Practice Questions
Concept Explanation
When a value is removed from a set, the new average is:
New average = (Old sum − Removed value) / (n − 1)
Key Idea
- Old sum = Old average × n
- New sum = Old sum − removed value
- Change in average = (Old average − Removed value) / (n − 1)
Placement Shortcut
Find total sum first, subtract the removed value, then divide by one less count.
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Q1 Easy
Average of 6 numbers is 25. If 40 is removed, the new average is:
ExplanationSum = 150 − 40 = 110. New average = 110/5 = 22. -
Q2 Easy
Average of 4 numbers is 30. If 42 is removed, the new average is:
ExplanationSum = 120 − 42 = 78. New average = 78/3 = 26. -
Q3 Medium
Average of 9 numbers is 24. If 36 is removed, the new average is:
ExplanationSum = 216 − 36 = 180. New average = 180/8 = 22.5. -
Q4 Easy
Average of 8 numbers is 22. If a number equal to the average is removed, the new average is:
ExplanationRemoving a value equal to the average leaves the average unchanged. -
Q5 Medium
Average of 5 numbers is 16. If the largest number 24 is removed, the new average is:
ExplanationSum = 80 − 24 = 56. New average = 56/4 = 14. -
Q6 Medium
Average of 6 numbers is 20. After removing one number, the average becomes 17. The removed number is:
ExplanationOld sum = 120. New sum = 85. Removed number = 35. -
Q7 Easy
Five students have average 72 kg. One student weighing 60 kg leaves. New average is:
ExplanationSum = 360 − 60 = 300. New average = 300/4 = 75 kg.
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Q8 Medium
Average of 10 numbers is 40. If 55 is removed, the new average is:
ExplanationSum = 400 − 55 = 345. New average = 345/9 = 38.33 (approx). -
Q9 Medium
Average of 7 numbers is 18. If 32 is removed, the new average is:
ExplanationSum = 126 − 32 = 94. New average = 94/6 = 15.67 (approx). -
Q10 Hard
Average of 5 numbers is 32. After removing one number, the average becomes 30. The removed number is:
ExplanationOld sum = 160. New sum = 120. Removed number = 40. -
Q11 Medium
Average of 12 numbers is 15. If 36 is removed, the new average is:
ExplanationSum = 180 − 36 = 144. New average = 144/11 = 13.09 (approx). -
Q12 Hard
A batsman's average after 10 innings is 45. If the highest score 95 is excluded, the new average is:
ExplanationSum = 450 − 95 = 355. New average = 355/9 = 39.44 (approx). -
Q13 Medium
Average of 5 numbers is 20. If 35 is removed, the new average is:
ExplanationSum = 100 − 35 = 65. New average = 65/4 = 16.25. -
Q14 Hard
Average of 15 numbers is 28. If 58 is removed, the new average is:
ExplanationSum = 420 − 58 = 362. New average = 362/14 = 25.86 (approx).
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DS1 Easy
What is the new average after removing one number?
Statement IThe average of 6 numbers is 24.
Statement IIThe number removed is 30.
ExplanationTogether: (144 − 30)/5 = 114/5 = 22.8. -
DS2 Medium
What is the removed number?
Statement IThe average of 8 numbers is 20.
Statement IIAfter removal, the average of 7 numbers is 18.
ExplanationOld sum = 160. New sum = 126. Removed number = 34.
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DS3 Easy
Is the new average less than the old average?
Statement IThe removed number is 50.
Statement IIThe old average is 45.
ExplanationNeed both: since 50 > 45, removing 50 lowers the average. -
DS4 Medium
What is the new average?
Statement IThere are 5 numbers with average 16.
Statement IIThe number removed equals the average.
ExplanationTogether: removing 16 from a set averaging 16 keeps the average at 16.