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7 Quant Based LR PYQ (Solutions)

Master Quant Based LR for CAT 2026 with practice questions and detailed explanations

CAT 2025

Quant-Based LR refers to logical reasoning sets that require mathematical calculations. These hybrid puzzles combine LR logic with quant skills, and they have become increasingly common in recent CAT papers.

Examples include puzzles involving equations, averages, revenues, or large number operations.
Notable appearances:

  • CAT 2019: Featured the “Addition of 6-digit numbers” set (moderate), a clearly quant-heavy LR puzzle.
  • CAT 2020:
    • Slot 1 had the “Average Marks” set (difficult).
    • Slot 2 had the “Elections” set (moderate–difficult), both requiring calculations along with reasoning.
  • CAT 2022: Marked an increase in quant-based LR sets.
  • CAT 2023–2024: These sets became quite prominent, often involving numerical constraints, schedules, or equation-formation within LR.

Overall Trend (2017–2024):
Almost every paper has at least one quant-heavy LR set. Typically, 1–2 sets per year (i.e., 4–8 questions) are classified as Quant-Based LR, especially after 2019.

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Weightage Over Past Years

YearQ.NODifficulty Level
20241Hard
20231Hard
20211Hard
20192Medium
20181Hard
20171Easy

CAT 2024 Quant Based LR questions

Question 1

Slot-1

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)%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% 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.

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

40%40 \%

64%

60%60 \%

36%36 \%

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

32%32 \%

40%40 \%

38%38 \%

36%36 \%

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

48%48 \%

44%44 \%

40%40 \%

36%36 \%

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

12%12 \%

15%15 \%

30%30 \%

18%18 \%

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

20%20 \%

29%

28%28 \%

26%

CAT 2023 Quant Based LR questions

Question 1

Slot-2

Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants' scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for Days 2 through 5.

Table 1: 2-day averages for Days 2 through 5

Day 2Day 3Day 4Day 5
1515.51617

Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2.

Table 2: Ranks of participants on each dayDay 1Day 2Day 3Day 4Day 5
Akhil12233
Bimal23211
Chatur31122

The following information is also known.

  1. Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil's score on Day 4.

  2. The total score on Day 3 is the same as the total score on Day 4.

  3. Bimal's scores are the same on Day 1 and Day 3.

What is Akhil's score on Day 1?

5

6

7

8

Who attains the maximum total score?

Chatur

Bimal

Cannot be determined

Akhil

What is the minimum possible total score of Bimal?

If the total score of Bimal is a multiple of 3, what is the score of Akhil on Day 2?

Cannot be determined

4

6

5

If Akhil attains a total score of 24, then what is the total score of Bimal?

CAT 2021 Quant Based LR questions

Question 1

Slot-3

Each of the bottles mentioned in this question contains 50 ml of liquid. The liquid in any bottle can be 100%100 \% pure content (P)(\mathrm{P}) or can have certain amount of impurity (I)(\mathrm{I}). Visually it is not possible to distinguish between P and I . There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is 10% or more.

For example, suppose bottle 1 contains only P , and bottle 2 contains 80%P80 \% \mathrm{P} and 20%I20 \% \mathrm{I}. If content from bottle 1 is tested, it will be found out that it contains only PP. If content of bottle 2 is tested, the test will reveal that it contains some amount of I . If 10 ml of content from bottle 1 is mixed with 20 ml content from bottle 2 , the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has I. However, if 10 ml of content from bottle 1 is mixed with 5 ml of content from bottle 2 . the test will not detect any impurity in the resultant mixture.

5 ml of content from bottle A is mixed with 5 ml of content from bottle B . The resultant mixture, when tested, detects the presence of II. If it is known that bottle AA contains only PP, what BEST can be concluded about the volume of I in bottle B?

1 ml

Less than 1 ml

10 ml

10 ml or more

There are four bottles. Each bottle is known to contain only PP or only I. They will be considered to be "collectively ready for dIspatch" if all of them contain only P . In minimum how many tests, is it possible to ascertain whether these four bottles are "collectively ready for dIspatch"?

There are four bottles. It is known that three of these bottles contain only PP, while the remaining one contains 80%P80 \% \mathrm{P} and 20%I20 \% \mathrm{I}. What is the minimum number of tests required to definitely identify the bottle containing some amount of II ?

There are four bottles. It is known that either one or two of these bottles contain(s) only PP, while the remaining ones contain 85%P85 \% \mathrm{P} and 15%I15 \% \mathrm{I}. What is the minimum number of tests required to ascertain the exact number of bottles containing only PP ?

