Averages & Ages Quiz: Quantitative Aptitude Practice

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. What is the average of the first 20 even natural numbers?

   • 20
   • 22
   • 19
   • 21

   Answer: 21. The average of the first n even numbers is n + 1, so 20 + 1 = 21 (sum 420 ÷ 20).

2. The average of 11 results is 50. The average of the first six is 49 and of the last six is 52. What is the sixth result?

   • 56
   • 54
   • 50
   • 58

   Answer: 56. The 6th result is in both groups: 6 × 49 + 6 × 52 - 11 × 50 = 294 + 312 - 550 = 56.

3. The average age of 30 students is 14 years. When the teacher's age is included, the average rises by 1 year. What is the teacher's age?

   • 44 years
   • 46 years
   • 45 years
   • 31 years

   Answer: 45 years. New total 31 × 15 = 465, old total 30 × 14 = 420, so the teacher is 45. Shortcut: 14 + 31 × 1 = 45.

4. A batsman scores 87 runs in his 17th innings and raises his average by 3. What is his average after the 17th innings?

   • 39
   • 36
   • 42
   • 40

   Answer: 39. New average = 87 - 16 × 3 = 39. Check: old average 36, and 16 × 36 + 87 = 663 = 17 × 39.

5. A car goes from P to Q at 40 km/h and returns along the same road at 60 km/h. What is its average speed for the whole journey?

   • 50 km/h
   • 45 km/h
   • 52 km/h
   • 48 km/h

   Answer: 48 km/h. Equal distances: 2xy/(x + y) = 2 × 40 × 60/100 = 48 km/h.

6. The average weight of 8 people rises by 2.5 kg when one of them, weighing 65 kg, is replaced by a new person. What is the new person's weight?

   • 80 kg
   • 85 kg
   • 75 kg
   • 87.5 kg

   Answer: 85 kg. The total rises by 8 × 2.5 = 20 kg, so the new person weighs 65 + 20 = 85 kg.

7. The ages of A and B are in the ratio 5:7. Four years from now the ratio will be 3:4. What is A's present age?

   • 28 years
   • 20 years
   • 24 years
   • 16 years

   Answer: 20 years. (5x + 4)/(7x + 4) = 3/4 gives 20x + 16 = 21x + 12, so x = 4 and A is 5 × 4 = 20.

8. A father is three times as old as his son. After 15 years he will be twice as old as his son. What is the father's present age?

   • 40 years
   • 48 years
   • 54 years
   • 45 years

   Answer: 45 years. 3s + 15 = 2(s + 15) gives s = 15, so the father is 45.

9. The sum of the ages of 5 children born at intervals of 3 years is 50 years. What is the age of the youngest child?

   • 4 years
   • 5 years
   • 6 years
   • 8 years

   Answer: 4 years. Ages y, y + 3, y + 6, y + 9, y + 12 add to 5y + 30 = 50, so y = 4. (The middle child is 10, the average.)

10. The average of five consecutive odd numbers is 61. What is the largest of them?

    • 63
    • 67
    • 65
    • 69

    Answer: 65. The average is the middle number, 61. The numbers are 57, 59, 61, 63, 65, so the largest is 65.