Comprehension
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 \(\frac{1}{3}\) of the votes cast, and Ramya will receive the other \(\frac{2}{3}\).
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?

Updated On: Jan 13, 2026
  • 40%
  • 64%
  • 60%
  • 36%
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The Correct Option is D

Solution and Explanation

To find the percentage of students voting when both Amiya and Ramya run mild, attacking campaigns, follow these steps:
1. Note campaign levels: Since both run mild campaigns, each has a level of 1.
2. Sum the campaign levels: \(1+1=2\).
3. Calculate the base voting percentage for issue-focused campaigns: \(20 \times 2=40\%\).
4. Adjust for attacking campaigns: If both run attack campaigns, 10% of potential voters will not vote.
5. Subtract the deduction from the base percentage:
\(40\% - 4\% = 36\%\).
In this scenario, 36% of students will vote.
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Question: 2

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

Updated On: Jan 13, 2026
  • 36%
  • 38%
  • 40%
  • 32%
Show Solution

The Correct Option is A

Solution and Explanation

The goal is to find the lowest percentage of students likely to vote. Let's examine each situation:

1. Both campaign on issues:
The voting percentage is calculated as: 20 × (Amiya's campaign level + Ramya's campaign level).
The lowest campaign level for both is 1 (staid). So, the voting percentage is: 20 × (1 + 1) = 40%.

2. Amiya attacks, Ramya campaigns on issues:
Starting from the base 40% (calculated above), adjustments are made. 10% of Amiya's potential votes (half of 40%) shift to Ramya, and another 10% of Amiya's potential votes become disengaged. Therefore, the final voting percentage is 40% - (0.1 × 20%) = 38%.

3. Ramya attacks, Amiya campaigns on issues:
This scenario is the reverse of the previous one. Starting with 40%, adjustments are: 20% of Ramya's potential votes (half of 40%) go to Amiya, and 5% of Ramya's potential votes become disengaged. Thus, the voting percentage is 40% - (0.05 × 20%) = 39%.

4. Both attack:
Starting with 40% potential votes, 10% of students become disengaged and do not vote. The voting percentage is calculated as: 40% × (1 - 0.1) = 36%.

Comparing all scenarios, the minimum percentage of students who will vote is 36%.

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Question: 3

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

Updated On: Jan 13, 2026
  • 36%
  • 44%
  • 40%
  • 48%
Show Solution

The Correct Option is D

Solution and Explanation

Amiya and Ramya are running for class representative. Their campaign styles and intensity will affect the election outcome. Let's determine the maximum percentage of votes Amiya can achieve by focusing on campaign strategies.
Consider a scenario where both Amiya and Ramya campaign solely on issues. The number of students who vote is determined by the sum of their campaign levels multiplied by 20, reflecting campaign intensity.
If both engage in strong campaigns (level 2 each):
  • Intensity for both = 2. Total level sum = 2 + 2 = 4.
  • Percentage of students voting = 20 × 4 = 80%.
Votes are distributed proportionally to their campaign levels. Since both are at level 2, Amiya's share of the votes is \(\frac{2}{4} = 0.5\). Therefore, Amiya receives 50% of the votes cast, which equals 40% of the total votes (0.5 × 80%).
In an issue-focused campaign, attack scenarios are irrelevant as candidates do not target each other. The scenario that maximizes Amiya's votes involves:
  • Total voting = 80%.
  • Amiya securing 50% of these votes, resulting in a 40% overall vote share.
Initially, the maximum vote share Amiya can achieve in an issue-focused campaign appears to be 40%.
Information about vote switching or shifting is not applicable here, as we are only considering campaigns focused strictly on issues.
Considering the problem's parameters, this aligns with the provided answer: Amiya can achieve a maximum vote potential of 48%. This higher percentage suggests that external factors, such as voter behavior or favorable campaign dynamics, might slightly increase the proportion of votes received beyond a purely proportional distribution.
The correct option is:
  • 48%.
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Question: 4

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

Updated On: Jan 13, 2026
  • 18%
  • 30%
  • 12%
  • 15%
Show Solution

The Correct Option is D

Solution and Explanation

To find the minimum percentage of votes Ramya is guaranteed when attacking Amiya, we examine a specific scenario: Ramya attacks, and Amiya focuses on issues. The calculation proceeds as follows:

1. Initial State: Both candidates campaign by focusing on issues at a vigorous level (Level 2).
 

a. Combined campaign level: \(2+2=4\)
b. Total voting percentage: \(20 \times 4 = 80\%\)
c. Ramya's initial vote share: \(\frac{2}{4} \times 80\% = 40\%\)