4

2

3

1

CAT 2019 Quant Based LR questions

Question 1

Slot-1

The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits.

Which digit does the letter A represent?

Which digit does the letter B represent?

Which among the digits 3,4,6 and 7 cannot be represented by the letter D ?

Which among the digits 4, 6, 7 and 8 cannot be represented by the letter G?

Question 2

Slot-2

Three doctors, Dr. Ben, Dr. Kane and Dr. Wayne visit a particular clinic Monday to Saturday to see patients. Dr. Ben sees each patient for 10 minutes and charges Rs. 100/-. Dr. Kane sees each patient for 15 minutes and charges Rs. 200/-, while Dr. Wayne sees each patient for 25 minutes and charges Rs. 300/-. The clinic has three rooms numbered 1,2 and 3 which are assigned to the three doctors as per the following table.

The clinic is open from 9 a.m. to 11.30 a.m. every Monday to Saturday. On arrival each patient is handed a numbered token indicating their position in the queue, starting with token number 1 every day. As soon as any doctor becomes free, the next patient in the queue enters that emptied room for consultation. If at any time, more than one room is free then the waiting patient enters the room with the smallest number. For example, if the next two patients in the queue have token numbers 7 and 8 and if rooms numbered 1 and 3 are free, then patient with token number 7 enters room number 1 and patient with token number 8 enters room number 3.

What is the maximum number of patients that the clinic can cater to on any single day?

12

30

31

15

The queue is never empty on one particular Saturday. Which of the three doctors would earn the maximum amount in consultation charges on that day?

Dr. Wayne

Dr. Kane

Dr. Ben

Both Dr. Wayne and Dr. Kane

Mr. Singh visited the clinic on Monday, Wednesday, and Friday of a particular week, arriving at 8:508: 50 a.m. on each of the three days. His token number was 13 on all three days. On which day was he at the clinic for the maximum duration?

Same duration on all three days

Friday

Monday

Wednesday

On a slow Thursday, only two patients are waiting at 9 a.m. After that two patients keep arriving at exact 15minute intervals starting at 9:15 a.m. -- i.e. at 9:15 a.m., 9:30 a.m., 9:45 a.m. etc. Then the total duration in minutes when all three doctors are simultaneously free is

30

10

15

0

CAT 2018 Quant Based LR questions

Question 1

Slot-2

According to a coding scheme the sentence: "Peacock is designated as the national bird of India" is coded as 56889993511355566785645813666689 13347913366

This coding scheme has the following rules:

a: The scheme is case-insensitive (does not distinguish between upper case and lower case letters).

b : Each letter has a unique code which is a single digit from among 1,2,3,,91,2,3, \ldots, 9.

c: The digit 9 codes two letters, and every other digit codes three letters.

d : The code for a word is constructed by arranging the digits corresponding to its letters in a non-decreasing sequence.

Answer these questions on the basis of this information.

What best can be concluded about the code for the letter L?

1

8

1 or 8

6

What best can be concluded about the code for the letter B ?

3 or 4

1 or 3 or 4

1

3

For how many digits can the complete list of letters associated with that digit be identified?

1

2

0

3

Which set of letters CANNOT be coded with the same digit?

S,E,Z

I,B,M

S,U,V

X, Y, Z

CAT 2017 Quant Based LR questions

Question 1

Slot-1

In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built. The heights (in metres) of individual platforms are as shown below:

Individuals (all of same height) are seated on these platforms. We say an individual A can reach an individual B if all the three following conditions are met:

i.) A and B are In the same row or column

ii.) A is at a lower height than B

iii.) If there is/are any individual(s) between A and B, such individual(s) must be at a height lower than that of A.

Thus in the table given above, consider the Individual seated at height 8 on 3rd row and 2nd column. He can be reached by four individuals. He can be reached by the individual on his left at height 7, by the two individuals on his right at heights of 4 and 6 and by the individual above at height 5. Rows in the layout are numbered from top to bottom and columns are numbered from left to right.

How many individuals in this layout can be reached by just one individual?

3

5

7

8

Which of the following is true for any individual at a platform of height 1m in this layout?

They can be reached by all the individuals in their own row and column.

They can be reached by at least 4 individuals.

They can be reached by at least one individual.

They cannot be reached by anyone.

We can find two individuals who cannot be reached by anyone in

the last row

the fourth row

the fourth column

the middle column

Which of the following statements is true about this layout?

Each row has an individual who can be reached by 5 or more individuals

Each row has an individual who cannot be reached by anyone

Each row has at least two individuals who can be reached by an equal number of individuals

All individuals at the height of 9 m can be reached by at least 5 individuals

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