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CAT 2024 Slot 1 DILR Question & Solution

Data InterpretationMedium

Data Set

Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Students will vote based on the intensity level of Amiya’s and Ramya’s campaigns and the type of campaigns they run. Each campaign is said to have a level of 1 if it is a staid campaign and a level of 2 if it is a vigorous campaign. Campaigns can be of two types, they can either focus on issues, or on attacking the other candidate.

If Amiya and Ramya both run campaigns focusing on issues, then
  • The percentage of students voting in the election will be 20 times the sum of the levels of campaigning of the two students. For example, if Amiya and Ramya both run vigorous campaigns, then 20 × (2+2)%, that is, 80% of the students will vote in the election.
  • Among voting students, the percentage of votes for each candidate will be proportional to the levels of their campaigns. For example, if Amiya runs a staid (i.e., level 1) campaign while Ramya runs a vigorous (i.e., level 2) campaign, then Amiya will receive 1/3 of the votes cast, and Ramya will receive the other 2/3. The above-mentioned percentages change as follows if at least one of them runs a campaign attacking their opponent.
  • If Amiya runs a campaign attacking Ramya and Ramya runs a campaign focusing on issues, then 10% of the students who would have otherwise voted for Amiya will vote for Ramya, and another 10% who would have otherwise voted for Amiya, will not vote at all.
  • If Ramya runs a campaign attacking Amiya and Amiya runs a campaign focusing on issues, then 20% of the students who would have otherwise voted for Ramya will vote for Amiya, and another 5% who would have otherwise voted for Ramya, will not vote at all.
  • If both run campaigns attacking each other, then 10% of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.

Question 1

If both of them run staid campaigns attacking the other, then what percentage of students will vote in the election?

40%
64%
60%
36%
Solution:

If both Ramya and Amiya run staid campaigns, the intensity of each staid campaign is 1
So total number of voters that would vote for them if they focused on issues will be 20x(1+1)%=40%

This means if they had both ran regarding issues, then they would get 20% of votes each. 
We are told that both of them run attacking campaigns, 
And the rule for mutual attacking campaign is 10% of voters who would have voted for each candidate will not vote. 
That means 10% of 20% of each candidate will not vote, now that it is a mutually attacking campaign. 
That means, each candidate receives 18% of the votes. 

Total votes received is 36%. 

Question 2

What is the minimum percentage of students who will vote in the election?

32%
40%
38%
36%
Solution:

We want the minimum vote share, that means both the candidates run staid campaigns. 
And, both the campaigns should be attacking, since we see that if one candidate runs an attacking campaign whereas the other candidate runs an issues campaign, a fair number of voters get transferred to the other candidate's vote share. 

This points to us to a scenario where both the campaigns are staid and attacking, which is nothing but the scenario described in the previous question. 

If both Ramya and Amiya run staid campaigns, the intensity of each staid campaign is 1
So total number of voters that would vote for them if they focused on issues will be 20x(1+1)%=40%

This means if they had both ran regarding issues, then they would get 20% of votes each.
We are told that both of them run attacking campaigns,
And the rule for mutual attacking campaign is 10% of voters who would have voted for each candidate will not vote.
That means 10% of 20% of each candidate will not vote, now that it is a mutually attacking campaign.
That means, each candidate receives 18% of the votes.

Total votes received is 36%, which is the minimum possible. 

Question 3

If Amiya runs a campaign focusing on issues, then what is the maximum percentage of votes that she can get?

48%
44%
40%
36%
Solution:

Amiya runs a campaign on issues, and we need to find the maximum vote share that she can get. 

We are trying to maximise the number of voters for Amiya, that means Amiya needs to run a vigorous campaign. 
Since, we are trying to increase the vote share for Amiya, we want as many voters as possible transferred from Ramya's share to Amiya's votes. 
As the number of votes a candidate receives is proportional to the intensity level of the campaign, we want Ramya also to run a vigorous AND attacking campaign, so that her votes are transferred to Amiya. 

In this scenario we have 20x(2+2)% of the people voting, 80% of the people. Of that, if both had ran issues campaign, they would have each received 40% of the votes. 

Now, we want Ramya to run an attacking campaign, where 20% of the people that would have voted for her vote for Amiya. 
So 20% of 40% of the votes are transferred to Amiya. That is 8% of the votes. And we are also told that, 5% that would have voted for her dont vote, so 5% of 40% dont vote, that is 2% of the voters. 

Final Tally is Amiya gets 48% of the votes, and Ramya gets 30% of the votes. 

Question 4

If Ramya runs a campaign attacking Amiya, then what is the minimum percentage of votes that she is guaranteed to get?

12%
15%
30%
18%
Solution:

We are looking for the minimum possible number of votes that Ramya can get when she runs an attacking campaign. 

To minimise the number of votes, we can have Ramya run a staid campaign to minimise the votes, so minimum intensity, which will get her 20% of the votes if she ran with issues. Now that she is running with attacking, she will loose 20% of the votes to Amiya and 5% of the votes will not vote anymore.

That is a total 25% loss. Remaining votes she will get is 75% of the 20% which will leave her with 15% of the votes. 

Question 5

What is the maximum possible voting margin with which one of the candidates can win?

20%
29%
28%
26%
Solution:

We are looking for the minimum possible number of votes that Ramya can get and maximise the number of votes that Amiya can get. 

We can borrow the scenario from the previous question where Ramya runs an attacking campaign, and we minimised the number of votes she can get. 

To minimise the number of votes, we can have Ramya run a staid campaign to minimise the votes, so minimum intensity, which will get her 20% of the votes if she ran with issues. Now that she is running with attacking, she will loose 20% of the votes to Amiya and 5% of the votes will not vote anymore.

That is a total 25% loss. Remaining votes she will get is 75% of the 20% which will leave her with 15% of the votes.

And to maximise the number of votes Amiya can get, we will have her run an vigorous issues campaign, which will give her 2x20% of the votes, that is 40% of the votes. And since Ramya has been running an attacking campaign, 20% of her votes are transferred to Amiya. 20% of the 20% of the votes which is 4% that were going to Ramya will now go to Amiya. That will bring up Amiya's tally up to 44% leaving Ramya's tally at 15%. 

The difference in the votes will be 44-15=29%. 

This is the maximum possible vote difference between the two candidates that is possible.