Q1:
Logical Reasoning
Coding/Decoding
Easy
Logical Reasoning
Coding/Decoding
Easy
The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits.
Which digit does the letter A represent?
Logical Reasoning
Coding/Decoding
Easy
The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits.
Which digit does the letter B represent?
Logical Reasoning
Coding/Decoding
Easy
The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits.
Which among the digits 3, 4, 6 and 7 cannot be represented by the letter D?
Logical Reasoning
Coding/Decoding
Easy
The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits.
Which among the digits 4, 6, 7 and 8 cannot be represented by the letter G?
Logical Reasoning
Arrangements
Easy
Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items.
The following additional facts are known.
Which of the following is true?
Logical Reasoning
Arrangements
Easy
Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items.
The following additional facts are known.
Which of the following is FALSE?
Logical Reasoning
Arrangements
Easy
Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items.
The following additional facts are known.
The sixth performance was composed by:
Logical Reasoning
Arrangements
Easy
Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items.
The following additional facts are known.
Which pair of performances were composed by the same composer?
Logical Reasoning
Math Puzzles
Medium
A new game show on TV has 100 boxes numbered 1, 2,..., 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, ..., in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.
What is the minimum possible number of different types of prizes?
Logical Reasoning
Math Puzzles
Medium
A new game show on TV has 100 boxes numbered 1, 2,..., 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, ..., in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.
What is the maximum possible number of different types of prizes?
Logical Reasoning
Math Puzzles
Medium
A new game show on TV has 100 boxes numbered 1, 2,..., 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, ..., in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.
Which of the following is not possible?
Logical Reasoning
Math Puzzles
Medium
A new game show on TV has 100 boxes numbered 1, 2,..., 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, ..., in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.
You ask for the type of item in box 45. Instead of being given a direct answer, you are told that there are 31 items of the same type as box 45 in boxes 1 to 44 and 43 items of the same type as box 45 in boxes 46 to 100.
What is the maximum possible number of different types of items?
Logical Reasoning
Arrangements
Medium
A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers.
The following additional facts are known.
In how many different ways can the items be arranged on the shelves?
Logical Reasoning
Arrangements
Medium
A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers.
The following additional facts are known.
Which of the following items is not a type of biscuit?
Logical Reasoning
Arrangements
Medium
A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers.
The following additional facts are known.
Which of the following can represent the numbers of the empty shelves in a possible arrangement?
Logical Reasoning
Arrangements
Medium
A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers.
The following additional facts are known.
Which of the following statements is necessarily true?
Logical Reasoning
Routes & Networks
Medium
The figure below shows the street map for a certain region with the street intersections marked from a through I. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.
Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.
The following additional facts are known.
Who is standing at intersection a?
Logical Reasoning
Routes & Networks
Medium
The figure below shows the street map for a certain region with the street intersections marked from a through I. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.
Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.
The following additional facts are known.
Who can V see?
Logical Reasoning
Routes & Networks
Medium
The figure below shows the street map for a certain region with the street intersections marked from a through I. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.
Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.
The following additional facts are known.
What is the minimum number of street segments that X must cross to reach Y?
Logical Reasoning
Routes & Networks
Medium
The figure below shows the street map for a certain region with the street intersections marked from a through I. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.
Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.
The following additional facts are known.
Should a new person stand at intersection d, who among the six would she see?
Logical Reasoning
Games & Tournaments
Hard
Six players - Tanzi, Umeza, Wangdu, Xyla, Yonita and Zeneca competed in an archery tournament. The tournament had three compulsory rounds, Rounds 1 to 3. In each round every player shot an arrow at a target. Hitting the centre of the target (called bull's eye) fetched the highest score of 5. The only other possible scores that a player could achieve were 4, 3, 2 and 1. Every bull's eye score in the first three rounds gave a player one additional chance to shoot in the bonus rounds, Rounds 4 to 6. The possible scores in Rounds 4 to 6 were identical to the first three.
A player's total score in the tournament was the sum of his/her scores in all rounds played by him/her. The table below presents partial information on points scored by the players after completion of the tournament. In the table, NP means that the player did not participate in that round, while a hyphen means that the player participated in that round and the score information is missing.
| Name | Round-1 | Round-2 | Round-3 | Round-4 | Round-5 | Round-6 |
|---|---|---|---|---|---|---|
| Tanzi | - | 4 | - | 5 | NP | NP |
| Umeza | - | - | - | 1 | 2 | NP |
| Wangdu | - | 4 | - | NP | NP | NP |
| Xyla | - | - | - | 1 | 5 | - |
| Yonita | - | - | 3 | 5 | NP | NP |
| Zeneca | - | - | - | 5 | 5 | NP |
The following facts are also known.
