ThinkCAT Logo
ThinkCAT
Sign up
QuestionsMocksResourcesAnalytics
CAT 2024 Slot 1 DILR · Set 5 of 5Logical ReasoningHard DifficultyQ18–Q22 · 5 MCQ

CAT 2024 Slot 1 DILR Set 5: Optimization (5 Questions) with Solutions

The Optimization set from the official CAT 2024 Slot 1 DILR paper: the caselet, all 5 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2024 Slot 1 DILR · Questions 18–22
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 11 if it is a staid campaign and a level of 22 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 2020 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)%20 \times(2+2) \%, that is, 80%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 1/31 / 3 of the votes cast, and Ramya will receive the other 2/32 / 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%10 \% of the students who would have otherwise voted for Amiya will vote for Ramya, and another 10%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%20 \% of the students who would have otherwise voted for Ramya will vote for Amiya, and another 5%5 \% who would have otherwise voted for Ramya, will not vote at all.
If both run campaigns attacking each other, then 10%10 \% of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q18. Optimization

MCQ · +3 / −1
If both of them run staid campaigns attacking the other, then what percentage of students will vote in the election?
  1. A) 60%60\%
  2. B) 64%64\%
  3. C) 40%40\%
  4. D) 36%36\%
Correct Answer
D) 36%36\%
Step-by-step solution
Clue Breakdown:
Both candidates run staid (level 1) campaigns attacking each other.
When both attack, 10% of the voters who would have voted in issue-focused campaigns don't vote.
Step-by-Step Deduction Grid:
1
Issue-Focused Campaigns:
Amiya: Level 1
Ramya: Level 1
Total voters: 20*(1+1) = 40%
2
Both Attack Campaigns:
10% of 40% voters don't vote.
Non-voters: 10% of 40% = 4%
Voters: 40% - 4% = 36%
Question Resolution: Under both attacking staid campaigns, 36% vote.
Final Answer Confirmation: Correct Answer: D
Answer: \boxed{D}

Q19. Optimization

MCQ · +3 / −1
What is the minimum percentage of students who will vote in the election?
  1. A) 32%32\%
  2. B) 40%40\%
  3. C) 36%36\%
  4. D) 38%38\%
Correct Answer
C) 36%36\%
Step-by-step solution
📌 Core Concept
Turnout is lowest when the voting base is small and attacks remove voters. Check each campaign combination and take the smallest turnout.
🔢 Step-by-Step Solution
1
Both on issues: turnout is 20×(sum of levels)20\times(\text{sum of levels}), so the smallest is 20×2=40%20\times 2 = 40\% (both staid).
2
Only Amiya attacks: 10%10\% of her base votes are lost to non-voting. With both staid, her base is 20%20\%, so turnout is 40−2=38%40 - 2 = 38\%. With other level pairs it stays higher: 56%56\% for (2,1), 58%58\% for (1,2) and 72%72\% for (2,2).
3
Only Ramya attacks: 5%5\% of her base votes are lost. With both staid, her base is 20%20\%, so turnout is 40−1=39%40 - 1 = 39\%. The other level pairs give 58%58\% or more.
4
Both attack: 10%10\% of all would-be voters stay home, so turnout is 0.9×0.9\times the issue-based turnout. The lowest is with both staid: 0.9×40=36%0.9\times 40 = 36\%. The other level pairs give 54%54\% or more.
5
Comparing 40,38,39,3640, 38, 39, 36, the minimum is 36%36\%.
Quick Check
Both staid and both attacking: 40%40\% base, 10%10\% of it lost, leaving 36%36\%. No other case gets lower.
Correct Answer: C

Q20. Optimization

MCQ · +3 / −1
If Amiya runs a campaign focusing on issues, then what is the maximum percentage of votes that she can get?
  1. A) 40%
  2. B) 36%
  3. C) 48%
  4. D) 44%
Correct Answer
C) 48%
Step-by-step solution
📌 Core Concept
Amiya's issue-based campaign is fixed, so her best case is the Ramya strategy that hands her the most votes. Ramya's attack campaign transfers 20% of Ramya's votes to Amiya, and a vigorous (level 2) Amiya campaign adds the most votes of her own.
🔢 Step-by-Step Solution
1
With both on issues, the turnout is 20 times the sum of the levels. Amiya's votes, as a percentage of all students, are 20a20a, where aa is her level. A vigorous campaign (a=2a=2) gives her 40%, and a staid one gives only 20%.
2
If Ramya also focuses on issues, Amiya stays at 40%. If Ramya attacks, 20% of Ramya's votes move to Amiya, so Amiya gains from Ramya's attack. Compare Ramya's two levels with a=2a=2.
3
Ramya attacking at level 2: turnout is 80%, split 40% each. Of Ramya's 40%, 20% (8 points) go to Amiya and 5% (2 points) stay home. Amiya gets 40+8=4840+8=48%, Ramya gets 30%.
4
Ramya attacking at level 1: Amiya has 40% and Ramya has 20%. The shift is 4 points, so Amiya gets 44%, which is less than 48%.
5
Amiya at level 1 gives her far fewer votes (at most 20+8=2820+8=28%), so it cannot beat 48%.
6
The maximum is 48%.
Why Not the Others
40%: this is Amiya's total when Ramya does not attack, and it ignores the 8 points she gains from Ramya's attack.
36%: it is below her own base vote of 40%, so it cannot be a maximum.
44%: this is the case where Ramya attacks at level 1, and a level 2 attack by Ramya gives Amiya more.
Correct Answer: C

