Practice Questions
Concept Explanation
The average (arithmetic mean) of n numbers is their sum divided by n.
Average = Sum of all values / Number of values
Key Formulas
- Sum = Average × Number of values
- Missing value = (Average × n) − Sum of known values
- If each value increases by k, the average also increases by k.
Placement Shortcut
First find total sum from the average, then subtract known values to get the missing number.
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Q1 EasyThe average of 20 girls is 42 and the average of 25 boys is 40. The average of the whole class is:ExplanationFormula: Combined average = (Sum of all values) / (Total count). Sum of girls = 20 × 42 = 840. Sum of boys = 25 × 40 = 1000. Total sum = 840 + 1000 = 1840. Total students = 20 + 25 = 45. Average of the whole class = 1840 / 45 = 40 8/9. Hence the answer is 40 8/9.
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Q2 EasyThere are two sections A and B of a class consisting of 36 and 44 students respectively. If the average marks of section A is 40 and that of section B is 35, the average marks of both the sections together is:ExplanationFormula: Combined average = (n1×A1 + n2×A2) / (n1 + n2). Sum of marks of A = 36 × 40 = 1440. Sum of marks of B = 44 × 35 = 1540. Total sum = 1440 + 1540 = 2980. Total students = 36 + 44 = 80. Average of the whole class = 2980 / 80 = 37.25. Hence the answer is 37.25.
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Q3 EasyThe average of 10 numbers is 23. If each number is increased by 4, the new average is:ExplanationRule: If each value increases by k, the average also increases by k. Original average = 23 and each number increases by 4, so new average = 23 + 4 = 27. Verification: original sum = 10 × 23 = 230; new sum = 230 + 10 × 4 = 270; new average = 270 / 10 = 27. Hence the answer is 27.
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Q4 EasyFind the average of all the numbers between 6 and 34 which are divisible by 5.ExplanationThe required numbers are 10, 15, 20, 25 and 30. Formula: Average = Sum / Count. Sum = 10 + 15 + 20 + 25 + 30 = 100. Count = 5. Average = 100 / 5 = 20. (Alternatively, for an AP the average equals the middle term = 20.) Hence the answer is 20.
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Q5 MediumThe average of 11 numbers is 10.9. If the average of the first 6 numbers is 10.5 and that of the last 6 numbers is 11.4, then the middle number is:ExplanationFormula: Middle number = (Sum of first 6) + (Sum of last 6) − (Sum of all 11), because the middle number is counted twice. Total sum of 11 numbers = 11 × 10.9 = 119.9. Sum of first 6 = 6 × 10.5 = 63. Sum of last 6 = 6 × 11.4 = 68.4. Middle number = 63 + 68.4 − 119.9 = 11.5. Hence the answer is 11.5.
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Q6 MediumThe average of 13 numbers is 65. If the average of the first 7 numbers is 60 and that of the last 7 numbers is 70, then the 7th (middle) number is:ExplanationFormula: Middle number = (Sum of first 7) + (Sum of last 7) − (Sum of all 13). Total sum = 13 × 65 = 845. Sum of first 7 = 7 × 60 = 420. Sum of last 7 = 7 × 70 = 490. The 7th number = 420 + 490 − 845 = 65. Hence the answer is 65.
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Q7 MediumThe average marks of 40 students in a class is 65. If the average marks of 25 boys is 60, the average marks of the girls is:ExplanationFormula: Sum = Average × Number. Total marks = 40 × 65 = 2600. Marks of boys = 25 × 60 = 1500. Marks of girls = 2600 − 1500 = 1100. Number of girls = 40 − 25 = 15. Average marks of girls = 1100 / 15 = 220/3 = 73 1/3. Hence the answer is 73 1/3.
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Q8 MediumA student's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by 1/2. The number of students in the class is:ExplanationIncrease in total marks = 83 − 63 = 20. Increase in average = 1/2. Formula: Increase in average = (Increase in sum) / n ⇒ 1/2 = 20 / n ⇒ n = 40. Hence the number of students in the class is 40.
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Q9 MediumThe average of 2, 7, 6 and x is 5 and the average of 18, 1, 6, x and y is 10. What is the value of y?ExplanationFrom the first average: (2 + 7 + 6 + x) / 4 = 5 ⇒ 15 + x = 20 ⇒ x = 5. From the second average: (18 + 1 + 6 + x + y) / 5 = 10 ⇒ (25 + 5 + y) / 5 = 10 ⇒ 30 + y = 50 ⇒ y = 20. Hence the answer is 20.