What was the highest total score?
Logical Reasoning
Games & Tournaments
Hard
Six players - Tanzi, Umeza, Wangdu, Xyla, Yonita and Zeneca competed in an archery tournament. The tournament had three compulsory rounds, Rounds 1 to 3. In each round every player shot an arrow at a target. Hitting the centre of the target (called bull's eye) fetched the highest score of 5. The only other possible scores that a player could achieve were 4, 3, 2 and 1. Every bull's eye score in the first three rounds gave a player one additional chance to shoot in the bonus rounds, Rounds 4 to 6. The possible scores in Rounds 4 to 6 were identical to the first three.
A player's total score in the tournament was the sum of his/her scores in all rounds played by him/her. The table below presents partial information on points scored by the players after completion of the tournament. In the table, NP means that the player did not participate in that round, while a hyphen means that the player participated in that round and the score information is missing.
| Name | Round-1 | Round-2 | Round-3 | Round-4 | Round-5 | Round-6 |
|---|---|---|---|---|---|---|
| Tanzi | - | 4 | - | 5 | NP | NP |
| Umeza | - | - | - | 1 | 2 | NP |
| Wangdu | - | 4 | - | NP | NP | NP |
| Xyla | - | - | - | 1 | 5 | - |
| Yonita | - | - | 3 | 5 | NP | NP |
| Zeneca | - | - | - | 5 | 5 | NP |
The following facts are also known.
What was Zeneca's total score?
Logical Reasoning
Games & Tournaments
Hard
Six players - Tanzi, Umeza, Wangdu, Xyla, Yonita and Zeneca competed in an archery tournament. The tournament had three compulsory rounds, Rounds 1 to 3. In each round every player shot an arrow at a target. Hitting the centre of the target (called bull's eye) fetched the highest score of 5. The only other possible scores that a player could achieve were 4, 3, 2 and 1. Every bull's eye score in the first three rounds gave a player one additional chance to shoot in the bonus rounds, Rounds 4 to 6. The possible scores in Rounds 4 to 6 were identical to the first three.
A player's total score in the tournament was the sum of his/her scores in all rounds played by him/her. The table below presents partial information on points scored by the players after completion of the tournament. In the table, NP means that the player did not participate in that round, while a hyphen means that the player participated in that round and the score information is missing.
| Name | Round-1 | Round-2 | Round-3 | Round-4 | Round-5 | Round-6 |
|---|---|---|---|---|---|---|
| Tanzi | - | 4 | - | 5 | NP | NP |
| Umeza | - | - | - | 1 | 2 | NP |
| Wangdu | - | 4 | - | NP | NP | NP |
| Xyla | - | - | - | 1 | 5 | - |
| Yonita | - | - | 3 | 5 | NP | NP |
| Zeneca | - | - | - | 5 | 5 | NP |
The following facts are also known.
Which of the following statements is true?
Logical Reasoning
Games & Tournaments
Hard
Six players - Tanzi, Umeza, Wangdu, Xyla, Yonita and Zeneca competed in an archery tournament. The tournament had three compulsory rounds, Rounds 1 to 3. In each round every player shot an arrow at a target. Hitting the centre of the target (called bull's eye) fetched the highest score of 5. The only other possible scores that a player could achieve were 4, 3, 2 and 1. Every bull's eye score in the first three rounds gave a player one additional chance to shoot in the bonus rounds, Rounds 4 to 6. The possible scores in Rounds 4 to 6 were identical to the first three.
A player's total score in the tournament was the sum of his/her scores in all rounds played by him/her. The table below presents partial information on points scored by the players after completion of the tournament. In the table, NP means that the player did not participate in that round, while a hyphen means that the player participated in that round and the score information is missing.
| Name | Round-1 | Round-2 | Round-3 | Round-4 | Round-5 | Round-6 |
|---|---|---|---|---|---|---|
| Tanzi | - | 4 | - | 5 | NP | NP |
| Umeza | - | - | - | 1 | 2 | NP |
| Wangdu | - | 4 | - | NP | NP | NP |
| Xyla | - | - | - | 1 | 5 | - |
| Yonita | - | - | 3 | 5 | NP | NP |
| Zeneca | - | - | - | 5 | 5 | NP |
The following facts are also known.
