CAT 2018 Slot 2 — DILR Question 4
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:
- High Q is better than Best Ed;
- Best Ed is better than Cosmopolitan; and
- Education Aid is better than A-one.
How many colleges have overall scores between 31 and 40, both inclusive?
Answer & solution
0
- B
1
- C
2
- D
3
We have already figured out that three colleges have overall score of 45 or above. Therefore we need to check for only the remaining five colleges.
The college that earned 0 on R (Global) lost 50 × 0.4 = 20 points on R. Therefore it can score maximum 30 points. We need not calculate the overall score of that college further.
There are three colleges that scored 20 on R (Cosmopolitan, Dominance and High Q).
They lost 30 × 0.4 = 12 points on R.
However, Cosmopolitan and Dominance colleges lost 30 × 0.3 = 9 more points on I. Therefore those colleges cannot score more than 30 points.
We have already figured out that High Q and Best Ed had an overall scores of 27 and 26 respectively.
Therefore no college scored between 31 and 40 points.
Hence, option (a).