Q21. Optimization

MCQ · +3 / −1
If Ramya runs a campaign attacking Amiya, then what is the minimum percentage of votes that she is guaranteed to get?
  1. A) 30%
  2. B) 15%
  3. C) 12%
  4. D) 18%
Correct Answer
B) 15%
Step-by-step solution
📌 Core Concept
Ramya's guaranteed minimum is her worst case over all of Amiya's possible responses. Ramya's attack costs her votes in every case, so compare the losses.
🔢 Step-by-Step Solution
1
Ramya's base share depends only on the levels: level 1 gives 20%20\% and level 2 gives 40%40\%. This is the same whichever level Amiya picks.
2
If Amiya runs issues, 20%20\% of Ramya's base votes go to Amiya and another 5%5\% do not vote. Ramya keeps 75%75\% of her base.
3
If Amiya also attacks, both lose 10%10\% of their issue-based votes. Ramya keeps 90%90\% of her base.
4
Ramya's attack is worst for her when Amiya runs issues, since she keeps only 75%75\%. Her lowest base is 20%20\%, from a staid campaign.
5
The minimum is 0.75×20=15%0.75\times 20 = 15\%.
6
The other case gives 0.9×20=18%0.9\times 20 = 18\%, which is higher.
Quick Check
Staid attack, Amiya on issues: 20%→15%20\% \to 15\%. No other combination leaves Ramya with less.
Correct Answer: B

Q22. Optimization

MCQ · +3 / −1
What is the maximum possible voting margin with which one of the candidates can win?
  1. A) 20%
  2. B) 29%
  3. C) 26%
  4. D) 28%
Correct Answer
B) 29%
Step-by-step solution
📌 Core Concept
Compare the margin in each of the four combinations of campaign types, using each candidate's base votes (as a percentage of all students) of 20a20a for Amiya and 20r20r for Ramya. Then pick the largest.
🔢 Step-by-Step Solution
1
Both on issues: the margin is 20∣a−r∣20|a-r|, so the most is 20 (levels 2 and 1).
2
Both attack: each candidate's votes fall by 10%, so the margin is 0.9×20∣a−r∣0.9\times 20|a-r|, at most 18.
3
Amiya attacks, Ramya on issues: Amiya keeps 0.8×20a0.8\times 20a and Ramya gets her own votes plus 0.1×20a0.1\times 20a. Ramya's margin is 20r−0.7×20a20r-0.7\times 20a. This is largest for r=2r=2, a=1a=1: 40−14=2640-14=26.
4
Ramya attacks, Amiya on issues: Amiya gets her own votes plus 20% of Ramya's, and Ramya keeps 75% of her own (20% move to Amiya, 5% stay home). Amiya's margin is 20a+0.2×20r−0.75×20r=20a−0.55×20r20a+0.2\times 20r-0.75\times 20r=20a-0.55\times 20r. This is largest for a=2a=2, r=1r=1: 40−11=2940-11=29.
5
The greatest of 20, 18, 26 and 29 is 29%, with Amiya winning when she is vigorous on issues and Ramya runs a staid attack.
Quick Check
With a=2a=2, r=1r=1: Amiya gets 40+4=4440+4=44%, and Ramya gets 20−4−1=1520-4-1=15%. The margin is 44−15=2944-15=29%.
Correct Answer: B
Timed Practice

Attempt the full CAT 2024 Slot 1 paper as a free mock

All three sections, 120 minutes, in the TCS iON-style simulator. Free, no sign-up.

Start Free Mock

CAT 2024 Slot 1 DILR at a Glance

Sets in this section5
Questions in this section22
Section time40 minutes
Convenor IIMIIM Calcutta

More CAT DILR Sets with Solutions