What was Tanzi's score in Round 3?
Data Interpretation
Tables
Hard
The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UT) of India. All cases refer to the ones registered against foreigners in 2016.
The number of cases – classified into three categories: IPC crimes, SLL crimes and other crimes – for nine states/UTs are shown in the figure below. These nine belong to the top ten states/UTs in terms of the total number of cases registered. The remaining state (among top ten) is West Bengal, where all the 520 cases registered were SLL crimes.
The table below shows the ranks of the ten states/UTs mentioned above among ALL states/UTs of India in terms of the number of cases registered in each of the three category of crimes. A state/UT is given rank r for a category of crimes if there are (r-1) states/UTs having a larger number of cases registered in the same category. For example, if two states have the same number of cases in a category, and exactly three other states/UTs have larger numbers of cases registered in the same category, then both the states are given rank 4 in that category. Missing ranks in the table are denoted by *.
| IPC Crimes | SLL Crimes | Other Crimes | |
|---|---|---|---|
| Delhi | * | * | * |
| Goa | * | 4 | * |
| Haryana | 8 | 6 | * |
| Karnataka | 3 | 2 | * |
| Kerala | * | 9 | * |
| Maharashtra | 3 | 4 | 8 |
| Puducherry | 13 | 29 | * |
| Tamil Nadu | 11 | 7 | * |
| Telangana | 6 | 9 | 8 |
| West Bengal | 17 | * | 16 |
What is the rank of Kerala in the 'IPC crimes' category?
Data Interpretation
Tables
Hard
The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UT) of India. All cases refer to the ones registered against foreigners in 2016.
The number of cases – classified into three categories: IPC crimes, SLL crimes and other crimes – for nine states/UTs are shown in the figure below. These nine belong to the top ten states/UTs in terms of the total number of cases registered. The remaining state (among top ten) is West Bengal, where all the 520 cases registered were SLL crimes.
The table below shows the ranks of the ten states/UTs mentioned above among ALL states/UTs of India in terms of the number of cases registered in each of the three category of crimes. A state/UT is given rank r for a category of crimes if there are (r-1) states/UTs having a larger number of cases registered in the same category. For example, if two states have the same number of cases in a category, and exactly three other states/UTs have larger numbers of cases registered in the same category, then both the states are given rank 4 in that category. Missing ranks in the table are denoted by *.
| IPC Crimes | SLL Crimes | Other Crimes | |
|---|---|---|---|
| Delhi | * | * | * |
| Goa | * | 4 | * |
| Haryana | 8 | 6 | * |
| Karnataka | 3 | 2 | * |
| Kerala | * | 9 | * |
| Maharashtra | 3 | 4 | 8 |
| Puducherry | 13 | 29 | * |
| Tamil Nadu | 11 | 7 | * |
| Telangana | 6 | 9 | 8 |
| West Bengal | 17 | * | 16 |
In the two states where the highest total number of cases are registered, the ratio of the total number of cases in IPC crimes to the total number in SLL crimes is closest to
Data Interpretation
Tables
Hard
The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UT) of India. All cases refer to the ones registered against foreigners in 2016.
The number of cases – classified into three categories: IPC crimes, SLL crimes and other crimes – for nine states/UTs are shown in the figure below. These nine belong to the top ten states/UTs in terms of the total number of cases registered. The remaining state (among top ten) is West Bengal, where all the 520 cases registered were SLL crimes.
The table below shows the ranks of the ten states/UTs mentioned above among ALL states/UTs of India in terms of the number of cases registered in each of the three category of crimes. A state/UT is given rank r for a category of crimes if there are (r-1) states/UTs having a larger number of cases registered in the same category. For example, if two states have the same number of cases in a category, and exactly three other states/UTs have larger numbers of cases registered in the same category, then both the states are given rank 4 in that category. Missing ranks in the table are denoted by *.
| IPC Crimes | SLL Crimes | Other Crimes | |
|---|---|---|---|
| Delhi | * | * | * |
| Goa | * | 4 | * |
| Haryana | 8 | 6 | * |
| Karnataka | 3 | 2 | * |
| Kerala | * | 9 | * |
| Maharashtra | 3 | 4 | 8 |
| Puducherry | 13 | 29 | * |
| Tamil Nadu | 11 | 7 | * |
| Telangana | 6 | 9 | 8 |
| West Bengal | 17 | * | 16 |
Which of the following is DEFINITELY true about the ranks of states/UT in the ‘other crimes’ category?
i) Tamil Nadu: 2
ii) Puducherry: 3
Data Interpretation
Tables
Hard
The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UT) of India. All cases refer to the ones registered against foreigners in 2016.
