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 EasyThe average of 7 consecutive numbers is 20. The largest of these numbers is:ExplanationFor an odd count of consecutive numbers, the average equals the middle term. Middle term = 20. The seven numbers are 17, 18, 19, 20, 21, 22, 23. The largest number is 23. Verification: Sum = 7 × 20 = 140 and 17 + 18 + 19 + 20 + 21 + 22 + 23 = 140. Hence the answer is 23.
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Q2 EasyThe average of the first 50 natural numbers is:ExplanationFormula: Average of the first n natural numbers = (n + 1) / 2. Here n = 50, so average = (50 + 1) / 2 = 51 / 2 = 25.5. Verification: Sum = 50 × 51 / 2 = 1275; average = 1275 / 50 = 25.5. Hence the answer is 25.5.
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Q3 EasyThe average of 5 consecutive odd numbers is 61. What is the highest number?ExplanationFor five consecutive odd numbers, the average equals the middle number. Middle = 61. The numbers are 57, 59, 61, 63, 65. The highest number is 65. Verification: Sum = 5 × 61 = 305 and 57 + 59 + 61 + 63 + 65 = 305. Hence the answer is 65.
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Q4 EasyThe sum of three consecutive even numbers is 78. What is the average of these numbers?ExplanationFormula: Average = Sum / Count. Average = 78 / 3 = 26. The numbers are 24, 26 and 28 (three consecutive even numbers averaging 26). Hence the average is 26.
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Q5 EasyThe average of nine consecutive numbers is 20. The largest of these numbers is:ExplanationFor nine consecutive numbers, average = middle term = 20. The numbers run from 20 − 4 = 16 to 20 + 4 = 24. The largest number is 24. Verification: Sum = 9 × 20 = 180 and 16 + 17 + … + 24 = 180. Hence the answer is 24.
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Q6 EasyWhat is the average of the first 40 natural numbers?ExplanationFormula: Average of first n natural numbers = (n + 1) / 2. For n = 40, average = (40 + 1) / 2 = 20.5. Verification: Sum = 40 × 41 / 2 = 820; average = 820 / 40 = 20.5. Hence the answer is 20.5.
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Q7 EasyThe average of 11 consecutive integers is 30. The middle integer is:ExplanationFor an odd number of consecutive integers, the average equals the middle integer. Therefore the middle integer is 30. The integers are 25 through 35. Hence the answer is 30.
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Q8 EasyThree consecutive odd numbers have an average of 27. The largest number is:ExplanationFor three consecutive odd numbers, average = middle number = 27. The numbers are 25, 27 and 29. The largest is 29. Verification: Sum = 3 × 27 = 81 and 25 + 27 + 29 = 81. Hence the answer is 29.
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Q9 EasyThe sum of the first 15 natural numbers is:ExplanationFormula: Sum of first n natural numbers = n(n + 1) / 2. For n = 15, sum = 15 × 16 / 2 = 120. Average would be 120 / 15 = 8. Hence the sum is 120.
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Q10 MediumThe average of 6 consecutive even numbers is 25. The smallest of these numbers is:ExplanationSix consecutive even numbers have two middle terms whose average is 25, so the middle terms are 24 and 26. The set is 20, 22, 24, 26, 28, 30. The smallest is 20. Verification: Sum = 6 × 25 = 150 and 20 + 22 + 24 + 26 + 28 + 30 = 150. Hence the answer is 20.
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Q11 MediumThe average of 8 consecutive integers is 19.5. The largest integer is:ExplanationFor eight consecutive integers, average = mean of the 4th and 5th terms = 19.5, so those terms are 19 and 20. The integers are 16, 17, 18, 19, 20, 21, 22, 23. The largest is 23. Verification: Sum = 8 × 19.5 = 156 and 16 + … + 23 = 156. Hence the answer is 23.
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Q12 MediumThe average of 4 consecutive multiples of 5 is 35. The largest of these numbers is:ExplanationFour consecutive multiples of 5 form an AP with difference 5. Average of the two middle terms = 35, so those terms are 30 and 40. The set is 25, 30, 35, 40. The largest is 40. Verification: Sum = 4 × 35 = 140 and 25 + 30 + 35 + 40 = 140. Hence the answer is 40.
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Q13 MediumThe sum of 6 consecutive integers is 87. What is their average?ExplanationFormula: Average = Sum / Count. Average = 87 / 6 = 14.5. The integers are 12, 13, 14, 15, 16, 17 (average of middle pair 14 and 15 is 14.5). Hence the answer is 14.5.
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Q14 HardThe average of 10 consecutive odd numbers is 44. The smallest of these numbers is:ExplanationLet the first odd number be a. The ten numbers are a, a + 2, …, a + 18. Sum = 10a + 2(0 + 1 + … + 9) = 10a + 90. Average = a + 9 = 44 ⇒ a = 35. The set is 35, 37, 39, 41, 43, 45, 47, 49, 51, 53. The smallest is 35. Hence the answer is 35.
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DS1 Easy
What is the middle number among three consecutive odd numbers?
Statement IThree consecutive odd numbers have sum 75.
Statement IIThe average of the three numbers is 25.
ExplanationStatement I: Average = 75 / 3 = 25, and for three consecutive odd numbers the middle equals the average, so middle = 25. Statement II: Average = 25 ⇒ middle = 25. Each statement alone is sufficient. Answer: D. -
DS2 Medium
In a campus drill on consecutive integers, candidates must find their average. What is the average of the consecutive integers?
Statement IThere are 5 consecutive integers.
Statement IITheir sum is 70.
ExplanationAverage = Sum / Count. Statement I gives count only. Statement II gives sum only. Together: Average = 70 / 5 = 14. Both are needed. Answer: C.
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DS3 Medium
What is the largest consecutive integer?
Statement IThe average of 4 consecutive integers is 15.
Statement IIThe smallest integer is 13.
ExplanationStatement I: For 4 consecutive integers with average 15, the set is 13, 14, 15, 16, so the largest is 16. Statement II alone gives only the smallest integer and does not fix the count or the largest. Statement I alone is sufficient. Answer: A. -
DS4 Hard
A company screening question asks for the average of consecutive even numbers. What is the average?
Statement IThere are 4 consecutive even numbers.
Statement IIThe smallest even number is 12.
ExplanationAverage of consecutive even numbers needs both the count and a fixed starting value (or an equivalent). Statement I alone does not fix the starting number. Statement II alone does not give the count. Together: the set is 12, 14, 16, 18; sum = 60; average = 60 / 4 = 15. Both are needed. Answer: C.