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

Three students Pankaj, Ravinder and Rahul took a Maths test of 25 marks. The passing marks were 38%. When asked about marks, the teacher said: 1. Each one of them secured different marks. 2. The sum of the marks secured by the highest and lowest scorers among the three is 13. 3. If 2 is added to the average marks secured by all three of them, the result is the marks secured by one of them who secured neither the lowest nor the highest marks. How many of them passed the test?

  1. 0

  2. 1

  3. 2

  4. Data inadequate

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Passing marks = 25 * 0.38 = 9.5. Let marks be x, y, z (x < y < z). x+z = 13. (x+y+z)/3 + 2 = y. x+y+z + 6 = 3y => x+z + 6 = 2y => 13 + 6 = 2y => y = 9.5. Since y=9.5 is not an integer (assuming marks are integers), this is tricky. If y=9.5, then x+z=13. Possible sets: (4, 9.5, 9) - no. If marks are not integers, 2 passed (y and z).

Multiple choice

There are 21 balls in a bag, out of which 20 are black and 1 is blue. The average of black balls is x kg and total weight of all the 21 balls is 61 kg. If none of the balls is more than 3 kg and weights of all balls are integers, find the weight of the blue ball.

  1. 1

  2. 2

  3. 3

  4. Data inadequate

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

The total weight is 61 kg for 21 balls. The average of 20 black balls is x, so their total weight is 20x. Thus, 20x + weight_blue = 61. Since weights are integers and max weight is 3, 20x must be 60 (if x=3) or 40 (if x=2). If 20x=60, blue=1. If 20x=40, blue=21 (impossible). However, the problem does not provide enough constraints to uniquely determine x.

Multiple choice

The average age of children in a room is 32 years. 9 more children join the children in the same room whose average age is 26 years, and thereby decrease the average age of the all the children in the room by 3 years. Find the number of children in the room initially.

  1. 5

  2. 9

  3. 11

  4. 17

  5. 22
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the initial number of children. Total age = 32n. New total age = 32n + 9 * 26. New average = (32n + 234) / (n + 9) = 32 - 3 = 29. 32n + 234 = 29n + 261 => 3n = 27 => n = 9.

Multiple choice

There are 60 students in a class. The students are divided into three groups A, B and C of 15, 20 and 25 students, respectively. The groups A and C are combined to form group D. What is the average weight of the students in group D?

  1. More than the average weight of students in group A

  2. More than the average weight of students in group C

  3. Less than the average weight of students in group C

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The average weight of group D depends on the individual weights of students in groups A and C. Since no information about the weights is provided, the combined average cannot be determined.

Multiple choice

Directions: The following problem consists of a question followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. 11 people appeared for examinations A and B each. The total marks scored by the people who appeared for examination A were 366. What is the total of the marks obtained by the people who appeared for examination B? (I) Average marks scored by the top five performers who appeared for examination B were 4 more than the average marks scored by the top five performers who appeared for examination A. (II) Total marks of the bottom six performers who appeared for examination B were 7 less than the total marks of the bottom six performers who appeared for examination A.

  1. The question can be answered by using statement I alone but cannot be answered using the other statement alone.

  2. The question can be answered by using statement II alone but cannot be answered using the other statement alone.

  3. The question can be answered by using either of the statements alone.

  4. The question can be answered using both of the statements together, but cannot be answered using either of the statements alone.

  5. The question cannot be answered even by using both the statements together.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives the average of the top 5, and Statement II gives the total of the bottom 6. Neither alone provides the total for all 11 people in exam B, as we do not know the marks of the middle person or the specific distribution. Together, we can relate the total marks of B to A, but the problem is missing the total marks for exam B's top 5 or bottom 6 specifically relative to A's total. However, standard logic for these types of problems usually requires both to establish a relationship.

Multiple choice

What is the average weight of the class? (1) The class has ten students. (2) If one more student, whose weight is twice the average weight of the class, joins the class, the average increases by 2.

  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

Statement 1 gives the count but not the weights. Statement 2 relates the new average to the old average but requires the number of students to solve for the specific average value. Together, we have n=10, and if the new student weight is 2A, the new average is (10A + 2A)/11 = A + 2. This allows solving for A.

Multiple choice

In an FBT recruitment class, the average weight of 48 candidates is 70 kg. If the heaviest candidate and the candidate who is 50 kg are rejected, then the average weight drops by 2 kg. Find the weight of the heaviest candidate.

  1. 76 kg

  2. 182 kg

  3. 112 kg

  4. 220 kg

  5. 190 kg
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial total weight = 48 * 70 = 3360. After removing two, weight = 46 * 68 = 3128. The sum of the two removed is 3360 - 3128 = 232. If one is 50, the other is 232 - 50 = 182.

Multiple choice

In an examination, the average was found to be 60 marks. Due to some error, marks of the 100 candidates had to be changed from 110 to 70 each and average came down to 40 marks. Total number of candidates who took the examination were

  1. 200

  2. 300

  3. 400

  4. 600

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let N be the number of candidates. Initial sum = 60N. Change = 100 * (70 - 110) = -4000. New sum = 60N - 4000. New average = 40 = (60N - 4000) / N. 40N = 60N - 4000. 20N = 4000. N = 200.