 11:05 am
- 11:20 am
- 11:00 am
- 10:50 am
- 11:20 am
- 11:05 am
- 50 Minutes
- 35 minutes
- 20 Minutes
- 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]
- 3000
- 22000
- 6000
- 19000
Q3. What was the base exchange rate of currency B with respect to currency L on that day? [TITA]
- 1.10
- 0.95
- 2.20
- 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
- none of the men wrote the same number as that of the chair he was sitting in.
- exactly three men guessed the chair numbers of their wives correctly.
- P is sitting three places to the right of Q, who is the wife of C
- R, the wife of A, is to the right of P and left of S.
- exactly three persons were sitting in the same numbered chairs as their wives.
- E’s wife
- D’s wife
- F’s wife
- CBD
Q2. Who among the following did not sit in the same numbered chair as her husband?
- S
- R
- P
- More than one of the above
- T is the wife of F
- T is the wife of D
- S is the wife of E
- P is the wife of E
- Q
- T
- U
- S
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:
- The cost per acre, in Rs. lakh, of each of the orchards is a prime number less than ten.
- B always lies.
- The Mango orchard is the costliest among the three.
- The Guava orchard is the cheapest among the three.
- No person working on this farm always speaks the truth.
- The cost per acre, in Rs.lakh, is an even number for one of the orchards.
- The Guava orchard is the costliest orchard.
- A always lies.
- The Mango orchard is cheaper than the Orange orchard.
- A
- B
- C
- CBD
- Orange
- Mango
- Guava
- CBD
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.
- 7
- 4
- 5
- CBD
- 13
- 17
- 10
- CBD
- 10
- 13
- 9
- 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.
- Square Circle Rectangle
- 2 Squares, 1 Oval
- 2 Squares, 1 Circle
- None of these
- Truth −> Truth −> Truth
- Truth −> Lie −> Lie
- Lie −> Lie −> Lie
- Truth −> Truth −> Lie
- A
- B
- C
- Cannot be determined
- A is not the alternator.
- All three figures are quadrilaterals.
- At most one of C’s statements is true.
- Liar
- Alternator
- Truth Teller
- CBD
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
- 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.
- 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.
- 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.
- Raj: I went to wish happy birthday to Seeta, but when I reached only Chintu and Bheem were there. Seeta joined us later.
- 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.
- 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
- Aadi
- Ram
- Chintu
- Jay
- 4
- 2
- 5
- CBD
Q3. Who was the fifth person to enter the garden?
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?
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.
- 1
- 2
- 3
- 4
- 3
- 4
- 6
- 7
- BG
- AFI
- CEG
- DHI
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.
- 1
- 2
- 3
- 4
- 3
- 4
- 6
- 7
- BG
- AFI
- CEG
- DHI
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.
- None of the five friends has more than two bikes.
- There are at least two and at the most three bikes of any given capacity.
- None of the five friends has both bikes of the same capacity. For example, ‘Amar has two 100 cc bikes’ is an invalid combination.
- 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.
- The sum of the capacities of the bikes with Ajay is the highest.
- Akash and Arjun do not have any bike of the same capacity.
- 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
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.
- A is always selected with K and vice versa.
- If B is selected, then N should not be selected and vice versa.
- Either of C, D or E, but not more than one of them must be selected in the team.
- 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.
- If the team size is 6, neither K nor L should be in the team.
- M is selected only if A and B are selected for the team.
- 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?
16. CAT - Project Management
An MBA college offers ten different courses to the students in the second year. Among the ten courses, some courses can be started only after the completion of the relevant prerequisite courses. Each course is assigned a certain number of credits which are earned by a student after the completion of the course. Further, each course requires a certain time to complete. Any student can study any number of courses at the same time as long as all the relevant prerequisite courses are completed. The following table provides for each course, the name of the course, the relevant prerequisite courses to be completed, the number of credits assigned to that course and the time required (in weeks) to complete the course:
Q1. What is the minimum number of weeks required for a student to complete all the ten courses?
Q2. What is the minimum number of weeks that will be required for a student to complete courses worth a total of at least 16 credits?
Q3. What is the maximum number of credits that a student can earn in 15 weeks?
Q4. If a student wants to complete FM before starting IDF, what is the minimum number of weeks required to complete all the ten courses?
17. CAT - Project Management
The graph given pertains to the recruitment and promotion details of a company called TFC. Every year, the company takes in new recruits, known popularly as “Nanos”, in the company for its off-shore projects. These Nanos remain Nanos for two years during which they undergo a rigorous training. Immediately after completion of two years of training, these Nanos appear for a screening test, following which they get promoted as Vets if they pass the test. For the number of Nanos that are recruited in a particular year, the number of Nanos getting converted into Vets is between 60% to 80% (only integral values of percentage), both values included. On conversion to Vets, these employees leave TFC operations in the country for on-shore projects. The Nanos who fail to get promoted as Vets continue as Nanos for one more year following which they are labeled as Vets without any test and are then transferred to its on-shore operations.
