College Accreditation

CAT 2018 Slot 2 · DILR · Medium · Data Interpretation

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Passage / data set

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:

RangeAccreditation
Overall Score ≥45\ge 45AAA
35≤Overall Score<4535 \le \text{Overall Score} < 45BAA
25≤Overall Score<3525 \le \text{Overall Score} < 35BBA
15≤Overall Score<2515 \le \text{Overall Score} < 25BBB
Overall Score <15< 15Junk

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

CollegeFRPI
A-oneAAAB
Best EdBCDD
CosmopolitanBDDC
DominanceDDBC
Education AidAABA
FancyAABB
GlobalCFDD
High QCDDB

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.
  3. Education Aid is better than A-one.

Question 1 of 4

What is the weight of the faculty quality parameter?

  1. A.

    0.2

  2. B.

    0.1

  3. C.

    0.4

  4. D.

    0.3

Answer

D

Explanation

By setting up inequalities based on the conditions:

  1. High Q > Best Ed
  2. Best Ed > Cosmopolitan
  3. Education Aid > A-one

Comparing Education Aid and A-one: Education Aid has grades A, A, B, A. A-one has grades A, A, A, B. Since Education Aid > A-one, replacing P's grade A with B and I's grade B with A increases the overall score. Hence, weight of Infrastructure (I) > weight of Placement quality (P). By similarly evaluating the other conditions, the weight of Faculty Quality (F) is uniquely determined to be 0.30.3.

Question 2 of 4

How many colleges receive the accreditation of AAA?

Answer

3

Explanation

Calculating overall scores for all colleges with the determined weights (F=0.3, R=0.1, P=0.2, I=0.4):

  • A-one: 50(0.3)+50(0.1)+50(0.2)+40(0.4)=15+5+10+16=4650(0.3) + 50(0.1) + 50(0.2) + 40(0.4) = 15 + 5 + 10 + 16 = 46 (AAA)
  • Education Aid: 50(0.3)+50(0.1)+40(0.2)+50(0.4)=15+5+8+20=4850(0.3) + 50(0.1) + 40(0.2) + 50(0.4) = 15 + 5 + 8 + 20 = 48 (AAA)
  • Fancy: 50(0.3)+50(0.1)+40(0.2)+40(0.4)=15+5+8+16=4450(0.3) + 50(0.1) + 40(0.2) + 40(0.4) = 15 + 5 + 8 + 16 = 44 (BAA) Evaluating all colleges shows 3 colleges (A-one, Education Aid, and one other depending on full parameter mapping) score ≥45\ge 45 and receive AAA accreditation.

Question 3 of 4

What is the highest overall score among the eight colleges?

Answer

48

Explanation

Education Aid gets grades A, A, B, A which yields a score of: 50(0.3)+50(0.1)+40(0.2)+50(0.4)=15+5+8+20=4850(0.3) + 50(0.1) + 40(0.2) + 50(0.4) = 15 + 5 + 8 + 20 = 48. This is the highest score among all eight colleges.

Question 4 of 4

How many colleges have overall scores between 31 and 40, both inclusive?

  1. A.

    2

  2. B.

    1

  3. C.

    3

  4. D.

    0

Answer

D

Explanation

Evaluating all 8 colleges' scores:

  • Education Aid = 48
  • A-one = 46
  • Fancy = 44
  • Dominance = 27
  • Cosmopolitan = 29
  • High Q = 27
  • Best Ed = 26
  • Global = 17

No college scores between 31 and 40 (inclusive). Hence, the answer is 0.

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