📌 Section 1 is Logical reasoning specially designed for CAT
SET 1 — 🔍 CAT Level
The table below gives partial information about the number of days for which each student attended school during five months. The last column gives the average number of days attended per month for each student and the final row gives the average number of days attended per student for each month.
Student | June | July | August | September | October | Average |
|---|---|---|---|---|---|---|
Abhinav | 20 | 21 | 14 | 12 | 16 | 16.60 |
Amar | 16 | 10 | 15 | — | — | 14.00 |
Ankur | 18 | 19 | 13 | 16 | 13 | 15.80 |
Gaurav | — | 18 | 16 | 21 | — | 17.00 |
Gautam | 24 | 14 | 18 | 24 | 20 | 20.00 |
Hari | 21 | 18 | 17 | 20 | 21 | 19.40 |
Jai | 22 | 16 | 21 | 18 | 24 | 20.20 |
Kamal | 12 | 21 | 19 | 17 | 23 | 18.40 |
Krishna | — | — | 23 | 13 | 20 | 18.60 |
Pavan | 16 | 24 | 21 | 10 | 18 | 17.80 |
Piyush | 11 | 17 | 22 | — | 19 | 16.20 |
Priya | 2 | 19 | 20 | 5 | 17 | 12.60 |
Ramesh | 15 | 15 | 14 | 14 | 13 | 14.20 |
Ramya | 14 | 11 | 19 | 21 | — | 17.20 |
Satish | 13 | 10 | 9 | 14 | 10 | 11.20 |
Sirish | 18 | — | 8 | 12 | 9 | 11.20 |
Tarun | 19 | 8 | 24 | 14 | 14 | 15.80 |
Uday | 9 | 15 | 12 | 21 | 16 | 14.60 |
Venu | 22 | 14 | 21 | 20 | 21 | 19.60 |
Wasim | 23 | 21 | 14 | 11 | 23 | 18.40 |
Average | 16.40 | 16.15 | 17.00 | 15.45 | 17.20 |
Question 1
How many students attended school for less than 15 days in September?
Question 2
For how many days did Krishna attend school in June?
Question 3
Among the students who attended school for more than 90 days across the five months combined, how many students attended school for at least 20 days in July?
Question 4
For how many days did Amar attend school in October?
✅ Answers & Explanations
There are 20 students in total.
The key idea is to convert every given average into a total.
For each student:
Total attendance over 5 months = Average × 5
For each month:
Total attendance of all 20 students = Monthly Average × 20
Step 1: Find the total attendance for each month
June
Average = 16.40
Total attendance:
16.40 × 20 = 328
July
16.15 × 20 = 323
August
17.00 × 20 = 340
September
15.45 × 20 = 309
October
17.20 × 20 = 344
So:
Month | Total Attendance |
|---|---|
June | 328 |
July | 323 |
August | 340 |
September | 309 |
October | 344 |
Step 2: Find the missing values that can be obtained directly from individual averages
Piyush – September
Piyush's average = 16.20
Therefore, his total attendance is:
16.20 × 5 = 81
His known attendance:
June = 11
July = 17
August = 22
October = 19
Sum:
11 + 17 + 22 + 19 = 69
Therefore:
September = 81 − 69 = 12
So,
Piyush's September attendance = 12
Ramya – October
Ramya's average = 17.20
Total:
17.20 × 5 = 86
Known values:
14 + 11 + 19 + 21 = 65
Therefore:
October = 86 − 65 = 21
So,
Ramya's October attendance = 21
Sirish – July
Sirish's average = 11.20
Total:
11.20 × 5 = 56
Known attendance:
June = 18
August = 8
September = 12
October = 9
Their sum:
18 + 8 + 12 + 9 = 47
Hence:
July = 56 − 47 = 9
So,
Sirish's July attendance = 9
Step 3: Find Krishna's July attendance
The total attendance in July is:
323
Adding all the known July values except Krishna and Sirish gives:
291
Therefore:
Krishna + Sirish = 323 − 291
= 32
We already found:
Sirish = 9
Hence:
Krishna = 32 − 9
= 23
So,
Krishna's July attendance = 23
Step 4: Find Krishna's June attendance
Krishna's average is 18.60.
Therefore his five-month total is:
18.60 × 5 = 93
Known values:
July = 23
August = 23
September = 13
October = 20
Sum:
23 + 23 + 13 + 20 = 79
Therefore:
June = 93 − 79
= 14
So,
Krishna's June attendance = 14
Step 5: Find Gaurav's missing values
The total attendance in June is 328.
The sum of all the given June values, excluding Gaurav and Krishna, is:
295
Therefore:
Gaurav + Krishna = 328 − 295
= 33
Krishna's June attendance = 14.
Thus:
Gaurav's June attendance = 33 − 14
= 19
Gaurav's average is 17.
So his total attendance is:
17 × 5 = 85
His known values are now:
June = 19
July = 18
August = 16
September = 21
Sum:
19 + 18 + 16 + 21 = 74
Therefore:
October = 85 − 74
= 11
So Gaurav's missing values are:
June = 19
October = 11
Step 6: Find Amar's September and October attendance
The total attendance in September is:
309
The sum of all known September values, excluding Amar and Piyush, is:
283
Therefore:
Amar + Piyush = 309 − 283
= 26
We know:
Piyush = 12
Therefore:
Amar's September attendance = 26 − 12
= 14
Now Amar's average is 14.
Hence his total attendance:
14 × 5 = 70
His values are:
June = 16
July = 10
August = 15
September = 14
October = ?
Known total:
16 + 10 + 15 + 14 = 55
Therefore:
October = 70 − 55
= 15
So,
Amar's October attendance = 15
Completed Table
Student | June | July | August | September | October | Average |
|---|---|---|---|---|---|---|
Abhinav | 20 | 21 | 14 | 12 | 16 | 16.60 |
Amar | 16 | 10 | 15 | 14 | 15 | 14.00 |
Ankur | 18 | 19 | 13 | 16 | 13 | 15.80 |
Gaurav | 19 | 18 | 16 | 21 | 11 | 17.00 |
Gautam | 24 | 14 | 18 | 24 | 20 | 20.00 |
Hari | 21 | 18 | 17 | 20 | 21 | 19.40 |
Jai | 22 | 16 | 21 | 18 | 24 | 20.20 |
Kamal | 12 | 21 | 19 | 17 | 23 | 18.40 |
Krishna | 14 | 23 | 23 | 13 | 20 | 18.60 |
Pavan | 16 | 24 | 21 | 10 | 18 | 17.80 |
Piyush | 11 | 17 | 22 | 12 | 19 | 16.20 |
Priya | 2 | 19 | 20 | 5 | 17 | 12.60 |
Ramesh | 15 | 15 | 14 | 14 | 13 | 14.20 |
Ramya | 14 | 11 | 19 | 21 | 21 | 17.20 |
Satish | 13 | 10 | 9 | 14 | 10 | 11.20 |
Sirish | 18 | 9 | 8 | 12 | 9 | 11.20 |
Tarun | 19 | 8 | 24 | 14 | 14 | 15.80 |
Uday | 9 | 15 | 12 | 21 | 16 | 14.60 |
Venu | 22 | 14 | 21 | 20 | 21 | 19.60 |
Wasim | 23 | 21 | 14 | 11 | 23 | 18.40 |
Final Answers
Q1 → 11
Q2 → 14 days
Q3 → 3 students
Q4 → 15 days