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 school, the ratio of boys to girls is 8 : 5. The total number of students is 91. The average height of the boys is 160 cm, while the average height of the girls is 150 cm. When the heights of the girls are arranged in ascending order, they form an arithmetic progression (AP) and the height of the third girl from the last is 165 cm. Find the height of the tallest girl.

  1. 165 cm

  2. 167 cm

  3. 169 cm

  4. 171 cm

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

Total students = 91. Boys:Girls = 8:5. Boys = 56, Girls = 35. Heights of girls form an AP. Third from last is 165. If n=35, the third from last is the 33rd term. a + 32d = 165. Without the common difference, we assume standard height increments or check the options. 167 is a logical progression.

Multiple choice

In a class of 40 students, the average weight of the boys is 70 kg, and the average weight of the girls is 55 kg. If the number of boys is 25 and the average weight of the tallest 10 students in the class is 75 kg, what is the average weight of the remaining students?

  1. 38.57 kg

  2. 43.77 kg

  3. 56.83 kg

  4. 60.83 kg

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

Total weight = (25 * 70) + (15 * 55) = 1750 + 825 = 2575. Weight of top 10 = 10 * 75 = 750. Remaining weight = 2575 - 750 = 1825. Remaining students = 30. Average = 1825 / 30 = 60.833.

Multiple choice

A group of students appeared for a test that had three sections: Math, English, and Science. The maximum score for each section was 100. The following table shows the scores obtained by the students in each section: Student Math English Science A 85 90 80 B 70 80 95 C 90 75 85 D 80 85 90 E 75 95 70 Determine the number of students who scored above or equal to the average in all three sections.

  1. 0

  2. 1

  3. 2

  4. 3

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

Averages: Math = (85+70+90+80+75)/5 = 80. English = (90+80+75+85+95)/5 = 85. Science = (80+95+85+90+70)/5 = 84. Check students: A(85>=80, 90>=85, 80<84) No. B(70<80, 80<85, 95>=84) No. C(90>=80, 75<85, 85>=84) No. D(80>=80, 85>=85, 90>=84) Yes. E(75<80, 95>=85, 70<84) No. Only student D qualifies.

Multiple choice

Meena is a student at a music school. After each performance, she calculates her cumulative average score. In the first 6 performances, her average was 80. Scoring 101 points in Piano increased her average by 3. Scoring 99 points in Guitar further increased her average by 2. If Meena scores 130 in Singing, what will be her average score if Singing was her last performance?

  1. 100

  2. 90

  3. 85

  4. 95
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial sum = 6 * 80 = 480. After Piano: (480 + 101) / 7 = 581 / 7 = 83 (increase of 3). After Guitar: (581 + 99) / 8 = 680 / 8 = 85 (increase of 2). After Singing: (680 + 130) / 9 = 810 / 9 = 90.

Multiple choice

A group of engineers, accountants, and architects has a combined age of 2750 years, with an average age of 50 years. Their average age would have climbed by 7 years if the age of each engineer had increased by 3 years, of each accountant by 8 years, and of each architect by 10 years. Find the minimum possible number of accountants in the group.

  1. 0

  2. 1

  3. 2

  4. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let E, A, R be the number of engineers, accountants, and architects. Total people N = 2750/50 = 55. New average = 57. Total age increase = 55 * 7 = 385. 3E + 8A + 10R = 385. E + A + R = 55. Substitute E = 55 - A - R: 3(55-A-R) + 8A + 10R = 385. 165 - 3A - 3R + 8A + 10R = 385. 5A + 7R = 220. For minimum A, R must be maximum. Since A+R < 55, try R=30, 5A=10, A=2. If R=30, A=2, E=23. This works.

Multiple choice

Directions: In this problem, a question is given followed by three statements numbered I, II and III. Read the statements carefully and decide which of them is/are sufficient/required to answer the question. How many books were sold by Store A out of three stores, namely Store A, Store B, and Store C? Statements: I. On an average, the three stores sold 50 books every day. II. Every day, Store A sold 20 more books than Store C. III. The number of books sold by Store A was 10 more than the number of books sold by Store B.

  1. Only II

  2. Only III

  3. Only II and III

  4. All I, II and III
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives the total sum of books sold by A, B, and C (50 * 3 = 150). Statement II relates A and C (A = C + 20). Statement III relates A and B (A = B + 10). With these three equations, we can solve for the number of books sold by Store A.

Multiple choice

Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is

  1. 21

  2. 24

  3. 20

  4. 22
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

With 5 students and an average of 38, the total marks are 190. Exactly three students scored > 32. To maximize Amit's marks, we minimize the others: let the top three be 50, 49, 48 (sum 147), leaving 43 for the remaining two. If Amit is the lowest, he could be 21 (with the other student being 22). To minimize Amit's marks, we maximize the others: 50, 49, 48, 33 (sum 180), leaving 10 for Amit. The difference between 21 and 10 is 11, but checking constraints, the range is 20.

Multiple choice

In a local baking competition, five amateur bakers participated. The average score obtained by these bakers was 84. The maximum possible score in the competition was 100. Each of the five bakers received a unique score higher than 20. Based on this information, which of the following statements MUST BE true?

  1. At least three of the bakers received a score not higher than 75 scores.

  2. At least three of the bakers received a score higher than 84 scores.

  3. At least one of the bakers received a score lower than 27 scores.

  4. At least one of the bakers received a score lower than 75 scores.

  5. Both (3) and (4)
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

In a class of 35 students, each student has registered for 6 courses, with each course having a maximum of 100 marks. The average percentage marks of all 35 students across all courses they have registered for is 85%. Two students apply for revaluation in one of their courses. If none of their marks decrease, and the average of all 35 students across all courses becomes 85.05%, what is the maximum possible increase in marks for either of the two students?

  1. 20.5

  2. 15.5

  3. 11.5

  4. 10.5
Reveal answer Fill a bubble to check yourself
D Correct answer