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Q10 MediumThe average of four consecutive numbers A, B, C and D is 45.5. What is the product of B and D?ExplanationLet the consecutive numbers be n, n + 1, n + 2 and n + 3. Then (4n + 6) / 4 = 45.5 ⇒ n + 1.5 = 45.5 ⇒ n = 44. So A, B, C, D = 44, 45, 46, 47. Product of B and D = 45 × 47 = 2115. Hence the answer is 2115.
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Q11 HardThe average of 15 numbers is 48. The average of the first 8 of these numbers is 45 and that of the last 8 is 52. Find the 8th number.ExplanationFormula: Overlapping (8th) number = (Sum of first 8) + (Sum of last 8) − (Sum of all 15). Total sum = 15 × 48 = 720. Sum of first 8 = 8 × 45 = 360. Sum of last 8 = 8 × 52 = 416. Eighth number = 360 + 416 − 720 = 56. Hence the answer is 56.
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Q12 HardThe mean of 100 items was found to be 30. If at the time of calculation two items were wrongly taken as 32 and 12 instead of 23 and 11, the correct mean is:ExplanationFormula: Correct sum = Wrong sum − (wrong entries) + (correct entries). Wrong sum = 100 × 30 = 3000. Excess due to error = (32 + 12) − (23 + 11) = 44 − 34 = 10. Correct sum = 3000 − 10 = 2990. Correct mean = 2990 / 100 = 29.9. Hence the answer is 29.9.
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Q13 HardThree years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is:ExplanationThree years ago, sum of ages of 5 members = 5 × 17 = 85 years. Today, without the baby, those 5 members total 85 + 5 × 3 = 100 years. With the baby, there are 6 members and the average is still 17, so present total = 6 × 17 = 102 years. Present age of the baby = 102 − 100 = 2 years. Hence the answer is 2 years.
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Q14 HardOut of 9 persons, 8 persons spend Rs. 30 each for their meals. The ninth spends Rs. 20 more than the average spend of all the nine. The total money spent by all of them is:ExplanationLet the average expenditure of all nine be Rs. A. Then the ninth person spends A + 20. Total expenditure = 8 × 30 + (A + 20) = 9A. So 240 + A + 20 = 9A ⇒ 260 = 8A ⇒ A = 32.5. Total money spent = 9 × 32.5 = 292.5. Hence the answer is Rs. 292.50.
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DS1 Easy
Trainees must find the average of a set of numbers. What is the average?
Statement IThe four numbers are 14, 22, 18 and 26.
Statement IIThe sum of the numbers is 80 and there are 4 numbers.
ExplanationFormula: Average = Sum / Count. Statement I: Sum = 14 + 22 + 18 + 26 = 80 and count = 4, so average = 80 / 4 = 20. Statement II: Average = 80 / 4 = 20. Each statement alone is sufficient. Answer: D. -
DS2 Easy
During a company aptitude mock, candidates must compute the average of a set. What is the average of the set?
Statement IThere are 6 numbers in the set.
Statement IIThe sum of the numbers is 144.
ExplanationAverage = Sum / Count. Statement I gives count but not sum. Statement II gives sum but not count. Together: Average = 144 / 6 = 24. Both are needed. Answer: C.
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DS3 Medium
For the missing observation in a data set. What is the missing number?
Statement IThe average of 5 numbers is 30.
Statement IIFour of the numbers are 25, 28, 32 and 35.
ExplanationFormula: Missing value = (Average × n) − Sum of known values. Statement I alone gives only the total sum 150, not the missing value. Statement II alone does not give the average or total. Together: Total sum = 5 × 30 = 150; known sum = 25 + 28 + 32 + 35 = 120; missing number = 150 − 120 = 30. Both are needed. Answer: C. -
DS4 Medium
An HR analytics quiz asks whether a batch average crosses 50. Is the average of the numbers greater than 50?
Statement IThe sum of 8 numbers is 400.
Statement IIThe smallest number in the set is 45.
ExplanationStatement I: Average = 400 / 8 = 50, which is not greater than 50, so the answer is No. Statement II alone cannot decide because the other numbers are unknown. Statement I alone is sufficient. Answer: A.