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 weight of a group of 3 people A, B and C is 70 kg. When D joins this group, the average weight becomes 60 kg. A man E, whose weight is 5 kg more than that of D, replaces A and the average weight of B, C, D, and E now becomes 59 kg. What is the average weight (in kg) of A, D and E? (correct to the nearest integer)

  1. 39

  2. 35

  3. 30

  4. 40
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: A+B+C = 3 * 70 = 210. A+B+C+D = 4 * 60 = 240, so D = 30. E = D + 5 = 35. New group: B+C+D+E = 4 * 59 = 236. Since B+C = 210 - A, we have (210 - A) + 30 + 35 = 236. 275 - A = 236, so A = 39. Average of A, D, E = (39 + 30 + 35) / 3 = 104 / 3 = 34.66, which is 35 rounded.

Multiple choice

The average marks of a student in 6 subjects are 80. If the maximum and the minimum marks are excluded, the average marks in the remaining subjects will be reduced by 2. If the maximum marks in a subject are 98, what would be the minimum marks?

  1. 90

  2. 89

  3. 72

  4. 70

  5. 68
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total marks = 6 * 80 = 480. Excluding max (98) and min (x), sum of 4 subjects = 480 - 98 - x = 382 - x. New average = (382 - x) / 4 = 80 - 2 = 78. 382 - x = 312, x = 70.

Multiple choice

A professor scores 15 of 20 exams himself and gives the other 5 to his teaching assistant to score. If the average score of the 15 exams graded by the professor is 87, and the average score of all 20 exams is 85, how many points lower is the average score of the teaching assistant’s 5 exams than the average score of the professor’s 15 exams?

  1. 8

  2. 10

  3. 79

  4. 81
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total points = 20 * 85 = 1700. Professor's points = 15 * 87 = 1305. TA's points = 1700 - 1305 = 395. TA's average = 395 / 5 = 79. Difference = 87 - 79 = 8.

Multiple choice

The table below shows the number of students enrolled in five colleges over the five years (2010 to 2014). Year/College A B C D E 2010 400 270 350 430 470 2011 430 300 330 450 490 2012 370 250 360 470 410 2013 410 310 370 420 430 2014 420 290 340 480 480 What is the average number of students studying in college D over the given years?

  1. 450

  2. 420

  3. 430

  4. 440
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The values for college D over the years 2010 to 2014 are 430, 450, 470, 420, and 480. The sum is 430 + 450 + 470 + 420 + 480 = 2250. The average is 2250 / 5 = 450.

Multiple choice

Let a, b and c be the ages of three persons P, Q and R, respectively where a ≤ b ≤ c are natural numbers. If the average age of P, Q, R is 32 years and if the age of Q is exactly 6 years more than that of P, then what is the minimum possible value of c?

  1. 34 years

  2. 36 years

  3. 38 years

  4. 32 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average age is 32, so a+b+c = 96. Given b = a+6, substituting gives a + (a+6) + c = 96, or 2a + c = 90. Since a <= b <= c, we have a <= a+6 <= c. To minimize c, we maximize a. From 2a + c = 90, c = 90 - 2a. The condition a+6 <= 90-2a implies 3a <= 84, so a <= 28. If a=28, b=34, c=34. This satisfies a <= b <= c.