CAT 2018 Slot 2 — DILR Question 3
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.
What is the highest overall score among the eight colleges?
Answer & solution
Answer: 48
The weight assigned to parameter R is highest and is at 0.4.
A college that receives 50 points on all the four parameters scores 50 out of 50.
A college that receives 40 on parameter R loses 4 points on R and can score maximum 46.
Further, a college that receives 30 or below on parameter R cannot score 45.
Therefore we need to consider only three colleges, namely A-one, Education Aid and Fancy.
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A-one lost 10 × 0.3 = 3 points on I.
Education Aid lost 10 × 0.2 = 2points on P.
Fancy lost 10 × 0.2 + 10 × 0.3 = 5points on P and I.
it can be seen that the highest overall score among the eight colleges is 50 - 2 = 48. Therefore the required answer is 48.
Answer: 48