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In an election several candidates contested for a constituency - CAT DILR questions – Data Interpretation

Since 2015, the CAT DILR section has become increasingly difficult. In order to tackle the tougher CAT Level DILR questions for the CAT Exam, it is important to understand the basics of CAT. Data Interpretation sets and Logical reasoning puzzles were distinct in DILR. Data Interpretation and Logical Reasoning used to be about computation and understanding charts, graphs, and tables. Within that one hour, you get 5 high-quality puzzles, with some of them being quite challenging. You will solve 30 actual CAT puzzles in CAT 2019 and CAT 2020. The purpose of this page is to help you prepare for that. Take a crack at those puzzles!

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The question below is from previous year CAT question from CAT 2020 exam comes from CAT Data Interpretation: In an election several candidates contested for a constituency . Find out by answering this question which tests an aspirant’s DILR Ability Skills:

CAT 2020 - Slot 2 - Question 3 - In an election several candidates contested for a constituency

Set-4: 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.

Constituency

A

B

C

D

No. of candidates contesting

10

12

5

8

Total No. of valid votes polled

5,00,000

3,25,000

6,00,030

No. of votes polled by the winning candidate

2,75,000

48,750

No. of votes polled by the first runner up

95,000

37,500

No. of votes polled by the second runner up

30,000

% of valid votes polled by the third runner up

10%

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.

Q13. What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A? (TITA)

13. 9.

Let’s try to fill the table first. Partially applying points 1 and 3 we can get the votes for the 2nd runner up in A and the winning candidate in D.

To begin answering this question, we need to first see what is the% of total votes between the candidates we already know about: Winner + 1st + 2nd Runner Up total: 455,000 (91%)
So the vote share among the remaining 7 candidates was only 9%
To lose security deposit, one must get less than or equal to 1/6th i.e. lesser than 16.67% of the total votes. Clearly that is indeed the case with the remaining candidates in A.
 

Q14. How many candidates who contested in constituency B lost their security deposit?

14. 11.

The winning candidate in B had a 15% vote share. Meaning everyone else (the other 11) had a less than 16.67% vote share as well so they all will lose their security deposits.

 

Q15. What BEST can be concluded about the number of votes polled by the winning candidate in constituency C?

a. between 1,40,005 and 1,40,010

b. 1,40,006 

c. less than 2,00,010

d. 1,40,010

15. B.

It is mentioned that none in C lost their security deposit and the delta in votes was at least 10,000

 

The least possible vote share is slightly more than 1/6th, meaning the lowest possible value here is: 600,030 / 6 +1 = 100,005 + 1. If noone lost the security deposit, then the least possible value is 100,006

Assuming a 100,00 vote delta just for the time being we get the following as our possible values

Clearly given the constraints, there isn’t too much we can do to flex the numbers here.This is the only possible way to satisfy the constraints. So this must be the answer.

16. What was the number of valid votes polled in constituency D?

a. 1,75,000

b. 62,500

c. 1,25,000

d. 1,50,000

16. A.

This is how the table looks for D as of now:

Check using the options. Clearly it cannot be 62,500 (Option C) because the total of 2, 3 adds up to a number greater than that

 

A: 175,000

The table looks like the following:

In this option, clearly the top 3 each have more than 16.67% and the rest have 35%. This option satisfies the constraints and hence is the correct answer.

Q17. 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?

a. B, D, C, A 

b. D, B, C, A

c. D, C, B, A  

d. B, C, D, A

17. D.

A clearly has the highest margin

With B, margin could be as low as possible since everyone lost their deposit. Highest could be as follows: assume that the first 11 people got 1 – 11 votes only (since there are no ties, we are increasing the numbers by 1 for each position). So the winning margin can be as high as ~48,000

C it is 10,000 as calculated earlier

D is less than 10,000 for sure since it is 5% of the valid votes

 

So D cannot be more than C. The only option which has D more than C is the last one

Q18. 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?

a. 32.00%

b. 38.25%

c. 23.54%

d. 23.91%

18. D.

Just calc using available data

 

For A: Votes that count towards a deposit loss=> 500,000 – (275,000 – 95,000 – 85,000) = 45,000

For B: All except the winner lost, i.e. =>325,000 – 48,750 = 276,250

For C: Noone lost

For D: 35% of the total i.e. 35% of 175,000 => 61,250

 

Answer: (45,000 + 276,250 + 61,250) / (500,000 + 325,000 + 600,003 + 175,000)

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