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CAT 2018 Slot 2 — DILR Question 1

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Passage / Data

Answer the following question based on the information given below.

An agency entrusted to accredit colleges looks at four parameters: faculty quality (F), reputation (R), placement quality (P), and infrastructure (I). The four parameters are used to arrive at an overall score, which the agency uses to give an accreditation to the colleges. In each parameter, there are five possible letter grades given, each carrying certain points: A
(50 points), B (40 points), C (30 points), D (20 points), and F (0 points). The overall score for a college is the weighted sum of the points scored in the four parameters. The weights of the parameters are 0.1, 0.2, 0.3 and 0.4 in some order, but the order is not disclosed. Accreditation is awarded based on the following scheme:

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Eight colleges apply for accreditation, and receive the following grades in the four parameters (F, R, P, and I):

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It is further known that in terms of overall scores:

  1. High Q is better than Best Ed;
  2. Best Ed is better than Cosmopolitan; and
  3. Education Aid is better than A-one.

What is the weight of the faculty quality parameter?

Answer & solution

  • 0.1

  • B

    0.2

  • C

    0.3

  • D

    0.4

Solution

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From point 2, Best Ed is better than Cosmopolitan. The grades of the two colleges on F and P are the same. If Best Ed is better than Cosmopolitan, the weightage assigned to R must be higher than that assigned for I.

From point 3, Education Aid is better than A-one. The grades of the two colleges on F and R are the same. If Education Aid is better than A-one, the weightage assigned to I must be higher than that assigned for P.

Therefore we have, R > I > P.

From point 1, High Q is better than Best Ed. High Q has worse grades than Best Ed on F and R and has same grade on P and a better grade only on I. We have already figured out that R > I > P. If a better grade only on I reverses the effect of worse grades on F and R, I must be assigned higher weightage than that assigned for F.

Therefore, we have the following two possibilities:

R > I > P > F or R > I > F > P.

That means R = 0.4, I = 0.3, P = 0.2 and F= 0.1 or R = 0.4, I = 0.3, F = 0.2 and P = 0.1 are the two possibilities.

Using the two possibilities, let us calculate the scores of High Q and Best Ed.

Possibility 1: R= 0.4, I = 0.3, P =0.2, F = 0.1

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Possibility 2: R= 0.4, I = 0.3, F =0.2, P = 0.1

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Since High Q is better than Best Ed, possibility 1 is valid and possibility 2 is ruled out.

Therefore, we have R = 0.4, I = 0.3, P = 0.2 and F = 0.1

Now all the questions can be answered.

Hence, option (a).

CAT 2018 Slot 2 DILR Q1: What is the weight of the faculty quality parameter? — Solution | TheCATExam