Practice Questions
Concept Explanation
When one value is replaced by another, the count stays the same but the sum changes.
New average = (Old sum − Old value + New value) / n
Key Idea
- Change in sum = New value − Old value
- Change in average = (New value − Old value) / n
Example
Average of 5 numbers is 20 (sum 100). Replace 15 with 25: new sum = 110, new average = 22.
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Q1 Easy
Average of 5 numbers is 20. If 15 is replaced by 25, the new average is:
ExplanationSum increases by 10. New average = 110/5 = 22. -
Q2 Medium
Average of 8 numbers is 30. If 42 is replaced by 22, the new average is:
ExplanationSum decreases by 20. New average = 220/8 = 27.5. -
Q3 Easy
Average of 6 numbers is 18. If 12 is replaced by 30, the new average is:
ExplanationSum increases by 18. New average = 126/6 = 21. -
Q4 Medium
Average of 10 numbers is 45. If 70 is replaced by 50, the new average is:
ExplanationSum decreases by 20. New average = 430/10 = 43. -
Q5 Easy
Average of 4 numbers is 25. If 20 is replaced by 40, the new average is:
ExplanationSum increases by 20. New average = 120/4 = 30. -
Q6 Hard
Average of 7 numbers is 16. Replacing x with 28 raises the average to 18. Find x.
ExplanationSum increase = 14. So 28 − x = 14 → x = 14. -
Q7 Hard
Average of 9 numbers is 24. Replacing 36 with y gives average 26. Find y.
ExplanationSum increase = 18. So y − 36 = 18 → y = 54.
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Q8 Medium
Average of 5 numbers is 32. Replacing 20 with 44 gives new average:
ExplanationSum increases by 24. New average = 160 + 24 over 5 = 34.4. -
Q9 Medium
Average of 20 students is 50. One score wrongly entered as 30 is corrected to 70. New average is:
ExplanationSum increases by 40. New average = 1040/20 = 52. -
Q10 Hard
Average of 12 numbers is 15. Replace 10 with 22 and 8 with 20. New average is:
ExplanationNet sum increase = 24. New average = 204/12 = 17. -
Q11 Medium
Average of 8 numbers is 22. The highest number 40 is replaced by 32. New average is:
ExplanationSum decreases by 8. New average = 168/8 = 21. -
Q12 Hard
Average of 11 numbers is 30. Replacing 45 with 15 gives new average:
ExplanationSum decreases by 30. New average = 300/11 = 27.27 (approx). -
Q13 Hard
Average of 5 numbers is 18. One number recorded as 12 instead of 21. Correct average is:
ExplanationCorrect sum = 90 − 12 + 21 = 99. Correct average = 19.8. -
Q14 Easy
Average of 6 numbers is 25. If each number is replaced by double its value, the new average is:
ExplanationDoubling every value doubles the average → 50.
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DS1 Easy
What is the new average after replacement?
Statement IThe average of 5 numbers is 20.
Statement II15 is replaced by 25.
ExplanationTogether: new average = (100 − 15 + 25)/5 = 22. -
DS2 Medium
What is the replaced value?
Statement IThe average of 7 numbers is 16.
Statement IIReplacing x with 28 gives average 18.
ExplanationOld sum = 112. New sum = 126. So 28 − x = 14 → x = 14.
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DS3 Easy
Does the average increase after replacement?
Statement IThe old value is 30.
Statement IIThe new value is 45.
ExplanationNeed both values. Replacing 30 with 45 increases the average. -
DS4 Medium
What is the new average?
Statement IAverage of 10 numbers is 45.
Statement II70 is replaced by 50.
ExplanationNeed count with old average and the replacement. Together: 430/10 = 43.