In the chart, the innermost circle represents the year of intake of the Nanos, while the outer circles represent the numbers of Nanos and Vets for that year. Further for any given year, the number of Nanos always exceeds the number of Vets in the same year.
For example, in the year 2005, the number of Nanos that TFC had was 65 and the number of Vets in the same year was 42.
No employee can bypass the process and get recruited as a Vet directly.
Q1. The number of Nanos from the 2006 batch who were promoted as Vets without a test was ______
Q2. The percentage of Nanos getting promoted as Vets in the first instance was highest for which of the following batches of Nanos?
2003 2004 2005 2006
Q3. What was the number of Nanos who did not get promoted as Vets at the first instance from the ones present in 2005?
Q4. If we consider the period from 2007 – 2009, then in which of the following years was the number of Vets the highest?
2007 2008 2009 CBD
18. CAT - Routes
The diagram given below is the network for transporting oil from refinery A to deports B, C, D, E, F and G. The arrows indicate the direction in which oil flows and the value above each depot denotes its capacity (in thousand liters). The supply is arranged such that only after a depot is full will the excess oil be transferred to the depots next in the supply line. The maximum capacity ( in thousands of liters ) of the pipeline connecting the refinery with the depots is 1500 and those connecting the depots is 750. The slack in a pipeline is defined as the extra flow required to bring the pipeline to full capacity. The flow in the pipeline is such that the demand at each depot is completely met.
Q1. What is minimum flow(in thousand liters) of in the pipeline connecting A and D?
Q2. If the pipeline connecting A nd B is in repair as a result of which its maximum capacity is reduced by 20%, what is the minimum flow in pipeline D and F?
Q3. What is the maximum value (in thousand litre) of the sum of slacks in all the pipelines applying oil to depot E?
Q4. If the slack in the pipeline connecting D and G is 50, then what is the minimum slack, in pipeline connecting E and F?
19. CAT - Routes
The network diagram below shows the distance between the various money transmission offices in a city. The values in percentage indicate percentage of the total amount being transferred that is charged by each transmission office as transmission charge. When an office is considered as a starting or destination office, the amount there is ignored i.e. while sending from B to G, the 1% at B and 4% at G are ignored. There is also an additional transmission charge of n% of the total amount being transferred where n km is the total distance between the starting and destination office. The transferred amount reaches the destination office after deducting the above mentioned charges. Note that the 2 written along the path joining A and B indicates that the distance between A and B is 2 km
Q1. What is the maximum amount that will reach office H if Rs. 500 are transferred from office A, such that no more than two intermediary offices are covered during the transit _________
Q2. In how many ways can one transmit money from office D to E using exactly three intermediary offices
Q3. What is the maximum additional transmission incurred while transmitting Rs. 8,000 from D to E. Consider data from the previous question.
Q4. A person wants to transfer money from A to I. He starts from A and keeps going in alphabetical order till possible. If a particular office in sequence is unavailable, he transmits to the next feasible office. What is his overall transmission loss in trying to send Rs. 7.5 lakhs?
20. CAT - DI Stocks
Lokesh, who trades in the commodity market, was interested in investing in two commodities – Commodity A and Commodity B. He followed the price of these two commodities for n days, from Day 1 to Day n, and he observed that they followed the following trends during the given period:
- At the beginning of a day, if the price of Commodity A was greater than that of Commodity B, the price of Commodity A increased by Rs.10 and the price of Commodity B increased by Rs.40 by the beginning of the next day.
- At the beginning of a day, if the price of Commodity A was less than or equal to that of Commodity B, the price of Commodity A increased by Rs.30 and the price of Commodity B increased by Rs.10 by the beginning of the next day.
At the beginning of Day 1, the price of Commodity A was Rs.130 and the price of Commodity B was Rs.140.
Consider that the price of a commodity indicates the price only at the beginning of a day
Q1. If n = 15, on how many days was the price of Commodity A greater than that of Commodity B?
Q2. If n = 100, what was the maximum difference between the prices of Commodity A and Commodity B on any day?
Q3. If Lokesh observed that the price of at least one of the two commodities was less than Rs. 500 on the nth day, what is the maximum possible value of n?
Q4. If n = 73, what is the difference between the average price (in Rs.) of Commodity A and that of Commodity B?
21. CAT - Routes/Pipes
There are six towns in a municipality namely A, B, C, D, E and F. The water distribution system of the municipality to its towns is shown in the figure. The total water requirement of the municipality in the month of March is 1450 cc/min and water is first fed to town A from the water source. The rate of water flow is such that the demand at all the locations is exactly met. The water requirement of town A is 400 cc/min. The flow in the pipe connecting towns A and E is same as that of the requirement of town B. The flow in the pipe connecting towns E and F is the same as that of the pipe connecting towns E and C, which in turn is one-fourth of the flow in the pipe connecting towns B and C. The requirement of towns E and F is equal. The flow in the pipe connecting towns F and D is same as that of the requirement of town C, which in turn is two-third of the flow in the pipe connecting towns C and D. There are 1000 households in town D. The average total water requirement for each of these households in the month of April is 10800 cc. Shown below is the water distribution map of the municipality. Consider that one month has 30 days.