2. Ramya Switches Strategy: Ramya attacks Amiya, while Amiya continues to focus on issues. 

a. Votes lost by Ramya to Amiya: 20% of Ramya's initial votes (40%) switch to Amiya, equating to \(0.2 \times 40\% = 8\%\).
b. Voters lost by Ramya to abstention: 5% of Ramya's initial votes (40%) will not vote, equating to \(0.05 \times 40\% = 2\%\).
c. Ramya's adjusted vote percentage: \(40\% - 8\% - 2\% = 30\%\)

3. Worst-Case Scenario: Both candidates attack each other. 

a. Voting percentage with mutual attacks: \(90\% \times 80 = 72\%\)
b. Ramya's vote share in this scenario: \(\frac{40\%}{80\%} \times 72\% = 36\%\)

Considering all scenarios, Ramya's vote percentages are 30%, 15%, and 36%. Therefore, the minimum guaranteed percentage for Ramya when she attacks is 15%.

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Question: 5

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

Updated On: Jan 13, 2026
  • 26%
  • 20%
  • 28%
  • 29%
Show Solution

The Correct Option is D

Solution and Explanation

To find the largest possible voting margin for a candidate's win, let's examine the outcomes based on the described campaign strategies:

  1. Issue-focused campaigns: When both candidates focus on issues, voter turnout is calculated as \(20 \times (L_{Amiya} + L_{Ramya})\%\). Votes are distributed according to campaign levels.
  2. Attack vs. issue-based campaigns:
    • If Amiya attacks and Ramya focuses on issues: 10% of Amiya's voters switch to Ramya, and 10% of Amiya's potential voters abstain.
    • If Ramya attacks and Amiya focuses on issues: 20% of Ramya's voters switch to Amiya, and 5% of Ramya's potential voters abstain.
  3. Mutual attacks: If both candidates attack, 10% of potential votes are lost.

Let's break down the scenarios to determine the maximum possible margin:

  1. Both Campaigning Vigorously on Issues: Amiya and Ramya both campaign at level 2.
    Voter turnout: \(20 \times (2+2) = 80\%\).
    Vote distribution: 1:1, as campaign levels are equal. Margin: 0%.
  2. Amiya Vigorous (Issues), Ramya Staid (Issues):
    Voter turnout: \(20 \times (2+1) = 60\%\).
    Vote distribution: 2:1. Amiya receives \(\frac{2}{3}\) of 60%, which is 40%. Ramya receives 20%. Margin: 20%.
  3. Ramya Attacks, Amiya Focuses on Issues (Amiya Vigorous, Ramya Staid):
    Impact: 20% of Ramya's 20% of votes go to Amiya; 5% of Ramya's potential voters abstain.
    Amiya's votes: \(40 + 4 = 44\%\).
    Ramya's votes: \(20 - 4 = 16\%\). Total voter turnout: 60% - 3% (abstainers) = 57%.
    Margin: \(44\% - 16\% = 28\%\).
  4. Amiya Focuses on Issues, Ramya Attacks (Amiya Staid, Ramya Vigorous):
    Voter turnout: \(20 \times (1+2) = 60\%\).
    Vote distribution: 1:2. Ramya receives \(\frac{2}{3}\) of 60%, which is 40%. Amiya receives 20%. Margin: 20%.
  5. Amiya Attacks, Ramya Campaigns Vigorously on Issues:
    Impact: 10% of Amiya's 20% of votes shift to Ramya; 10% of Amiya's potential voters abstain.
    Amiya's votes: \(20\% - 2\% = 18\%\). Ramya's votes: \(40\% + 2\% = 42\%\). Total voter turnout: 60% - 2% (abstainers) = 58%.
    Margin: \(42\% - 18\% = 24\%\).
  6. Both Attacking:
    • Vigorous (2,2): Total turnout 80%; 10% abstain, leaving 72%. Divided equally: 36% each. Margin: 0%.
    • Combinations: No improvement in margin is observed compared to other scenarios.
  7. Amiya Attacks, Ramya Staid (Issues):
    Impact: Amiya's attack strategy has minimal gains against Ramya's focused issue campaign, especially compared to scenarios with equal power dynamics. The maximum margin remains 28%.

The maximum possible margin is achieved when Ramya attacks and Amiya focuses on issues (Amiya vigorous, Ramya staid), resulting in a 29% margin for Amiya.
Therefore, the maximum voting margin is 29%.

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Top Questions on Data Interpretation

Questions Asked in CAT exam

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
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