Practice Questions
Concept Explanation
For any set of consecutive numbers, the average equals the middle term (odd count) or the average of the two middle terms (even count).
Key Rules
- Average of n consecutive integers starting at a: a + (n − 1)/2
- Average of first n natural numbers = (n + 1)/2
- Sum of n consecutive numbers = n × average
Example
Average of 7, 8, 9, 10, 11 = 9. Average of 4, 5, 6, 7 = 5.5.
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Q1 Easy
Average of 5 consecutive integers is 14. The largest is:
ExplanationMiddle = 14. Set: 12, 13, 14, 15, 16. -
Q2 Medium
Average of 6 consecutive even numbers is 25. The smallest is:
ExplanationMiddle evens average 25 → 24 and 26. Set: 20 to 30. Smallest = 20. -
Q3 Easy
Average of first 20 natural numbers is:
Explanation(20 + 1)/2 = 10.5. -
Q4 Easy
Three consecutive odd numbers have average 27. The largest is:
ExplanationMiddle odd = 27. Numbers: 25, 27, 29. -
Q5 Easy
Average of 9 consecutive numbers is 18. Their sum is:
ExplanationSum = 9 × 18 = 162. -
Q6 Medium
Average of 4 consecutive multiples of 5 is 35. The largest is:
ExplanationSet: 25, 30, 35, 40. Largest = 40. -
Q7 Easy
Average of 11 consecutive integers is 30. The middle integer is:
ExplanationWith odd count, average equals the middle term = 30.
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Q8 Easy
Sum of first 15 natural numbers is:
ExplanationSum = n(n + 1)/2 = 15 × 16/2 = 120. -
Q9 Easy
Average of 7 consecutive numbers starting from 13 is:
ExplanationSet 13 to 19. Average = 16. -
Q10 Easy
If average of 5 consecutive integers is n, their sum is:
ExplanationSum = count × average = 5n. -
Q11 Hard
Average of 10 consecutive odd numbers is 45. The smallest is:
ExplanationSet: 35, 37, 39, 41, 43, 45, 47, 49, 51, 53. Smallest = 35. -
Q12 Medium
Average of 8 consecutive integers is 19.5. The largest is:
ExplanationSet: 16 to 23. Largest = 23. -
Q13 Easy
Average of three consecutive multiples of 4 is 28. The middle number is:
ExplanationMiddle multiple equals the average = 28. -
Q14 Medium
Sum of 6 consecutive integers is 87. The average is:
ExplanationAverage = 87/6 = 14.5.
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DS1 Medium
What is the average of the consecutive integers?
Statement IThere are 5 consecutive integers.
Statement IITheir sum is 70.
ExplanationTogether: average = 70/5 = 14. -
DS2 Medium
What is the largest consecutive integer?
Statement IThe average of 4 consecutive integers is 15.
Statement IIThe smallest integer is 13.
ExplanationStatement I gives set 13, 14, 15, 16 → largest 16. Statement II alone is insufficient.
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DS3 Easy
What is the middle number?
Statement IThree consecutive odd numbers have sum 75.
Statement IIThe average of the three numbers is 25.
ExplanationEach statement alone gives middle = 25. -
DS4 Hard
Is the average an integer?
Statement IThere are 4 consecutive even numbers.
Statement IIThe smallest even number is 12.
ExplanationSet 12, 14, 16, 18 has average 15 — an integer. Both needed to fix the set.