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CAT 2020 Slot 2 DILR · Set 3 of 5Data InterpretationModerate DifficultyQ11–Q16 · 4 MCQ + 2 TITA

CAT 2020 Slot 2 DILR Set 3: Tables (6 Questions) with Solutions

The Tables set from the official CAT 2020 Slot 2 DILR paper: the caselet, all 6 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 2020 Slot 2 DILR · Questions 11–16
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election.
In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits.
The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election.
ConstituencyABCD
No. of candidates contesting101258
Total No. of valid votes polled5,00,0003,25,0006,00,030
No. of votes polled by the winning candidate2,75,00048,750
No. of votes polled by the first runner up95,00037,500
No. of votes polled by the second runner up30,000
% of valid votes polled by the third runner up10%
The following additional facts are known:
1
The first runner up polled 10,000 more votes than the second runner up in constituency A.
2
None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.
3
The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q11. Tables

TITA · +3 / 0
What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A?
Correct Answer
9
Step-by-step solution
Clue Breakdown:
1
Security Deposit Loss Condition: Candidates lose their security deposit if they poll ≤1/6 of the total valid votes.
2
Constituency A Details:
Total valid votes: 5,00,000.
Winning candidate: 2,75,000 votes.
First runner-up: 95,000 votes.
Second runner-up: 85,000 votes (since first runner-up has 10,000 more).
3
Number of Candidates in A:
10
Thus, 7 candidates besides the top three.
Step-by-Step Deduction Grid:
ConstituencyTotal Valid VotesWinning Candidate VotesFirst Runner-Up VotesSecond Runner-Up VotesCandidates Losing DepositTotal Votes by Losing Candidates% of Total Votes
A5,00,0002,75,00095,00085,000745,0009%
Question Resolution:
In Constituency A, the total votes by losing candidates are 45,000. The percentage is (45,000 / 5,00,000) * 100 = 9%.
Final Answer Confirmation:
Correct Answer: 9

Q12. Tables

TITA · +3 / 0
How many candidates who contested in constituency B lost their security deposit?
Correct Answer
11
Step-by-step solution
📌 Core Concept
A defeated candidate loses the deposit if the votes polled are not more than 16\frac{1}{6} of the valid votes. Compare the best defeated candidate's possible vote count with that cut-off.
🔢 Step-by-Step Solution
1
Valid votes in B are 3,25,000, so the cut-off is 3250006≈54,167\frac{325000}{6} \approx 54{,}167 votes. A defeated candidate needs more than this to keep the deposit.
2
The winner polled 48,750 votes, which is already below 54,167.
3
Every other candidate polled fewer votes than the winner, because there are no ties and the winner has the highest count. So each of them has fewer than 48,750 votes, which is below the cut-off.
4
The winner never loses a deposit, since only defeated candidates do. The other 12−1=1112 - 1 = 11 candidates all fall below the cut-off and lose their deposits.
Quick Check
The winner has 48750325000=15%\frac{48750}{325000} = 15\%, which is less than 16.67%16.67\%. Nobody else can exceed this share.
Correct Answer: 11

Q13. Tables

MCQ · +3 / −1
What BEST can be concluded about the number of votes polled by the winning candidate in constituency C?
  1. A) less than 2,00,010
  2. B) 1,40,010
  3. C) between 1,40,005 and 1,40,010
  4. D) 1,40,006
Correct Answer
D) 1,40,006
Step-by-step solution
📌 Core Concept
In C nobody loses a deposit, so every defeated candidate has more than 16\frac{1}{6} of the votes. Together with the gap of at least 10,000 between any two candidates, this pins down the winner's votes.
🔢 Step-by-Step Solution
1
The cut-off is 6000306=100,005\frac{600030}{6} = 100{,}005. Fact 2 says all four defeated candidates keep their deposits, so each polled at least 1,00,006 votes.
2
Any two candidates differ by at least 10,000. The four defeated candidates therefore have at least 1,00,006, 1,10,006, 1,20,006 and 1,30,006 votes, in increasing order.
3
The winner is at least 10,000 above the first runner up, so the winner has at least 1,40,006 votes.
4
The defeated candidates together have at least 100006+110006+120006+130006=460,024100006 + 110006 + 120006 + 130006 = 460{,}024 votes. The winner therefore has at most 600030−460024=140,006600030 - 460024 = 140{,}006 votes.
5
The winner's votes are at least 1,40,006 and at most 1,40,006, so the winner polled exactly 1,40,006.
Why Not the Others
A: true but loose, since the exact value is known.
B: 1,40,010 is above the maximum of 1,40,006.
C: the exact value is 1,40,006, not a range up to 1,40,010.
Correct Answer: D

