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CAT 2019 | SLOT - 1 | DILR

CAT 2019 | Slot 1 | Quantitative Ability 

Dive into the 8 sets - question CAT 2019 | Slot 1 DILR paper, designed to test your quantitative skills. Includes solutions and explanations for all questions to help you understand key concepts. Uploaded on MBA Litmus to help aspirants practice and prepare effectively.

Set 1: Game Show

A new game show on TV has 100 boxes numbered 1 to 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 type a, a diamond ring, and there is exactly one of these. 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. The prizes can be in any order in the boxes.

Q1. What is the minimum possible number of different types of prizes? [TITA]

Q2. What is the maximum possible number of different types of prizes? [TITA]

Q3. Which of the following is not possible?

  • There are exactly 30 items of type b.
  • There are exactly 75 items of type e.
  • There are exactly 60 items of type d.
  • There are exactly 45 items of type c.

Q4. Type of item in box 45: 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?

  • 3
  • 4
  • 5
  • 6

Set 2: Street Intersection

The figure below shows the street map for a certain region with intersections marked from a through l. 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 at intersections b, c, e, f, h, and k. In particular, the person at intersection g can see the person at intersection e irrespective of whether there is a person 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 facts are known:

  1. X, U, and Z are standing at the three corners of a triangle formed by three street segments.
  2. X can see only U and Z.
  3. Y can see only U and W.
  4. U sees V standing in the next intersection behind Z.
  5. W cannot see V or Z.
  6. No one among the six is standing at intersection d.

Q1. Who is standing at intersection a?

  • W
  • Y
  • No one
  • V

Q2. Who can V see?

  • U, W and Z only
  • U and Z only
  • Z only
  • U only

Q3. What is the minimum number of street segments that X must cross to reach Y?

  • 3
  • 2
  • 1
  • 4

Q4. Should a new person stand at intersection d, who among the six would she see?

  • V and X only
  • U and Z only
  • U and W only
  • W and X only

Set 3: Crimes

The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UTs) of India. All cases refer to those 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. These nine belong to the top ten states/UTs in terms of total cases registered. The remaining state is West Bengal, where all 520 registered cases were SLL crimes.

The table below shows the ranks of the ten states/UTs among all states/UTs of India in each crime category. A state/UT is given rank r for a category if there are (r-1) states/UTs with a larger number of cases. Missing ranks in the table are denoted by *.

Q1. What is the rank of Kerala in the ‘IPC crimes’ category? [TITA]

Q2. In the two states with the highest total number of cases, what is the ratio of total IPC cases to total SLL cases?

  • 19 : 20
  • 11 : 10
  • 1 : 9
  • 3 : 2

Q3. Which of the following is DEFINITELY true about ranks in the ‘other crimes’ category?

  • i) Tamil Nadu: 2
  • ii) Puducherry: 3
  • only ii)
  • both i) and ii)
  • only i)
  • neither i) nor ii)

Q4. What is the sum of the ranks of Delhi in the three categories of crimes? [TITA]

Set 4: Vendor

Five vendors are being considered for a service. The evaluation committee assessed each vendor on six aspects – Cost, Customer Service, Features, Quality, Reach, and Reliability – on a scale of 0 (worst) to 100 (perfect). For example, Vendor 1 scores 52 on Reliability, Vendor 2 scores 45 on Features, and Vendor 3 scores 90 on Cost.

Q1. On which aspect is the median score of the five vendors the least?

  • Cost
  • Quality
  • Reliability
  • Customer Service

Q2. A vendor's final score is the average of scores on all six aspects. Which vendor has the highest final score?

  • Vendor 1
  • Vendor 3
  • Vendor 4
  • Vendor 2

Q3. List all vendors among the top two scorers on the maximum number of aspects.

  • Vendor 1 and Vendor 2
  • Vendor 2, Vendor 3 and Vendor 4
  • Vendor 2 and Vendor 5
  • Vendor 1 and Vendor 5

Q4. List all vendors among the top three vendors on all six aspects.

  • None of the Vendors
  • Vendor 1
  • Vendor 1 and Vendor 3
  • Vendor 3

Set 5: Supermarket

A supermarket has 12 items (coded A to L) to be placed in shelves numbered 1 to 16. Five items are biscuits, three are candies, and the rest are savouries. Only one item can be placed per shelf. Items of the same type must be clustered together with no empty shelf between them, and at least one empty shelf must separate different types. At most two consecutive shelves can be empty.

