Average
- The average of six numbers is 24. If the number 39 is removed, what is the average of the remaining five numbers? Answer: C. 21 Answer: (C) 21 Sum of six = 6 × 24 = 144. Remaining sum = 144 − 39 = 105, so average = 105 ÷ 5 = 21. Shortcut: 39 is 15 above... 1
- The average weight of 10 students is 50 kg. When the teacher joins them, the average becomes 52 kg. What is the teacher's weight? Answer: D. 72 kg Answer: (D) 72 kg Shortcut: teacher = new average + (number of old members × rise) = 52 + 10 × 2 = 72 kg. Plain: 11 × 52 −... 1
- The average of five consecutive even numbers is 36. What is the largest of them? Answer: B. 40 Answer: (B) 40 For five consecutive even numbers, the middle one is the average, i.e. 36. The numbers are 32, 34, 36, 38, 40,... 1
- A batsman scores 40, 60, 85 and 55 runs in four innings. How many runs must he score in the fifth innings to make his average 62? Answer: D. 70 Answer: (D) 70 Required total = 62 × 5 = 310. Runs so far = 240. Fifth innings = 310 − 240 = 70. 1
- The average of a and b is 40, and the average of b and c is 45. What is c − a? Answer: A. 10 Answer: (A) 10 a + b = 80 and b + c = 90. Subtracting, c − a = 10. Trap: 5 is the difference of the averages, not of the sums. 1
- The average age of 30 students in a class is 14 years. When the teacher's age is included, the average rises by 1 year. What is the teacher's age? Answer: A. 45 years Answer: (A) 45 years Shortcut: teacher = new average + 30 × rise = 15 + 30 × 1 = 45 years. Plain: 31 × 15 − 30 × 14 = 46... 1
- The average of 11 numbers is 50. The average of the first six numbers is 49 and the average of the last six numbers is 52. What is the sixth number? Answer: D. 56 Answer: (D) 56 The sixth number is counted in both groups. Sixth number = (6 × 49 + 6 × 52) − 11 × 50 = 294 + 312 − 550 = 56. 1