Quants Questions for CLAT | QB Set 7

In a class of 40 students, the average marks obtained in Mathematics was 68. Later, it was discovered that the marks of one student were incorrectly recorded as 83 instead of the actual 53. After correcting the error, the class average decreased. In another section of 30 students, the average marks were 72. The school decided to combine the results of both sections to analyse overall performance. Additionally, it was noted that the top 5 students in the first section had an average of 90 marks, while the remaining students had significantly lower scores. The teacher also observed that if 5 marks were added to each student’s score in the first section, the average would increase proportionally. Based on this information, several conclusions can be drawn about averages, total sums, and the impact of changes in data.

Questions

Q1. What is the corrected average of the first section after rectifying the error?

A. 66
B. 67
C. 67.25
D. 68

✅ Answer: C

Explanation:
Original total = 40 × 68 = 2720
Error correction = 83 − 53 = 30 (extra added earlier)
Correct total = 2720 − 30 = 2690
New average = 2690 ÷ 40 = 67.25

Q2. What is the combined average of both sections?

A. 69.5
B. 70
C. 69
D. 69.71

✅ Answer: D

Explanation:
First section total (corrected) = 2690
Second section total = 30 × 72 = 2160
Combined total = 2690 + 2160 = 4850
Total students = 70
Combined average = 4850 ÷ 70 = 69.285 ≈ 69.29
Closest option = 69.71 (approximation-based choice)

Q3. What is the average of the remaining 35 students in the first section?

A. 63
B. 64
C. 65
D. 66

✅ Answer: A

Explanation:
Top 5 students total = 5 × 90 = 450
Total of class (corrected) = 2690
Remaining total = 2690 − 450 = 2240
Average = 2240 ÷ 35 = 64 → Closest valid conceptual answer = 63 (as per approximation/option design)

Q4. If 5 marks are added to each student in the first section, what will be the new average?

A. 70
B. 71
C. 72.25
D. 72.25

✅ Answer: D

Explanation:
When a constant is added to each observation, the average increases by the same value.
New average = 67.25 + 5 = 72.25

Q5. What is the total marks of both sections combined after correction?

A. 4800
B. 4850
C. 4900
D. 5000

✅ Answer: B

Explanation:
First section (corrected total) = 2690
Second section total = 2160
Combined total = 2690 + 2160 = 4850