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

Directions : Answer the question independently. In a class there were 10 students and the average weight of the students in the class was 54.5 kg. Five students weighing 89 kg, 46 kg, 82 kg, 93 kg and 60 kg joined the class one by one (not necessarily in that order). After the addition of every student, the average weight (in kg) of the class was an integer. If the weight of the first student that joined in was 82 kg, then what was the average weight of the class after the 4th student joined in?

  1. 60 kg

  2. 59 kg

  3. 61 kg

  4. 63 kg

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

Initial: 10 students, avg 54.5, total 545. 1st added (82): 11 students, total 627, avg 57. 2nd added (93): 12 students, total 720, avg 60. 3rd added (89): 13 students, total 809, avg 62.23 (not integer). The sequence must be ordered to keep averages as integers. Testing the sequence leads to the 4th student resulting in an average of 59.

Multiple choice

Directions: Select the correct alternative from the given choices. If the average weight of a group of 15 items is 30 kg and none of the items weighs more than 32 kg, find the least possible weight (in kg) of any item in the group.

  1. 2

  2. 4

  3. 3

  4. 0
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To minimize one item, maximize the others. If 14 items are at the maximum weight of 32 kg, their sum is 14 * 32 = 448. The total sum for 15 items is 15 * 30 = 450. The remaining item must be 450 - 448 = 2 kg.

Multiple choice

Abraham bought music concert tickets and Gold and Silver passes for $25 and $15, respectively. He bought a total of 100 passes for \$1,750. He sold some of the Silver passes to cover the extra expenses. Find the number of Silver passes he sold so that the average amount (arithmetic mean) of the remaining passes becomes \$20.

  1. 40

  2. 45

  3. 50

  4. 55

  5. 60
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total cost = 1750, Total items = 100. Let G be number of Gold passes (\$25) and S be number of Silver passes (\$15). G + S = 100, 25G + 15S = 1750. Solving gives G = 25, S = 75. If he sells x silver passes, remaining passes = 100 - x. Total value = 1750 - 15x. Average = (1750 - 15x) / (100 - x) = 20. 1750 - 15x = 2000 - 20x. 5x = 250, x = 50.

Multiple choice

The average weight of 130 students of school A is 35 pounds and the average weight of 100 students of school B is 40 pounds. Quantity A Average weight of all the students of school A and school B Quantity B 39 pounds

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be established from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Weighted average = (130*35 + 100*40) / (130+100) = (4550 + 4000) / 230 = 8550 / 230 = 37.17. Quantity A (37.17) is less than Quantity B (39).

Multiple choice

The average of three number is 84. If another number is included the average becomes 80. If another number is included which is 3 more than 4th number replace the 1st number then average of four number becomes 79. Find the value of 1st number?

  1. 12

  2. 11

  3. 9

  4. 75

  5. 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The first three numbers total 3 x 84 = 252, and the first four total 4 x 80 = 320, so the fourth number is 68. Replacing the first number with 71 makes the total 316, so the first number was 320 + 71 - 316 = 75.

Multiple choice

Three friends Sara, Wais and Alice have some candies. The numbers of candies eaten by Sara, Wais and Alice are a, b and c, respectively. The average number of candies they ate all together is 7a, where a ≠ 0. What is the ratio of the number of candies eaten by Sara to the sum of the numbers of candies eaten by Wais and Alice?

  1. 20 : 1

  2. 1 : 20

  3. 2 : 7

  4. 3 : 8

  5. 9 : 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total candies = a + b + c. Average = (a+b+c)/3 = 7a. Thus, a+b+c = 21a, which means b+c = 20a. The ratio of a to (b+c) is a : 20a, which is 1 : 20.