PlacementPrepThe average of 9 consecutive even numbers is 73. What is the largest of them?
Solution
For consecutive numbers, the average is the middle term: 73.
There are 4 numbers above it, each 2 apart, so the largest = 73 + 8 = 81.
Answer: (C) 81
Quantitative Aptitude · Arithmetic
Averages: placement practice questions
30 moderate questions in the pattern of campus placement tests. Pick an option to check your answer, then open the step-by-step solution.
The average of 9 consecutive even numbers is 43. What is the largest of them?
Solution
For consecutive numbers, the average is the middle term: 43.
There are 4 numbers above it, each 2 apart, so the largest = 43 + 8 = 51.
Answer: (B) 51
The average of 9 consecutive even numbers is 54. What is the largest of them?
Solution
For consecutive numbers, the average is the middle term: 54.
There are 4 numbers above it, each 2 apart, so the largest = 54 + 8 = 62.
Answer: (B) 62
A batsman has an average of 32 runs after 16 innings. How many runs must he score in the next innings to raise his average to 37?
Solution
Required total = 17 × 37 = 629.
Current total = 16 × 32 = 512.
Runs needed = 629 − 512 = 117.
Answer: (C) 117
The average age of 38 students is 29 years. When the teacher's age is included, the average rises by 3. What is the teacher's age?
Solution
New total = 39 × 32 = 1248; old total = 38 × 29 = 1102.
Teacher's age = 1248 − 1102 = 146.
Answer: (D) 146 years
The average of 7 consecutive even numbers is 61. What is the largest of them?
Solution
For consecutive numbers, the average is the middle term: 61.
There are 3 numbers above it, each 2 apart, so the largest = 61 + 6 = 67.
Answer: (C) 67
The average age of 36 students is 57 years. When the teacher's age is included, the average rises by 3. What is the teacher's age?
Solution
New total = 37 × 60 = 2220; old total = 36 × 57 = 2052.
Teacher's age = 2220 − 2052 = 168.
Answer: (D) 168 years
The average weight of 10 people increases by 1.5 kg when a person weighing 51 kg is replaced by a new person. What is the new person's weight?
Solution
Total increase = 10 × 1.5 = 15 kg.
New person = 51 + 15 = 66 kg.
Answer: (A) 66 kg
The average of 7 consecutive even numbers is 37. What is the largest of them?
Solution
For consecutive numbers, the average is the middle term: 37.
There are 3 numbers above it, each 2 apart, so the largest = 37 + 6 = 43.
Answer: (D) 43
The average of five numbers is 44. The average of four of them is 42. What is the fifth number?
Solution
Total of five = 5 × 44 = 220; total of four = 4 × 42 = 168.
Fifth = 220 − 168 = 52.
Answer: (C) 52
The average age of 27 students is 54 years. When the teacher's age is included, the average rises by 3. What is the teacher's age?
Solution
New total = 28 × 57 = 1596; old total = 27 × 54 = 1458.
Teacher's age = 1596 − 1458 = 138.
Answer: (C) 138 years
The average weight of 12 people increases by 2.5 kg when a person weighing 68 kg is replaced by a new person. What is the new person's weight?
Solution
Total increase = 12 × 2.5 = 30 kg.
New person = 68 + 30 = 98 kg.
Answer: (D) 98 kg
The average of 7 consecutive even numbers is 39. What is the largest of them?
Solution
For consecutive numbers, the average is the middle term: 39.
There are 3 numbers above it, each 2 apart, so the largest = 39 + 6 = 45.
Answer: (D) 45
The average age of 25 students is 29 years. When the teacher's age is included, the average rises by 3. What is the teacher's age?
Solution
New total = 26 × 32 = 832; old total = 25 × 29 = 725.
Teacher's age = 832 − 725 = 107.
Answer: (B) 107 years
The average weight of 6 people increases by 1.5 kg when a person weighing 50 kg is replaced by a new person. What is the new person's weight?
