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

Five Scores in a classroom are broken into Fiverespective different ranges:51-60,61-70,71-80,81-90 and91-100.The number of students who have scored ineach range is given below.51 to 60-3 students,61 to 70 - 8 students,71 to 80-7 students,81 to 90-4 students, and91 o 100-3 students.Furthermore, we know that the number ofstudents who scored 76 or more is atleast onemore than those who scored below 75. What isthe minimum possible average overall of thisclass?

  1. 74.2

  2. 75

  3. 69.2

  4. 70.6

  5. 72.6
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

The average age of 10 students and their teacher is 15 years. The average age ofthe first seven students is 15 yr and that of the last three is 11 yr. What is the teacher'sage?

  1. 33 years

  2. 30 years

  3. 27 years

  4. 24 years

  5. 23 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The total age of the 10 students and teacher is 11 x 15 = 165 years. The first seven students contribute 7 x 15 = 105 years, and the last three contribute 3 x 11 = 33 years. The teacher's age is 165 - 105 - 33 = 27 years.

Multiple choice

DIRECTION for the question: Solve thefollowing question and mark the best possibleoption.The average of 10 numbers is 40.2. Later it isfound that two numbers have been wronglycopied. The first is 18 greater than the actualnumber and the second number added is 13instead of 31. Find the correct average.

  1. 40.2

  2. 40.6

  3. 40.4

  4. 40.8

  5. 40.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial sum = 10 * 40.2 = 402. Error 1: 18 added instead of subtracted (or vice versa). The problem says 18 greater than actual, so subtract 18. Error 2: 13 added instead of 31, so add (31-13) = 18. Net change = -18 + 18 = 0. Correct sum = 402. Average = 40.2.

Multiple choice

A school's Science and Math clubs have different average ages. The average age of students in the Science club is 15 years, while the average age of students in the Math club is 17 years. If the average age of all students in both clubs combined is 16 years, what is the ratio of the number of students in the Science club to the number of students in the Math club?

  1. 1 : 1

  2. 1 : 3

  3. 1 : 2

  4. 2 : 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the allegation method, the difference between the average ages (15, 17) and the combined average (16) gives the ratio. |17-16| : |15-16| = 1 : 1.

Multiple choice

In a town, there were 35 students who took part in a quiz. The overall average score of these students was 76. Later, it was discovered that the average score of the first 18 students was 72.6, while the average score of the last 18 students was 77.4. When the score of the 18th student was excluded from the calculation, what was the new average score of the remaining students?

  1. 72.24

  2. 75.04

  3. 76.06

  4. 77.06
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total score of all 35 students is 35 * 76 = 2,660. The sum of the first 18 and last 18 students' scores is (18 * 72.6) + (18 * 77.4) = 1,306.8 + 1,393.2 = 2,700. Since the 18th student is included in both groups, their score is 2,700 - 2,660 = 40. Excluding this student leaves a total score of 2,620 for the remaining 34 students, resulting in a new average of 2,620 / 34 = 77.06.