Quantitative Aptitude

Averages

1,527 Questions
All Basic average and reverse calculation 405 Adding or removing an observation 342 Weighted and combined averages 320 Replacement and correction of a recorded value 233 Ratio shortcut for two-group mixtures 111 Equal-distance average speed 59 Age, score, weight, and spending applications 32 Consecutive terms and arithmetic progressions 25

Averages Questions

Multiple choice

The average of 8 numbers is 40. If the average of the first six numbers is 30 and that of the last three numbers is 60, the sixth number is

  1. 35

  2. 30

  3. 25

  4. 40

  5. 48
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of 8 numbers = 8 * 40 = 320. Sum of first 6 = 6 * 30 = 180. Sum of last 3 = 3 * 60 = 180. The 6th number is counted in both the first 6 and the last 3. Sum of 8 = (Sum of first 5) + (6th) + (Sum of last 2) = 320. (Sum of first 6) + (Sum of last 3) = 180 + 180 = 360. The overlap is the 6th number: 360 - 320 = 40.

Multiple choice

There are three classes X, Y and Z. Average score of class X is 83. Average score of class Y is 76. Average score of class Z is 85. Average score of classes X and Y is 79, average score of classes Y and Z is 81. Find the average score of all three classes.

  1. 81

  2. 81.5

  3. 82

  4. 84
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let nX, nY, nZ be the number of students. Average of X and Y: (83nX + 76nY)/(nX + nY) = 79 => 4nX = 3nY => nY = 4/3 nX. Average of Y and Z: (76nY + 85nZ)/(nY + nZ) = 81 => 5nY = 4nZ => nZ = 5/4 nY = 5/4 * 4/3 nX = 5/3 nX. Total average = (83nX + 76(4/3 nX) + 85(5/3 nX)) / (nX + 4/3 nX + 5/3 nX) = (83 + 304/3 + 425/3) / (1 + 4/3 + 5/3) = (249 + 304 + 425)/3 / (12/3) = 978 / 12 = 81.5.

Multiple choice

The leader of a group of 8 members is 31 years old and one of the members is four years older than the leader. If the ages of these two are excluded, the average age of the remaining 6 members is two year less than the average of the whole group. What is the average of the group?

  1. 27 years

  2. 39 years

  3. 22 years

  4. 17 years

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total members be 8, average A. Total age = 8A. Leader = 31, member = 35. Remaining 6 members sum = 8A - 66. Average = (8A-66)/6 = A - 2. 8A - 66 = 6A - 12. 2A = 54, A = 27.

Multiple choice

The average weight of X, Y and Z is 74 kg. If the average weight of X and Y be 68 kg and that of Y and Z be 78 kg, then the weight (in kg) of Y is

  1. 72

  2. 70

  3. 68

  4. 66
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sum of the weights of X, Y, and Z is 74 * 3 = 222 kg. The sum of the weights of X and Y is 136 kg, and the sum of the weights of Y and Z is 156 kg. Adding these two equations gives X + 2Y + Z = 292 kg, and subtracting the total sum of 222 kg leaves the weight of Y as 70 kg.

Multiple choice

The average age of 30 students of a class is 12 years. Out of the 30 students, the average age of a group of 5 students is 10 years, and that of another group of 5 students is 14 years. What is the average age of the remaining students?

  1. 8 years

  2. 10 years

  3. 12 years

  4. 14 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total age = 30 * 12 = 360. Sum of 5 = 5 * 10 = 50. Sum of another 5 = 5 * 14 = 70. Remaining 20 students = 360 - 120 = 240. Average = 240 / 20 = 12.