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

A zoo has a group of 30 animals consisting of elephants and zebras. The average weight of an elephant is 6,000 kg, and the average weight of a zebra is 400 kg. If the total weight of all animals is 79,200 kg, how many elephants are there in the zoo?

  1. 8

  2. 9

  3. 10

  4. 12

  5. 15
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let E be elephants and Z be zebras. E + Z = 30, so Z = 30 - E. 6000E + 400(30 - E) = 79200. 6000E + 12000 - 400E = 79200. 5600E = 67200. E = 67200 / 5600 = 12.

Multiple choice

In a community sports event, there are 60 participants comprising athletes and coaches. The average score of the athletes is 82 points, while the average score of the coaches is 90 points. If the overall average score of all participants is 84 points, what is the ratio of the number of athletes to the number of coaches in the event?

  1. 3 : 1

  2. 1 : 3

  3. 2 : 5

  4. 5 : 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the allegation method: (Athletes average 82, Coaches average 90, Total average 84). The difference between 90 and 84 is 6, and between 84 and 82 is 2. The ratio of athletes to coaches is 6:2, which simplifies to 3:1.

Multiple choice

A total of 30 students are arranged in a grid for morning assembly, with 6 rows and 5 columns. Each of the 30 positions in the grid represents the height of a student. The average height (in cm) of the students in row i is Ri (1 ≤ i ≤ 6). The average height of the students in column j is Cj (1 ≤ j ≤ 5). What is the value of R6? (1) C1 + C2 + C3 + C4 + C5 = 850 (2) R1 + R2 + R3 + R4 + R5 = 850

  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 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
C Correct answer
Multiple choice

In a certain class, some students donated cans of food to a local food bank. What was the average (arithmetic mean) number of cans donated per student in the class? 1. The students donated a total of 56 cans of food. 2. The total number of cans donated was 40 greater than the total number of students in the class.

  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 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
C Correct answer
Explanation

Let C be total cans and S be total students. We want C/S. Statement 1: C = 56. We don't know S. Statement 2: C = S + 40. We have two variables and only one equation. Together: 56 = S + 40 => S = 16. Average = 56/16 = 3.5. Both are needed.

Multiple choice

Last school year, each of the 200 students at a certain high school attended the school for the entire year. If there were 8 cultural performances at the school during the last school year, what was the average (arithmetic mean) number of students attending each cultural performance? 1. Last school year, each student attended at least one cultural performance. 2. Last school year, the average number of cultural performances attended per student was 4.

  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 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
B Correct answer
Explanation

Statement 2 gives the average number of performances per student (4). Total attendances = 200 students * 4 = 800. Average per performance = 800 / 8 = 100. Statement 1 is insufficient as it doesn't provide the total number of attendances.

Multiple choice

Directions: The below table gives the details of three categories of students studied in an institution. Study the table carefully and answer the following questions. (Rounded off to two decimal points) Details of students over the given years Level Primary Level Secondary level Higher secondary level Grade Average Good Outstanding Average Good Outstanding Average Good Outstanding 2012 120 75 35 100 68 24 98 82 29 2013 115 68 34 98 75 22 89 78 37 2014 132 54 30 105 60 25 95 90 29 2015 145 64 25 110 70 28 102 75 34 2016 128 60 28 125 78 18 99 88 28 2017 110 80 32 120 56 21 110 90 32 Write the increasing order of outstanding students according to their percentage.

  1. 2016 < 2015 < 2017 < 2014 < 2012 < 2013

  2. 2016 > 2017 > 2015 > 2012 > 2014 > 2013

  3. 2016 < 2015 < 2017 < 2014 < 2013 < 2012

  4. 2016 < 2017 < 2015 < 2014 < 2012 < 2013

  5. 2017 > 2015 < 2016 < 2014 < 2013 < 2012
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labeled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. If the average score of three students, Alice, Ben, and Chris, in a mathematics test is 75, what could be the score of Chris? (1) The total score obtained by all three is 225. (2) The average score of Alice and Ben is 80.

  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 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
B Correct answer
Explanation

The average of three students is 75, so the sum is 225. Statement (1) just confirms the sum, which is already known from the average, so it is not sufficient to find an individual score. Statement (2) gives the average of Alice and Ben as 80, so their sum is 160. Subtracting this from the total sum of 225 gives Chris's score as 65, which is sufficient.

Multiple choice

In a classroom, three students - Alice, Bob, and Charlie have different scores in mathematics test. Alice scored 60 marks, Bob scored 70 marks, and Charlie scored 80 marks. After re-evaluation, Alice's marks increased by 5%, Bob's marks increased by 10%, and Charlie's marks decreased by 10%. What is the approximate percentage increase in the average score of the these three students after the re-evaluation?

  1. 0.81%

  2. 0.75%

  3. 0.25%

  4. 0.96%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial average = (60+70+80)/3 = 70. New scores: Alice 60*1.05 = 63, Bob 70*1.10 = 77, Charlie 80*0.90 = 72. New sum = 63+77+72 = 212. New average = 212/3 = 70.666. Percentage increase = ((70.666-70)/70)*100 = 0.666/70 * 100 = 0.952%.

Multiple choice

DIRECTION for the question: Solve the following question and mark the best possible option. A team of 8 person joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored?

  1. 588

  2. 645

  3. 665

  4. 672

  5. 555
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the best marksman had scored 92, the total would be 8 * 84 = 672. His actual score was 7 points lower, so the team's actual total was 672 - 7 = 665.

Multiple choice

Alifa's marks in 5 subjects are in ratio 10:9:8:7:6. Passing marks = 50%. If she scores an average of 60%, how many subjects did she pass?

  1. 1

  2. 2

  3. 3

  4. 4

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

Let the marks be 10x, 9x, 8x, 7x, 6x. Total = 40x. Average = 8x. Given average = 60%, so 8x = 60, x = 7.5. The marks are 75, 67.5, 60, 52.5, 45. Passing marks = 50% of 100 (assuming max 100) = 50. The subjects with marks >= 50 are 75, 67.5, 60, 52.5. That is 4 subjects.