CAT 2023 Slot 3 DILR Set 1 Q1–Q5

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2023 Slot 3, with 5 questions (Quant-based Puzzles). Answers are CAT's official key.

The set

There are only three female students – Amala, Koli and Rini – and only three male students – Biman, Mathew and Shyamal – in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1.

The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project.

The following additional facts are known about the scores in the project and the test.

1. The minimum, maximum and the average of both project and test scores were identical – 40, 80 and 60, respectively.
2. The test scores of the students were all multiples of 10; four of them were distinct and the remaining two were equal to the average test scores.
3. Amala's score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score.
4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate.
5. Biman scored the second lowest in the test and the lowest in the aggregate.
6. Mathew scored more than Rini in the project, but less than her in the test.

Question 1

What was Rini's score in the project?

TITA: type in the answer. There are no options and no negative marking.

Answer: 60 Quant-based Puzzles TITA

Solution

  1. Project: three pair scores with min 40, max 80, average 60, so they are 40, 60, 80. Amala = 2 x Koli gives Amala 80, Koli 40, Rini 60; Mathew beats Rini, so Mathew pairs with Amala (80).
  2. So Rini's project score is 60.

Question 2

What was the weight of the test component?
  1. A
    0.75
  2. B
    0.50
  3. C
    0.60
  4. D
    0.40

Answer: (C) 0.60 Quant-based Puzzles MCQ

Solution

  1. Project: three pair scores with min 40, max 80, average 60, so they are 40, 60, 80. Amala = 2 x Koli gives Amala 80, Koli 40, Rini 60; Mathew beats Rini, so Mathew pairs with Amala (80).
  2. Test: sum 360, two scores are 60, the other four are distinct multiples of 10 including 40 and 80, so the scores are 40, 50, 60, 60, 70, 80. Shyamal (2nd highest) = 70, Biman (2nd lowest) = 50.
  3. Amala, Koli, Rini, Mathew share 40, 60, 60, 80 with Koli = Amala + 20 and Mathew < Rini: either (A 40, K 60, R 80, M 60) or (A 60, K 80, R 60, M 40).
  4. Amala - Koli aggregate = 4. With test weight w: case 1 gives \(40-60w=4\), w = 0.6, but then Shyamal (54) needs project 30, impossible. Case 2 gives w = 0.6, Amala 68, Koli 64, Shyamal 66, so Shyamal's project is 60 (paired with Rini) and Biman pairs with Koli (40).
  5. Check: Biman \(0.6(50)+0.4(40)=46\) is lowest, Mathew 56, Rini 60, Amala 68 highest. Final: tests A 60, K 80, R 60, M 40, S 70, B 50; teams Amala-Mathew 80, Rini-Shyamal 60, Koli-Biman 40.
  6. The test weight is 0.60.

Question 3

What was the maximum aggregate score obtained by the students?
  1. A
    66
  2. B
    68
  3. C
    80
  4. D
    62

Answer: (B) 68 Quant-based Puzzles MCQ

Solution

  1. Project: three pair scores with min 40, max 80, average 60, so they are 40, 60, 80. Amala = 2 x Koli gives Amala 80, Koli 40, Rini 60; Mathew beats Rini, so Mathew pairs with Amala (80).
  2. Test: sum 360, two scores are 60, the other four are distinct multiples of 10 including 40 and 80, so the scores are 40, 50, 60, 60, 70, 80. Shyamal (2nd highest) = 70, Biman (2nd lowest) = 50.
  3. Amala, Koli, Rini, Mathew share 40, 60, 60, 80 with Koli = Amala + 20 and Mathew < Rini: either (A 40, K 60, R 80, M 60) or (A 60, K 80, R 60, M 40).
  4. Amala - Koli aggregate = 4. With test weight w: case 1 gives \(40-60w=4\), w = 0.6, but then Shyamal (54) needs project 30, impossible. Case 2 gives w = 0.6, Amala 68, Koli 64, Shyamal 66, so Shyamal's project is 60 (paired with Rini) and Biman pairs with Koli (40).
  5. Check: Biman \(0.6(50)+0.4(40)=46\) is lowest, Mathew 56, Rini 60, Amala 68 highest. Final: tests A 60, K 80, R 60, M 40, S 70, B 50; teams Amala-Mathew 80, Rini-Shyamal 60, Koli-Biman 40.
  6. The maximum aggregate is Amala's: \(0.6(60)+0.4(80)=68\).

