12 Minute Test: Data Caselets | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

• Caselets in the CAT’s DILR section present a compact passage of interconnected data—combining numbers, conditions, and scenarios in one mini-case. They test your skill in multitasking: parsing text, organising facts, and drawing conclusions under time pressure.
• This 12-minute Caselet Test is tailored to mirror the CAT’s intense tempo, guiding you through practising rapid data extraction, logical sequencing, and targeted computation from these multi-statement setups.
• By mastering this focused, timed exercise, you’ll build the agility and accuracy needed to tackle caselet questions confidently on exam day. Let’s dive in and make caselets one of your strongest assets!

Set 1

Instructions

4 colleges A, B, C and D participated in 3 surveys BS, KIRF and GT. All the 4 colleges managed to secure a rank less than 7 in all the 3 surveys. Further, it is known that no 2 colleges were tied for the same position in any of the surveys.
Only A had a better rank than D in the survey conducted by KIRF.
B managed to get a better rank than C in 2 of the 3 surveys.
D was ranked second in the survey conducted by KIRF. It is the only survey in which D managed to bag a rank within the top 3.
GT deemed C to be a better college than A.
The average rank secured by D was 4.
D had a better rank in the survey conducted by BS than the one conducted by GT.
No college had the same rank in 2 surveys.
D was ranked the worst among the 4 colleges in 2 of the 3 surveys.
A managed a position within the top 3 in all 3 surveys.

Q1: If B was ranked third in the survey conducted by BS and the average ranks of B and C were not equal, then the rank of B in the survey conducted by KIRF is  
(a) 3 
(b) 4 
(c) 5 
(d) 6

Ans: b

Sol: No college had the same rank in 2 surveys.

A managed a position within the top 3 in all the surveys.

Only A had a better rank than D in all 3 surveys.

Average rank of D is 4.

=> Sum of the ranks secured by D = 12.

We know that D secured the second rank in the survey by KIRF.

=> Sum of ranks secured by D in the BS and GT surveys = 10.

10 can be represented as (5,5) or (6,4).

We know that no college secured the same rank in 2 surveys.

Therefore, the ranks secured by D must be 6 and 4.

D had a better rank in the survey conducted by BS than the one conducted by GT.

We know that A managed a position within the top 3 in all 3 surveys.

Therefore, A must have secured second and third positions in the other 2 surveys.

Also, the average rank secured by A must be 2.

Let us solve each question separately now. The points that one must bear in mind while filling the table are

(I) B managed to get a better rank than C in 2 of the 3 surveys.
(II) GT deemed C to be a better college than A.

B was ranked third in the survey conducted by BS. Also, we know that the average ranks of B and C were not equal.

Now, A must have secured second rank and C must have secured first rank in the survey conducted by BS.

In the other 2 surveys, B must have a better rank than C. A must have secured third rank in the survey conducted by GT.
C must have secured second rank (since GT deems C to be a better college than C) and B must have secured first rank.

Since B has secured third rank in BS rankings, it must have secured the fourth or fifth rank in the KIRF rankings.
Had B secured fifth rank, C must have secured the sixth rank (Since 2 of the 3 surveys place B above C).

In this case, the average rank secured by both B and C will be equal (3).
Therefore, we can eliminate this possibility.

B must have secured 4th rank and C must have secured sixth rank.

Therefore, option B is the right answer.

Q2: If the average rank secured by C is 3 and B is 2 in the 3 surveys, what is the rank secured by C in the survey conducted by KIRF? 
(a)  3
(b)  4
(c)  5
(d)  6

Ans: c

Sol: We know that no college secured the same rank in 2 surveys.

Therefore, the ranks secured by D must be 6 and 4.

D had a better rank in the survey conducted by BS than the one conducted by GT.

We know that A managed a position within the top 3 in all 3 surveys.

Therefore, A must have secured second and third positions in the other 2 surveys.

Also, the average rank secured by A must be 2.

Let us solve each question separately now. The points that one must bear in mind while filling the table are

(I) B managed to get a better rank than C in 2 of the 3 surveys.
(II) GT deemed C to be a better college than A.

Average rank secured by B is 2 and C is 3.

Therefore, sum of the ranks secured by B and C must be 6 and 9 respectively.
Sum of ranks secured by B is 6. Therefore, the ranks must be 1,2 and 3.
B must have secured third rank in the survey conducted by KIRF (Since the first 2 ranks are already taken up).
C had a better rank than A in the survey conducted by GT.

Had C secured first rank in the survey conducted by BS, then C must have secured second rank in the survey conducted by GT.
A must have secured third rank in the survey conducted by GT and second rank in the survey conducted by BS. However, B could not have secured third rank in the survey conducted by BS since A has secured third rank. Therefore, this case can be eliminated.

Had C secured first rank in the survey conducted by GT, B must have secured first rank in the survey conducted by BS. A must have secured second rank in the survey conducted by BS and C must have secured the third rank. The rankings will be as follows:

As we can see, C must have secured fifth rank in the survey conducted by KIRF.

Therefore, option C is the right answer.

Q3: If the average rank secured by C is the same as the average rank secured by B and the rank secured by A in GT is better than the one it secured in BS, then the rank secured by B in GT survey is
(The average rank secured across the 3 surveys is an integer for all the 4 colleges) 
(a)  3 or 5
(b)  5 or 6
(c)  4 or 5
(d)  1 or 3

Ans: a

Sol: We know that no college secured the same rank in 2 surveys.
Therefore, the ranks secured by D must be 6 and 4.

