Question

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

• A. 40%
• B. 64%
• C. 60%
• D. 36%
• A. 36%
• B. 38%
• C. 40%
• D. 32%
• A. 36%
• B. 44%
• C. 40%
• D. 48%
• A. 18%
• B. 30%
• C. 12%
• D. 15%
• A. 26%
• B. 20%
• C. 28%
• D. 29%

Answer 1

The Correct Option is D

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.

Answer 2

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%.

Answer 3

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%.

Answer 4

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).Nbsp;
Nbsp;

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.Nbsp;

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.Nbsp;

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%.

Answer 5

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%.