Practice Questions
Concept Explanation
When a new value is added to a set, the new average is:
New average = (Old sum + New value) / (n + 1)
Key Idea
- Old sum = Old average × n
- New sum = Old sum + added value
- Change in average = (New value − Old average) / (n + 1)
Placement Shortcut
Find the old total first. Add the new value, then divide by the new count.
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Q1 Easy
Average of 4 numbers is 25. A fifth number 40 is added. New average is:
ExplanationSum = 100 + 40 = 140. New average = 140/5 = 28. -
Q2 Medium
Average of 9 numbers is 30. One more number is added and average becomes 32. The added number is:
ExplanationOld sum = 270. New sum = 320. Added number = 50. -
Q3 Easy
Average of 5 students' marks is 70. A new student scoring 88 joins. New average is:
ExplanationSum = 350 + 88 = 438. Average = 438/6 = 73. -
Q4 Easy
Average of 8 numbers is 18. Adding 18 makes the new average:
ExplanationSum = 144 + 18 = 162. New average = 162/9 = 18. -
Q5 Easy
Average of 5 numbers is 12. A sixth number 30 is added. New average is:
ExplanationSum = 60 + 30 = 90. New average = 90/6 = 15. -
Q6 Medium
Average of 11 numbers is 24. Adding 36 gives new average:
ExplanationSum = 264 + 36 = 300. New average = 300/12 = 25. -
Q7 Easy
Three numbers have average 20. A fourth number 32 is added. New average is:
ExplanationSum = 60 + 32 = 92. New average = 92/4 = 23.
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Q8 Medium
Average of 6 numbers is 18. One more number is added and average becomes 20. The added number is:
ExplanationOld sum = 108. New sum = 140. Added number = 32. -
Q9 Easy
Average of 20 numbers is 35. Adding 35 keeps the average at:
ExplanationAdding a value equal to the old average keeps the average unchanged. -
Q10 Medium
Average of 8 numbers is 22. Adding x makes the average 24. Find x.
ExplanationOld sum = 176. New sum = 216. x = 40. -
Q11 Hard
A batsman's average after 10 innings is 40. To raise it to 44 after the 11th innings, he must score:
ExplanationRequired total = 484. Current total = 400. Needed score = 84. -
Q12 Medium
Average weight of 5 men is 65 kg. A man weighing 80 kg joins. New average is:
ExplanationSum = 325 + 80 = 405. New average = 405/6 = 67.5 kg. -
Q13 Medium
Average of 10 numbers is 45. One more number is added and average becomes 46. The added number is:
ExplanationOld sum = 450. New sum = 506. Added number = 56. -
Q14 Hard
Average of 15 numbers is 28. Adding a number equal to the old average gives new average:
ExplanationAdding a value equal to the current average does not change the average.
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DS1 Easy
What is the new average after adding one number?
Statement IThe average of 6 numbers is 20.
Statement IIThe number added is 32.
ExplanationNeed old sum and the added value. Together: (120 + 32)/7 = 152/7 ≈ 21.7. -
DS2 Medium
What is the added number?
Statement IThe average of 8 numbers is 25.
Statement IIAfter addition, the average of 9 numbers is 27.
ExplanationOld sum = 200. New sum = 243. Added number = 43.
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DS3 Easy
Is the new average greater than the old average?
Statement IThe added number is 50.
Statement IIThe old average is 45.
ExplanationNeed both: since 50 > 45, the new average exceeds the old average. -
DS4 Medium
What is the new average?
Statement IThere are 5 numbers with average 18.
Statement IIA sixth number equal to 18 is added.
ExplanationTogether: adding 18 to a set averaging 18 keeps the average at 18.