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.
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
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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