Solution
Total increase = 6 × 1.5 = 9 kg.
New person = 50 + 9 = 59 kg.
Answer: (B) 59 kg
The average age of 27 students is 60 years. When the teacher's age is included, the average rises by 3. What is the teacher's age?
Solution
New total = 28 × 63 = 1764; old total = 27 × 60 = 1620.
Teacher's age = 1764 − 1620 = 144.
Answer: (B) 144 years
The average weight of 9 people increases by 1 kg when a person weighing 70 kg is replaced by a new person. What is the new person's weight?
Solution
Total increase = 9 × 1 = 9 kg.
New person = 70 + 9 = 79 kg.
Answer: (A) 79 kg
The average age of 32 students is 53 years. When the teacher's age is included, the average rises by 3. What is the teacher's age?
Solution
New total = 33 × 56 = 1848; old total = 32 × 53 = 1696.
Teacher's age = 1848 − 1696 = 152.
Answer: (C) 152 years
The average weight of 8 people increases by 2.5 kg when a person weighing 66 kg is replaced by a new person. What is the new person's weight?
Solution
Total increase = 8 × 2.5 = 20 kg.
New person = 66 + 20 = 86 kg.
Answer: (B) 86 kg
The average marks of 24 students in section A is 55 and of 18 students in section B is 48. What is the average of all students?
Solution
Total = 24 × 55 + 18 × 48 = 2184.
Average = 2184 / 42 = 52.
Answer: (A) 52
The average weight of 8 people increases by 1.5 kg when a person weighing 66 kg is replaced by a new person. What is the new person's weight?
Solution
Total increase = 8 × 1.5 = 12 kg.
New person = 66 + 12 = 78 kg.
Answer: (C) 78 kg
The average marks of 23 students in section A is 58 and of 20 students in section B is 58. What is the average of all students?
Solution
Total = 23 × 58 + 20 × 58 = 2494.
Average = 2494 / 43 = 58.
Answer: (B) 58
The average marks of 22 students in section A is 70 and of 23 students in section B is 70. What is the average of all students?
Solution
Total = 22 × 70 + 23 × 70 = 3150.
Average = 3150 / 45 = 70.
Answer: (C) 70
The average marks of 30 students in section A is 50 and of 20 students in section B is 55. What is the average of all students?
Solution
Total = 30 × 50 + 20 × 55 = 2600.
Average = 2600 / 50 = 52.
Answer: (B) 52
A batsman has an average of 47 runs after 10 innings. How many runs must he score in the next innings to raise his average to 54?
Solution
Required total = 11 × 54 = 594.
Current total = 10 × 47 = 470.
Runs needed = 594 − 470 = 124.
Answer: (C) 124
The average marks of 30 students in section A is 49 and of 40 students in section B is 49. What is the average of all students?
Solution
Total = 30 × 49 + 40 × 49 = 3430.
Average = 3430 / 70 = 49.
Answer: (A) 49
A batsman has an average of 39 runs after 20 innings. How many runs must he score in the next innings to raise his average to 42?
Solution
Required total = 21 × 42 = 882.
Current total = 20 × 39 = 780.
Runs needed = 882 − 780 = 102.
Answer: (D) 102
The average of five numbers is 24. The average of four of them is 19. What is the fifth number?
Solution
Total of five = 5 × 24 = 120; total of four = 4 × 19 = 76.
Fifth = 120 − 76 = 44.
Answer: (B) 44
The average marks of 24 students in section A is 52 and of 40 students in section B is 50. What is the average of all students?
Solution
Total = 24 × 52 + 40 × 50 = 3248.
Average = 3248 / 64 = 50.75.
Answer: (B) 50.75
A batsman has an average of 37 runs after 12 innings. How many runs must he score in the next innings to raise his average to 43?
Solution
Required total = 13 × 43 = 559.
Current total = 12 × 37 = 444.
Runs needed = 559 − 444 = 115.
Answer: (B) 115
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