The number of cases – classified into three categories: IPC crimes, SLL crimes and other crimes – for nine states/UTs are shown in the figure below. These nine belong to the top ten states/UTs in terms of the total number of cases registered. The remaining state (among top ten) is West Bengal, where all the 520 cases registered were SLL crimes.
The table below shows the ranks of the ten states/UTs mentioned above among ALL states/UTs of India in terms of the number of cases registered in each of the three category of crimes. A state/UT is given rank r for a category of crimes if there are (r-1) states/UTs having a larger number of cases registered in the same category. For example, if two states have the same number of cases in a category, and exactly three other states/UTs have larger numbers of cases registered in the same category, then both the states are given rank 4 in that category. Missing ranks in the table are denoted by *.
| IPC Crimes | SLL Crimes | Other Crimes | |
|---|---|---|---|
| Delhi | * | * | * |
| Goa | * | 4 | * |
| Haryana | 8 | 6 | * |
| Karnataka | 3 | 2 | * |
| Kerala | * | 9 | * |
| Maharashtra | 3 | 4 | 8 |
| Puducherry | 13 | 29 | * |
| Tamil Nadu | 11 | 7 | * |
| Telangana | 6 | 9 | 8 |
| West Bengal | 17 | * | 16 |
What is the sum of the ranks of Delhi in the three categories of crimes?
Data Interpretation
Other Charts
Easy
Five vendors are being considered for a service. The evaluation committee evaluated each vendor on six aspects – Cost, Customer Service, Features, Quality, Reach, and Reliability. Each of these evaluations are on a scale of 0 (worst) to 100 (perfect). The evaluation scores on these aspects are shown in the radar chart. For example, Vendor 1 obtains a score of 52 on Reliability, Vendor 2 obtains a score of 45 on Features and Vendor 3 obtains a score of 90 on Cos
On which aspect is the median score of the five vendors the least?
Data Interpretation
Other Charts
Easy
Five vendors are being considered for a service. The evaluation committee evaluated each vendor on six aspects – Cost, Customer Service, Features, Quality, Reach, and Reliability. Each of these evaluations are on a scale of 0 (worst) to 100 (perfect). The evaluation scores on these aspects are shown in the radar chart. For example, Vendor 1 obtains a score of 52 on Reliability, Vendor 2 obtains a score of 45 on Features and Vendor 3 obtains a score of 90 on Cos
A vendor's final score is the average of their scores on all six aspects. Which vendor has the highest final score?
Data Interpretation
Other Charts
Easy
Five vendors are being considered for a service. The evaluation committee evaluated each vendor on six aspects – Cost, Customer Service, Features, Quality, Reach, and Reliability. Each of these evaluations are on a scale of 0 (worst) to 100 (perfect). The evaluation scores on these aspects are shown in the radar chart. For example, Vendor 1 obtains a score of 52 on Reliability, Vendor 2 obtains a score of 45 on Features and Vendor 3 obtains a score of 90 on Cos
List of all the vendors who are among the top two scorers on the maximum number of aspects is:
Data Interpretation
Other Charts
Easy
Five vendors are being considered for a service. The evaluation committee evaluated each vendor on six aspects – Cost, Customer Service, Features, Quality, Reach, and Reliability. Each of these evaluations are on a scale of 0 (worst) to 100 (perfect). The evaluation scores on these aspects are shown in the radar chart. For example, Vendor 1 obtains a score of 52 on Reliability, Vendor 2 obtains a score of 45 on Features and Vendor 3 obtains a score of 90 on Cos
List of all the vendors who are among the top three vendors on all six aspects is:
Every question from the CAT 2019 Data Interpretation & Logical Reasoning paper is here in full, with the correct answer and a step by step solution for each one. It is completely free, there is no login and no paywall, and you can read the whole paper online or download it to revise offline.
You can also attempt it instead of only reading it. Take the paper as a full length mock under exam conditions, or filter it by topic and attempt just that topic as a topic test. Both are free, and you get a breakdown of your accuracy, your timing and your weak areas once you submit.
CAT past year questions (PYQs) are the closest thing to the real exam, so working through them is the quickest way to learn the paper pattern, the marking scheme and the level of difficulty to expect on the day.