CAT 2024 Set-1 | Data Interpretation and Logical Reasoning | Question: 18

Question

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 $20 \times(2+2) \%$, 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.

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

• A. $60 \%$
• B. $64 \%$
• C. $36 \%$
• D. $40 \%$