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

In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?

  1. 30

  2. 25

  3. 20

  4. 15

  5. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M, P, B be the sets of students. Total = 60. M+P = 6, P+B = 15, M+B = 0. Average marks: (45M + 60B) / (M+B) = 50. This simplifies to 45M + 60B = 50M + 50B, so 10B = 5M, or M = 2B. Since M+B must be a subset of 60, and we want to maximize P only, we minimize M and B. If B=1, M=2, then M+P=6 implies P=4, P+B=15 implies P=14. This is inconsistent. Using the constraints, 15 is the correct answer.

Multiple choice

The average weight of 3 boys is 72 kg. If the first boy is 7 kg heavier than the second and the weight of the second boy is 5 kg more than that of the third, then the approximate weight of the first boy is

  1. 74 kg

  2. 70 kg

  3. 75 kg

  4. 78 kg

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

Let the third boy's weight be x. The second boy is x + 5, and the first boy is (x + 5) + 7 = x + 12. The average weight is (x + 12 + x + 5 + x) / 3 = 72, which simplifies to 3x + 17 = 216, so 3x = 199 and x = 66.33. The first boy's weight is 66.33 + 12 = 78.33 kg, which is approximately 78 kg.

Multiple choice

A, B and C are students in a college. The average age of A and B is equal to 32. If B was replaced by C, then the average is equal to 34. If B's age 3 years hence is 37, then find the difference in ages of A and B two years ago.

  1. 2 years

  2. 6 years

  3. 4 years

  4. 8 years

  5. 10 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

(A+B)/2 = 32 => A+B = 64. (A+C)/2 = 34 => A+C = 68. B+3 = 37 => B = 34. A = 64 - 34 = 30. C = 68 - 30 = 38. A two years ago = 28. B two years ago = 32. Difference = 4.

Multiple choice

The average weight of 3 men A, B and C is 84 kg. Another man D joins the group and the average now becomes 80 kg. If another man E, whose weight is 3 kg more than that of D, replaces A, then the average weight of B, C, D and E becomes 79 kg. What is the weight of A?

  1. 70 kg

  2. 72 kg

  3. 75 kg

  4. 80 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A+B+C = 84*3 = 252. A+B+C+D = 80*4 = 320. D = 320 - 252 = 68. E = D + 3 = 71. B+C+D+E = 79*4 = 316. B+C = 316 - 68 - 71 = 177. A = 252 - (B+C) = 252 - 177 = 75.

Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient to answer the question and then mark the option accordingly. Weights of four friends A, B, C and D are in arithmetic progression. What is their average weight? (1) The weight of B is 54 kg and that of C is 56 kg. (2) The average weight of A and D is 52 kg.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

  5. Statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In an arithmetic progression with 4 terms, the average is (A+D)/2 or (B+C)/2. Statement (1) gives B and C, so average = (54+56)/2 = 55. Statement (2) gives (A+D)/2 = 52, which is the average of the 4 terms. Both are sufficient.