D had a better rank in the survey conducted by BS than the one conducted by GT.

We know that A managed a position within the top 3 in all 3 surveys.
Therefore, A must have secured second and third positions in the other 2 surveys. Also, the average rank secured by A must be 2.

Let us solve each question separately now. The points that one must bear in mind while filling the table are

(I) B managed to get a better rank than C in 2 of the 3 surveys.
(II) GT deemed C to be a better college than A.

Average rank secured by B and C is the same.

Average rank secured by B and C cannot be 2 since in KIRF one of the 2 must have secured a rank greater than 3.
Average rank cannot be 6 as well.
Average rank cannot be 5 since both of them have a rank less than 4 in the BS survey.

Let us consider the possibility that the average rank is 4.
Therefore, sum of ranks must be 12.
Also, we know that rank secured by A in GT is better than the one it secured in the survey by BS.
Therefore, A must have secured second rank in GT and third rank in BS.
In the BS survey, B and C must have secured first and second ranks, respectively.
Since C is ranked better than A by GT, C must have secured the first rank in the GT survey.
Now, C must have secured a rank of 8 in the KIRF ranking for the average rank to be 4. As we can see, this case is impossible.

Therefore, the average rank of both B and C must be 3.
C must have secured first rank in the GT survey and second rank in the BS survey.
For the average rank to be 6, C must have secured sixth rank in the KIRF survey.

B must have secured first rank in the BS survey.
Now, the sum of the ranks secured by B in the other 2 surveys must be 9-1 = 8.
8 can be represented as (4,4), (5,3) or (6,2).

We can eliminate the case (4,4) since no college secured the same ranking in 2 colleges.
We can eliminate (6,2) too since no 2 colleges secured the same ranking in a survey.
Therefore, the final ranking will be as follows:

Rank secured by B in the GT survey will be 3 or 5.
Therefore, option A is the right answer.

Q4: If the average rank secured by B is one more than the average rank secured by A, then the rank secured by C in the survey conducted by BS is 
(a)  1
(b)  2
(c)  3
(d)  Can be more than one of the above

Ans: d

Sol: We know that no college secured the same rank in 2 surveys.
Therefore, the ranks secured by D must be 6 and 4.

D had a better rank in the survey conducted by BS than the one conducted by GT.

We know that A managed a position within the top 3 in all 3 surveys.
Therefore, A must have secured second and third positions in the other 2 surveys. Also, the average rank secured by A must be 2.

Let us solve each question separately now. The points that one must bear in mind while filling the table are

(I) B managed to get a better rank than C in 2 of the 3 surveys.
(II) GT deemed C to be a better college than A.

Average rank secured by B = Average rank secured by A + 1.

Therefore, the average rank secured by B must be 3.
Sum of the ranks secured by B = 9.
Now, had A secured second rank in the GT survey and third rank in the BS survey, C must have secured the first rank in the GT survey and second rank in BS survey.
B must have secured the first rank in the BS survey.

Now, B must have secured either fifth or third rank in the KIRF and GT surveys.

In this case, the rank secured by C is two.

Let us consider the other possibility.

Had A secured third rank in the GT survey, A would have secured second rank in the BS survey.
C must have secured the second or first rank in the GT survey.

Had C secured first rank in the GT survey, it would have secured third rank in the BS survey.
B would have secured first rank in the BS survey.

Had C secured second rank in the GT survey, C could have secured first or third rank in the BS survey.

As we can see, C could have secured any of the top 3 ranks and hence, option D is the right answer.

Set 2

DIRECTIONS: A man goes on dividing a certain sum of money into half. He does this 9 times. He gives the amount in round 1 and round 4 and round 7 to A. To B he gives the amount in rounds 2, 5 and 8. To C he gives the amount in rounds 3, 6 and 9. Assume that the balance sum at the end of Round 9 is Rs. 195.31. 

Q1: What is the original sum of money?
A: Rs. 10 x 10⁴
B: Rs. 104
C: Rs. 106
D: Rs. 2.5 x 10⁵

Ans: A
Sol:
If the original amount is x at the end of round 9, the amount left is x / 2⁹ = x / 512. 
Since the amount is Rs. 195.31 the original sum, x = 195.31 x 512. 
Approximately 200 x 500 = 10 x 10⁴.

Q2: What is the ratio of shares of A : B : C?
A: 10 : 5 : 2
B: 12 : 6 : 2
C: 4 : 2 : 1
D: 1 : 1 : 1

Ans: C
Sol:
Ratio of shares cannot be equal. 
The ratio has to be such that share of C is half of B which is half of A. So answer is 3.

Q3: If A gets amounts in Rounds 1, 2 and 3, ; B in rounds 4, 5 and 6 ; C in Rounds 7 , 8 and 9 what is the ratio of shares of A : B : C?
A: 64 : 8 : 1
B: 256 : 128 : 4
C: 128 : 64 : 8
D: 12 : 4 : 1

Ans: A
Sol:
A:B:C = (1/2 + 1/4 + 1/8) : (1/16 + 1/32 + 1/64) : (1/128 + 1/256 + 1/512) = 64:8:1

Q4: If the balance at the end of Round 9 is Rs. 390.625, the original sum is
A: Rs. 2.5 x 10⁴
B: Rs. 2 x 10⁵
C: Rs. 2 x 10⁶
D: Rs. 3 x 10⁸

Ans: B
Sol:
If the sum at the end of round 9 is Rs. 195.31, original sum is 10. If amount is Rs. 390.625, then the original amount is 2 x 10⁵.