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📌 Section 1 is Logical reasoning specially designed for CAT
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SET 1 — 🔍 CAT Level
At a business school, 10 students – Aman, Bhavya, Chirag, Dev, Esha, Farhan, Gauri, Harsh, Ishita and Juhi – were evaluated during the final placement process on the basis of three parameters: Aptitude Test (A), Group Discussion (G), and Personal Interview (P).
Each parameter was scored on an integer scale from 1 to 7.
The final placement score of a student was obtained by adding the scores of the three parameters.
Based on the final placement score, credit points were awarded according to the slabs given in the table below.
Total Score | Credit Points |
|---|---|
0–5 | 5 |
6–9 | 10 |
10–14 | 15 |
15–18 | 20 |
The frequency distribution of scores across the three parameters is given in the table below.
Score | A | G | P |
|---|---|---|---|
1 | 0 | 2 | 1 |
2 | 1 | 1 | 2 |
3 | 3 | 2 | 3 |
4 | 2 | 1 | 2 |
5 | 2 | 3 | 1 |
6 | 1 | 1 | 1 |
7 | 1 | 0 | 0 |
The additional information is also known:
Aman and Chirag scored identical scores in all the three parameters, and they were the only students who obtained the lowest final placement score of 7 points each.
The students were ranked from 1st to 10th according to their final placement scores.
The three students who received 20 credit points occupied the top three positions in each of the three parameters. Also, each of these three students topped exactly one parameter.
Ishita secured the 6th position and was the only student with a total score of 9.
Question 1
What is the sum of the total scores of the students finishing 4th and 5th?
Question 2
If the students finishing 7th and 8th both scored 4 in Aptitude Test (A), then Chirag's score in the Personal Interview (P) must have been:
Question 3
What is the maximum possible number of students who could have scored at least 12 in total?
3
4
5
Question 4
What is the maximum possible total credit points awarded to all 10 students?
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✅ Answers & Explanations
Set 1
Total score across all students
= Total A + Total G + Total P
= 42 + 35 + 33
= 110
From the conditions:
Aman and Chirag each scored 7.
Ishita scored 9 and finished 6th.
So the score pattern must be:
Top 3 students: 15–18 each
4th and 5th students: between 10 and 14
6th student: 9
7th and 8th students: 8 each
9th and 10th students: 7 each
Now, the top 3 students received 20 credit points, so they must have total scores between 15 and 18.
Also, these top 3 students occupied the top three positions in each parameter.
From the frequency table:
For A, top three scores are: 7, 6, 5
For G, top three scores are: 6, 5, 5
For P, top three scores are: 6, 5, 4
So total score of the top 3 students together:
= 7 + 6 + 5 + 6 + 5 + 5 + 6 + 5 + 4
= 49
Now total score of all 10 students = 110
Known scores except 4th and 5th:
Top 3 = 49
Ishita = 9
7th and 8th = 8 + 8 = 16
Aman and Chirag = 7 + 7 = 14
Total known = 49 + 9 + 16 + 14 = 88
So, score of 4th and 5th together:
= 110 – 88
= 22
Question 1: 22
Question 2
If 7th and 8th both scored 4 in A, their total scores are both 8.
Aman and Chirag had identical scores and total 7 each.
After checking the possible distribution, Aman and Chirag must have scored:
A = 3, G = 1, P = 3
So Chirag’s score in Personal Interview was:
Answer 2: 3
Question 3
Students scoring at least 12:
The top 3 students definitely scored at least 15, so they are counted.
Among 4th and 5th students, their total is 22.
To maximize the number scoring at least 12, they can be:
12 and 10
So only one more student can score at least 12.
Maximum possible students scoring at least 12:
= 3 + 1
= 4
Question 4
Credit points:
Top 3 students: 20 each = 60
4th and 5th students: 15 each = 30
Ishita: 10
7th and 8th: 10 each = 20
Aman and Chirag: 10 each = 20
Total credit points:
= 60 + 30 + 10 + 20 + 20
= 140
⚡ Brain teasers are not just about getting the right answer — they train you to think differently under pressure.
Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.
See you in tomorrow’s challenge!