Additional facts:

  1. A and B are placed in consecutive shelves in increasing order.
  2. I and J are placed in consecutive shelves, both higher than A and B.
  3. D, E, and F are savouries and are placed consecutively after all biscuits and candies.
  4. K is placed in shelf number 16.
  5. L and J are of the same type; H is of a different type.
  6. C is a candy and is placed in a shelf preceded by two empty shelves.
  7. L is placed in a shelf preceded by exactly one empty shelf.

Q1. In how many different ways can the items be arranged on the shelves?

  • 2
  • 1
  • 4
  • 8

Q2. Which of the following items is not a type of biscuit?

  • B
  • A
  • L
  • G

Q3. Which of the following can represent the numbers of the empty shelves in a possible arrangement?

  • 1, 7, 11, 12
  • 1, 5, 6, 12
  • 1, 2, 6, 12
  • 1, 2, 8, 12

Q4. Which of the following statements is necessarily true?

  • There are two empty shelves between the biscuits and the candies.
  • All candies are kept before biscuits.
  • All biscuits are kept before candies
  • There are at least four shelves between items B and C.

Set 6: Archery

Six players – Tanzi, Umeza, Wangdu, Xyla, Yonita, and Zeneca competed in an archery tournament. There were three compulsory rounds, Rounds 1 to 3. Each round allowed each player to shoot one arrow. Hitting the centre (bull’s eye) scored 5 points; other possible scores were 4, 3, 2, and 1. Each bull’s eye in the first three rounds gave a bonus shot in Rounds 4 to 6 with identical scoring. Total score is the sum of all rounds played. NP means the player did not participate in that round, and a hyphen means the score is missing.

Additional facts:

  1. Tanzi, Umeza, and Yonita had the same total score.
  2. Total scores for all players, except one, were multiples of three.
  3. The highest total score was one more than double the lowest total score.
  4. The number of players hitting bull’s eye in Round 2 was double that in Round 3.
  5. Tanzi and Zeneca had the same score in Round 1 but different scores in Round 3.

Q1. What was the highest total score?

  • 23
  • 24
  • 25
  • 21

Q2. What was Zeneca's total score?

  • 21
  • 22
  • 23
  • 24

Q3. Which of the following statements is true?

  • Zeneca’s score was 23.
  • Zeneca was the highest scorer
  • Xyla was the highest scorer.
  • Xyla’s score was 23

Q4. What was Tanzi's score in Round 3?

  • 1
  • 5
  • 3
  • 4

Set 7: Letter Coding

The table represents the addition of two six-digit numbers in the first and second rows, with the sum in the third row. Each digit 0-9 is coded with a distinct letter among A, B, C, D, E, F, G, H, J, K.

Q1. Which digit does the letter A represent? [TITA]

Q2. Which digit does the letter B represent? [TITA]

Q3. Which among the digits 3, 4, 6, and 7 cannot be represented by the letter D? [TITA]

Q4. Which among the digits 4, 6, 7, and 8 cannot be represented by the letter G? [TITA]

Set 8: Dance Competition

Princess, Queen, Rani, and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan, and Dyu were the four music composers assigning items. Each dancer performed two items assigned by different composers. The first items by the four dancers were assigned by different composers. No dancer performed her second item before all first items were performed. Second performances followed the same sequence as first performances.

Additional facts:

  1. No composer assigned an item to both Princess and Queen.
  2. No composer assigned an item to both Rani and Samragni.
  3. The first performance was by Princess; this item was assigned by Badal.
  4. The last performance was by Rani; this item was assigned by Gagan.
  5. Items assigned by Ashman were performed consecutively. The spacing between items by other composers was equal.

Q1. Which of the following is true?

  • The third performance was composed by Ashman.
  • The second performance was composed by Dyu.
  • The second performance was composed by Gagan.
  • The third performance was composed by Dyu.

Q2. Which of the following is FALSE?

  • Queen did not perform in any item composed by Gagan.
  • Rani did not perform in any item composed by Badal.
  • Samragni did not perform in any item composed by Ashman.
  • Princess did not perform in any item composed by Dyu.

Q3. The sixth performance was composed by:

  • Gagan
  • Ashman
  • Badal
  • Dyu

Q4. Which pair of performances were composed by the same composer?

  • The third and the seventh
  • The first and the seventh
  • The first and the sixth
  • The second and the sixth