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 tests in John's arithmetic class always have 100 points. The teacher gives ten tests to the class. If the scores of John's first five tests are 80, 40, 60, 70, and 50 and he does not score lower than 50 in any of the remaining tests, his average points will always be

  1. greater than 50

  2. greater than 60

  3. between 40 and 50

  4. between 50 and 60

  5. between 80 and 90
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

John has 5 tests with scores 80, 40, 60, 70, 50 (sum = 300). For the remaining 5 tests, he scores at least 50 each (minimum sum = 250). The total sum is at least 550, so the average is at least 550/10 = 55.

Multiple choice

The average weight of A, B and C is 66 kg. If D joins the group, then the average weight of the group becomes 70 kg. If another man E, whose weight is 4 kg more than D, replaces A, then the average of B, C, D and E becomes 76 kg. How much does A weigh?

  1. 62 kg

  2. 65 kg

  3. 72 kg

  4. 86 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A+B+C = 66*3 = 198. A+B+C+D = 70*4 = 280. D = 280 - 198 = 82. E = D+4 = 86. B+C+D+E = 76*4 = 304. B+C+82+86 = 304. B+C = 304 - 168 = 136. A = (A+B+C) - (B+C) = 198 - 136 = 62.

Multiple choice

A certain college has a student-to-teacher ratio of 11 to 1. The average (arithmetic mean) annual salary of a teacher is \$26,000. If the college pays a total of \$3,380,000 in annual salaries to its teachers, how many students does the college have?

  1. 130

  2. 1690

  3. 1,300

  4. 1,430

  5. 1,560
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total salary paid is 3,380,000 and average salary is 26,000, so the number of teachers is 3,380,000 / 26,000 = 130. Given the student-to-teacher ratio is 11:1, the number of students is 130 * 11 = 1430.

Multiple choice

The given table shows the heights of football players in cm ||| |---|---| | Height (in cm)| Frequency| | 170| 2| | 172| 4| | 174| 0| | 176| 6| | 178| 8| | 180| 4| | Total| 24| What is the average height of players rounded to one decimal place?

  1. 176.2 cm

  2. 177.2 cm

  3. 178.4 cm

  4. 180.4 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The average is calculated by finding the sum of all heights (170*2 + 172*4 + 176*6 + 178*8 + 180*4) and dividing by the total number of players (24). The sum is 4228, and 4228 / 24 equals approximately 176.166, which rounds to 176.2.