Course Evaluation Scores and Team Assignments

CAT 2023 Slot 3 · DILR · Hard · Logical Reasoning

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Passage / data 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 of 5

What was Rini's score in the project?

Answer

60

Explanation

Project scores must be multiples such that Amala's project score is double Koli's. With min 40, max 80, and average 60, the project scores are 80, 60, 40. Thus, Amala's project score = 80 and Koli's project score = 40. The remaining project score for Rini must be 60.

Question 2 of 5

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

Explanation

Let ww be the weight of the test component. Then (1−w)(1-w) is the weight of the project component. Amala's Aggregate = 80(1−w)+wTA=80−80w+wTA80(1-w) + w T_A = 80 - 80w + w T_A. Koli's Aggregate = 40(1−w)+w(TA+20)=40−20w+wTA40(1-w) + w (T_A + 20) = 40 - 20w + w T_A. Shyamal's aggregate is 2 more than Koli's and 2 less than Amala's, so Amala's aggregate - Koli's aggregate = 4. (80−80w+wTA)−(40−20w+wTA)=40−60w=4  ⟹  60w=36  ⟹  w=0.60(80 - 80w + w T_A) - (40 - 20w + w T_A) = 40 - 60w = 4 \implies 60w = 36 \implies w = 0.60.

Question 3 of 5

What was the maximum aggregate score obtained by the students?

  1. A.

    66

  2. B.

    68

  3. C.

    80

  4. D.

    62

Answer

B

Explanation

Since test component weight is 0.60 and project weight is 0.40: Test scores set: {40, 50, 60, 60, 70, 80}. Since Koli scored 20 more than Amala in the test and Shyamal is 2nd highest (70), Koli's test score = 80 and Amala's test score = 60. Amala's aggregate score = 0.40(80)+0.60(60)=32+36=680.40(80) + 0.60(60) = 32 + 36 = 68. Amala had the highest aggregate score, which is 68.

Question 4 of 5

What was Mathew's score in the test?

Answer

40

Explanation

The test scores are {40, 50, 60, 60, 70, 80}. Koli = 80, Shyamal = 70, Amala = 60, Biman = 50 (second lowest). The remaining test scores are 40 and 60 for Mathew and Rini. Since Mathew scored less than Rini in the test, Mathew's test score = 40 and Rini's test score = 60.

Question 5 of 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

Explanation

Mathew's project score is greater than Rini's (60), so Mathew's project score = 80. Thus Mathew is paired with Amala. Shyamal's aggregate is 66, so 0.40(Shyamal’s project)+0.60(70)=66  ⟹  Shyamal’s project=600.40(\text{Shyamal's project}) + 0.60(70) = 66 \implies \text{Shyamal's project} = 60. Thus Shyamal is paired with Rini. Therefore, Biman is paired with Koli (project score = 40). Neither pair i) nor ii) is correct.

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