Q14. Tables

MCQ · +3 / −1
What was the number of valid votes polled in constituency D?
  1. A) 1,75,000
  2. B) 1,50,000
  3. C) 62,500
  4. D) 1,25,000
Correct Answer
A) 1,75,000
Step-by-step solution
📌 Core Concept
The candidates who lose deposits polled 35% in total. The remaining 65% belongs to the top three candidates. Setting up an equation in the total VV gives the answer.
🔢 Step-by-Step Solution
1
Let the valid votes in D be VV. The third runner up has 10%, which is below 16≈16.67%\frac{1}{6} \approx 16.67\%, so this candidate and everyone below lose their deposits.
2
Assume the winner, first runner up and second runner up keep their deposits. Then they polled 100%−35%=65%100\% - 35\% = 65\% of VV together.
3
By fact 3, the winner polled 37500+0.05V37500 + 0.05V. Adding the first runner up (37,500) and the second runner up (30,000): (37500+0.05V)+37500+30000=0.65V(37500 + 0.05V) + 37500 + 30000 = 0.65V.
4
This gives 105000=0.60V105000 = 0.60V, so V=1,75,000V = 1{,}75{,}000.
5
Check the assumption. The second runner up has 30000175000≈17.14%\frac{30000}{175000} \approx 17.14\%, which is more than 16.67%16.67\%, so that candidate does keep the deposit.
Quick Check
The winner has 46,250 votes. Then 46250+37500+30000=113,75046250 + 37500 + 30000 = 113{,}750, which is 65%65\% of 1,75,000. The remaining 61,250 is 35%35\%.
Correct Answer: A

Q15. Tables

MCQ · +3 / −1
The winning margin of a constituency is defined as the difference of votes polled by the winner and that of the first runner up. Which of the following CANNOT be the list of constituencies, in increasing order of winning margin?
  1. A) B, C, D, A
  2. B) D, B, C, A
  3. C) B, D, C, A
  4. D) D, C, B, A
Correct Answer
A) B, C, D, A
Step-by-step solution
📌 Core Concept
Find the winning margin of each constituency, or its possible range. Then test each listed order against those values.
🔢 Step-by-Step Solution
1
A: the margin is 275000−95000=1,80,000275000 - 95000 = 1{,}80{,}000.
2
C: the winner has exactly 1,40,006 votes, and the first runner up is at least 10,000 below the winner. The smallest allowed values for the defeated candidates (1,00,006 to 1,30,006) force the first runner up to be 1,30,006. The margin is exactly 10,000.
3
D: the winner has 37500+0.05×175000=46,25037500 + 0.05 \times 175000 = 46{,}250 votes. The margin is 46250−37500=8,75046250 - 37500 = 8{,}750.
4
B: the winner has 48,750 votes. The other 11 candidates share 2,76,250 votes, so the first runner up has at least about 25,114 votes. The margin is therefore positive but below about 23,640.
5
A has the largest margin in every case. D (8,750) is smaller than C (10,000).
6
Option A lists the order B, C, D, A, which needs C's margin to be less than D's. That is impossible because 10000>875010000 > 8750.
Why Not the Others
B: D, B, C, A works if B's margin lies between 8,750 and 10,000.
C: B, D, C, A works if B's margin is below 8,750.
D: D, C, B, A works if B's margin lies between 10,000 and 23,640.
Correct Answer: A

Q16. Tables

MCQ · +3 / −1
For all the four constituencies taken together, what was the approximate number of votes polled by all the candidates who lost their security deposit expressed as a percentage of the total valid votes from these four constituencies?
  1. A) 23.91%
  2. B) 23.54%
  3. C) 32.00%
  4. D) 38.25%
Correct Answer
A) 23.91%
Step-by-step solution
📌 Core Concept
Find the deposit-losers in each constituency, add their votes, and divide by the combined valid votes of the four constituencies.
🔢 Step-by-Step Solution
1
A: the cut-off is 5000006≈83,333\frac{500000}{6} \approx 83{,}333. The second runner up has 95000−10000=85,00095000 - 10000 = 85{,}000, which is above the cut-off. The winner, first runner up and second runner up total 275000+95000+85000=4,55,000275000 + 95000 + 85000 = 4{,}55{,}000. The other 7 candidates share 45,000 votes in total, so each is below the cut-off. They polled 45,000 votes.
2
B: all 11 defeated candidates lose their deposits (as in the first question). They polled 325000−48750=2,76,250325000 - 48750 = 2{,}76{,}250 votes.
3
C: no one loses a deposit, so the figure is 0.
4
D: the valid votes are 1,75,000. The deposit-losers polled 35%35\% of this, which is 61,250.
5
The deposit-losers' total is 45000+276250+0+61250=3,82,50045000 + 276250 + 0 + 61250 = 3{,}82{,}500.
6
The combined valid votes are 500000+325000+600030+175000=16,00,030500000 + 325000 + 600030 + 175000 = 16{,}00{,}030.
7
The percentage is 3825001600030×100≈23.91%\frac{382500}{1600030} \times 100 \approx 23.91\%.
Quick Check
About 3.825 lakh out of about 16 lakh is roughly 3.82516≈23.9%\frac{3.825}{16} \approx 23.9\%.
Correct Answer: A
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CAT 2020 Slot 2 DILR at a Glance

Sets in this section5
Questions in this section24
Section time40 minutes
Convenor IIMIIM Indore

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