Q1. What is the flow in the pipe connecting towns B and F (in cc/min)?
Q2. In order to reduce the wear and tear in the pipeline the municipality decided to keep the maximum flow in all the pipes which connect any two towns to 650 cc/min. It was further decided that if this change were to affect the supplies to the towns then only town D must be the one to suffer. What will be the flow in pipe connecting towns B and C in that case?
Q3. Using information given in the previous question, find out the capacity of an additional pipe that needs to be put in place connecting town D with the water source so as to restore the supplies of town D to its original level.
Q4. The earlier conditions of water distribution are now discarded. Water requirement of town A falls by 150 cc/min but the volume of water fed (in cc/min) to it remains the same. What is the average monthly water consumption (in cc) for each household in Town D if the water requirement for towns B, C, E and F remains the same as before? The flow of water in the two outlet pipes of any of the towns A, B and E is equal under this new system of water distribution.
22. CAT - THE DI SAPPHIRE
Telomia Inc. manufactures and sells four different types of products – Pens, Pencils, Markers and Sketch Pens – for Rs.30, Rs.10, Rs.40 and Rs.25 per unit respectively. It costs the company Rs.10, Rs.6, Rs.25 and Rs.20 per unit respectively to manufacture each type of product.
The total revenue of the company is calculated as sum of the products of the price per unit and number of units sold of each type.
The total cost of the company is calculated as the sum of the products of the cost per unit and the number of units sold of each type.
The profit percentage of the company is calculated as the profit of the company as a percentage of the total cost of the company.
Q1. If, during a particular year, the number of units of Pens, Pencils, Markers and Sketch Pens sold by Telomia Inc. are in the ratio 1:2:3:4, what is the profit percentage of the company for this year?
Q2. If, during a particular year, the revenues of Telomia Inc. from the sale of Pens, Pencils, Markers and Sketch Pens were in the ratio of 1:2:4:5, what is the profit percentage of Telomia Inc. for this year?
Q3. If, during a particular year, the number of units of Pens, Pencils and Markers sold by Telomia Inc. are in the ratio 1:3:5 and the company made a profit percentage of 35%, what is the ratio of the number of Sketch Pens sold to the number of Markers sold?
Q4. During a particular year, the total Revenue of Telomia Inc. was Rs.21 mn and Telomia Inc. sold an equal number of Pens, Pencils, Markers and Sketch Pens. What is the total number of Markers that Telomia Inc. sold?
23. CAT - THE NAÏVE ROUTES
Seven localities, A through G, in a city were connected by certain two-way and one-way roads as shown in the figure below.
This morning, Kishore, the newly appointed Traffic Commissioner of the city, changed all the existing two-way roads into one-way roads while ensuring that any locality can be reached from any other locality.
Q1. What is the minimum number of localities that a person must pass through to go from G to D (excluding G and D)?
Q2. In how many ways can a person travel from F to C without passing through any locality twice?
Q3. If a person travelled from one locality to another and passed through all the localities exactly once, how many of the seven localities can be the locality from which he started?
24. CAT - Ranks Marking Set
Eight students – A, 8, C, D, E, F, G and H – wrote an exam conducted by an assistant professor, Asim. Asim ranked the students in the decreasing order of their marks in the exam, such that two or more students who get the same mark will get the same rank (say N) and the student who has the next highest mark will get the next rank (i.e., N + 1) and so on.
Later, Asim submitted the same to his superior, professor Ganesh. The professor was not satisfied and asked Asim to give revised ranks, from 1 to 8, to the eight students in the decreasing order of their marks. If two or more students get the same mark and compete for the same rank (say N), then the student with the least number of attempts among them should be ranked the best (i.e., N), the one with the next least number of attempts, the next best (i.e., N + 1) and so on. When Asim ranked the students accordingly, it was observed that
i. Of the students whose ranks were changed, the change in the rank of B was less than that of any other student and the change in the rank of G was more than that of any other student.
ii. only D”s rank changed by 3.
iii. the number of questions attempted by C was less than that by A, but his revised rank was not better than that of A, which, in turn, was 6.
iv. initially D and E had the same rank.
v. initially, there was no rank which was given to more than three students
vi. no two students had the same number of attempts.
Note: Between any two ranks, the numerically lower rank is considered to be the better rank.
Q1. What was the revised rank of D?
Q2. How many students got first rank?
Q3. By how much did C’s rank change?
Q4. Who got the revised rank of 1?
B F E CBD
Q5. Who among the following can’t be the student with the least number of attempts?
H F D E
25. CAT - DILR Miscellaneous
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.
Q1. What is the time taken (in minutes) to travel across road I? Disregard possible delays at node 6.
- 1
- 2
- 3
- 4
- 3
- 4
- 6
- 7
- BG
- AFI
- CEG
- DHI
26. CAT - DILR Miscellaneous
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.
Q1. What is the time taken (in minutes) to travel across road I? Disregard possible delays at node 6.
- 1
- 2
- 3
- 4
- 3
- 4
- 6
- 7
- BG
- AFI
- CEG
- DHI
