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CAT 2018 Slot 2 DILR · Set 5 of 8Data InterpretationModerate DifficultyQ17–Q20 · 2 MCQ + 2 TITA

CAT 2018 Slot 2 DILR Set 5: Tables (4 Questions) with Solutions

The Tables set from the official CAT 2018 Slot 2 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2018 Slot 2 DILR · Questions 17–20
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 ≥ 45AAA
35 ≤ Overall score < 45BAA
25 ≤ Overall score < 35BBA
15 ≤ Overall score < 25BBB
Overall score < 15Junk
Eight colleges apply for accreditation, and receive the following grades in the four parameters (F, R, P, and I):
FRPI
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; and
3
Education Aid is better than A-one.

In the exam this set competed with 7 others for 60 minutes. Budget about 8 minutes if you attempt it.

Q17. Tables

MCQ · +3 / −1
What is the weight of the faculty quality parameter?
  1. A) 0.3
  2. B) 0.1
  3. C) 0.2
  4. D) 0.4
Correct Answer
B) 0.1
Step-by-step solution
📌 Core Concept
Each ranking clue compares two colleges whose grades differ in only a few parameters. The shared parameters cancel, which leaves inequalities between the weights. Let wF,wR,wP,wIw_F, w_R, w_P, w_I be the weights, and use points in tens: A = 5, B = 4, C = 3, D = 2.
🔢 Step-by-Step Solution
1
Clue 3 compares Education Aid (A, A, B, A) with A-one (A, A, A, B). F and R cancel, so the difference is −wP+wI>0-w_P + w_I > 0. Hence wI>wPw_I > w_P.
2
Clue 2 compares Best Ed (B, C, D, D) with Cosmopolitan (B, D, D, C). F and P cancel, so the difference is wR−wI>0w_R - w_I > 0. Hence wR>wIw_R > w_I.
3
Steps 1 and 2 give wR>wI>wPw_R > w_I > w_P. So wIw_I cannot be 0.4, because wRw_R would have to be larger.
4
Clue 1 compares High Q (C, D, D, B) with Best Ed (B, C, D, D). The difference is −wF−wR+2wI>0-w_F - w_R + 2w_I > 0, so 2wI>wF+wR2w_I > w_F + w_R.
5
Try wI=0.2w_I = 0.2. Then wP=0.1w_P = 0.1, and wR,wFw_R, w_F are 0.3 and 0.4 in some order. This needs 0.4>0.70.4 > 0.7, which is false.
6
Try wI=0.3w_I = 0.3. Then wR=0.4w_R = 0.4, and wP,wFw_P, w_F are 0.1 and 0.2 in some order. Clue 1 needs 0.6>wF+0.40.6 > w_F + 0.4, so wF<0.2w_F < 0.2. Hence wF=0.1w_F = 0.1 and wP=0.2w_P = 0.2.
7
The only valid assignment is wF=0.1w_F = 0.1, wR=0.4w_R = 0.4, wP=0.2w_P = 0.2, wI=0.3w_I = 0.3.
Why Not the Others
0.2: wF=0.2w_F = 0.2 forces wP=0.1w_P = 0.1, and then clue 1 fails.
0.3: wF=0.3w_F = 0.3 fails the same way, since wF+wRw_F + w_R would be too large.
0.4: wR>wIw_R > w_I requires wR=0.4w_R = 0.4, so wFw_F cannot be 0.4.
Quick Check
With wI=0.3w_I = 0.3 and wF+wR=0.5w_F + w_R = 0.5, clue 1 gives 0.6>0.50.6 > 0.5, which holds.
Correct Answer: B

Q18. Arrangements

TITA · +3 / 0
How many colleges receive the accreditation of AAA?
Correct Answer
3
Step-by-step solution
📌 Core Concept
First fix the weights from the three ordering clues, then compute every college's overall score and count those scoring at least 45.
🔢 Step-by-Step Solution
1
The clues give r>ir > i (Best Ed > Cosmopolitan), i>pi > p (Education Aid > A-one) and 2i>f+r2i > f+r (High Q > Best Ed). The only consistent assignment is f=0.1f=0.1, r=0.4r=0.4, i=0.3i=0.3, p=0.2p=0.2.
2
Score = 0.1F+0.4R+0.2P+0.3I0.1F+0.4R+0.2P+0.3I, using A = 50, B = 40, C = 30, D = 20, F = 0.
3
A-one: 5+20+10+12=475+20+10+12 = 47.
4
Education Aid: 5+20+8+15=485+20+8+15 = 48.
5
Fancy: 5+20+8+12=455+20+8+12 = 45.
6
The others are Best Ed 26, Cosmopolitan 25, Dominance 27, Global 13 and High Q 27. All are below 45.
7
AAA needs a score of at least 45. A-one, Education Aid and Fancy qualify.
Correct Answer: 3

Q19. Tables

TITA · +3 / 0
What is the highest overall score among the eight colleges?
Correct Answer
48
Step-by-step solution
📌 Core Concept
The ordering clues fix the weights uniquely. Computing each college's weighted score then shows the maximum.
🔢 Step-by-Step Solution
1
The clues give r>ir > i, i>pi > p and 2i>f+r2i > f+r. Only f=0.1f=0.1, r=0.4r=0.4, i=0.3i=0.3, p=0.2p=0.2 satisfies all three.
2
Score = 0.1F+0.4R+0.2P+0.3I0.1F+0.4R+0.2P+0.3I.
3
A-one: 5+20+10+12=475+20+10+12 = 47.
4
Education Aid (A, A, B, A): 5+20+8+15=485+20+8+15 = 48.
5
Fancy: 5+20+8+12=455+20+8+12 = 45.
6
Every other college scores 27 or less. Dominance and High Q score 27, Best Ed 26, Cosmopolitan 25 and Global 13.
7
The highest score is Education Aid's 48.
Correct Answer: 48

Q20. Tables

MCQ · +3 / −1
How many colleges have overall scores between 31 and 40, both inclusive?
  1. A) 1
  2. B) 2
  3. C) 3
  4. D) 0
Correct Answer
D) 0
Step-by-step solution
📌 Core Concept
Fix the weights from the ordering clues, compute all eight overall scores, and count those in the range 31 to 40.
🔢 Step-by-Step Solution
1
The clues give r>ir > i, i>pi > p and 2i>f+r2i > f+r. Only f=0.1f=0.1, r=0.4r=0.4, i=0.3i=0.3, p=0.2p=0.2 works.
2
The overall scores are:
A-one 47
Best Ed 26
Cosmopolitan 25
Dominance 27
Education Aid 48
Fancy 45
Global 13
High Q 27
3
The scores are either 27 or below, or 45 or above. None lies between 31 and 40.
4
The count is 0.
Why Not the Others
A, B and C would require one, two or three colleges to score from 31 to 40. The score list has none in that range.
Correct Answer: D
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CAT 2018 Slot 2 DILR at a Glance

Sets in this section8
Questions in this section32
Section time60 minutes
Convenor IIMIIM Calcutta

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