Question 4

What was Mathew's score in the test?

TITA: type in the answer. There are no options and no negative marking.

Answer: 40 Quant-based Puzzles TITA

Solution

  1. Project: three pair scores with min 40, max 80, average 60, so they are 40, 60, 80. Amala = 2 x Koli gives Amala 80, Koli 40, Rini 60; Mathew beats Rini, so Mathew pairs with Amala (80).
  2. Test: sum 360, two scores are 60, the other four are distinct multiples of 10 including 40 and 80, so the scores are 40, 50, 60, 60, 70, 80. Shyamal (2nd highest) = 70, Biman (2nd lowest) = 50.
  3. Amala, Koli, Rini, Mathew share 40, 60, 60, 80 with Koli = Amala + 20 and Mathew < Rini: either (A 40, K 60, R 80, M 60) or (A 60, K 80, R 60, M 40).
  4. Amala - Koli aggregate = 4. With test weight w: case 1 gives \(40-60w=4\), w = 0.6, but then Shyamal (54) needs project 30, impossible. Case 2 gives w = 0.6, Amala 68, Koli 64, Shyamal 66, so Shyamal's project is 60 (paired with Rini) and Biman pairs with Koli (40).
  5. Check: Biman \(0.6(50)+0.4(40)=46\) is lowest, Mathew 56, Rini 60, Amala 68 highest. Final: tests A 60, K 80, R 60, M 40, S 70, B 50; teams Amala-Mathew 80, Rini-Shyamal 60, Koli-Biman 40.
  6. Mathew's test score is 40.

Question 5

Which of the following pairs of students were part of the same project team?
i) Amala and Biman
ii) Koli and Mathew
  1. A
    Neither i) nor ii)
  2. B
    Both i) and ii)
  3. C
    Only i)
  4. D
    Only ii)

Answer: (A) Neither i) nor ii) Quant-based Puzzles MCQ

Solution

  1. Project: three pair scores with min 40, max 80, average 60, so they are 40, 60, 80. Amala = 2 x Koli gives Amala 80, Koli 40, Rini 60; Mathew beats Rini, so Mathew pairs with Amala (80).
  2. Test: sum 360, two scores are 60, the other four are distinct multiples of 10 including 40 and 80, so the scores are 40, 50, 60, 60, 70, 80. Shyamal (2nd highest) = 70, Biman (2nd lowest) = 50.
  3. Amala, Koli, Rini, Mathew share 40, 60, 60, 80 with Koli = Amala + 20 and Mathew < Rini: either (A 40, K 60, R 80, M 60) or (A 60, K 80, R 60, M 40).
  4. Amala - Koli aggregate = 4. With test weight w: case 1 gives \(40-60w=4\), w = 0.6, but then Shyamal (54) needs project 30, impossible. Case 2 gives w = 0.6, Amala 68, Koli 64, Shyamal 66, so Shyamal's project is 60 (paired with Rini) and Biman pairs with Koli (40).
  5. Check: Biman \(0.6(50)+0.4(40)=46\) is lowest, Mathew 56, Rini 60, Amala 68 highest. Final: tests A 60, K 80, R 60, M 40, S 70, B 50; teams Amala-Mathew 80, Rini-Shyamal 60, Koli-Biman 40.
  6. Amala is with Mathew and Koli is with Biman, so neither pair is a team.

Same concept in other years

See every question on Reconstruct individual values from mean, median, mode, range or min/max.

More Quant-based Puzzles questions from CAT

All 127 Quant-based Puzzles questions asked since 2017.