In CAT problems on averages is a concept that is covered in Arithmetic topics like mixtures and allegations is an important concept since it forms the base of many other topics in the Quantitative ability section. Out of the total questions from this concepts, average concept forms around 10% of the questions. Other than the Quantitative ability section, this topic becomes of use in solving the Data interpretation and CAT Questions also.
You can use MBAP’s Free Actual average Questions and answer with Detailed Video and Text Solutions, which will help you crack CAT exam. For now, you can scroll down and Take Quick Quiz on this arithmetic absolutely free.
Some important averages concepts in aptitude from previous year CAT papers are given below which can help in the preparation of CAT 2021
1. 1. In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by.
Here a2 to a9 is common to both the terms
So, a1 + (a2 to a9) = 42 × 9
a10 + (a2 to a9) = 47 × 9
Solving these two a10 – a1 = 45
a1, a2, a3,……………, a9, (a1 + 45)
One instance is every number is 42
42, 42, …………………, 42, 42+45 (a1 to a9 are equal) ———–(1)
Another instance is every number is 47
47 – 45, 47, …………………, 47, 47 (a2 to a10 are equal) ———(2)
Mean of (1) = 46.5
Mean of (2) = 42.5
1. – (2) = 4
2. A batsman played n + 2 innings and got out on all occasions. His average score in these n + 2 innings was 29 runs scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first n innings. In these innings, his average score was 30 runs, and lowest score was x runs. The smallest possible value of x is
Let’s consider Tom’s age to be ‘x’ years.
Dick is thrice as old as Tom,
Dick’s age = 3 × x = 3x
Harry is twice as old as Dick,
Harry’s age = 2 × 3x = 6x
Dick’s age is 1 year less than the average age of all three,
3x = Average (x, 3x, 6x) – 1
3x = ((x + 3x + 6x)/3) – 1
3x = (10x/3) – 1
1 = (10x/3) – 3x
1 = (10x – 9x)/3
1 = x/3
x = 1
3. Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is [CAT 2019]
Let the score of Gautam =x
Total marks of all the students = 21*62 +x
As per question The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh,
Or (21*62 +x)/22 -1 = (21*62 +x – 82.5)/21
(21*62 + x -22)/22 = (21*62 +x – 82.5)/21
On solving x =51
4. 4. The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed What is the highest possible value of the average of these 20 integers? [CAT 2019]
Sum of all 30 integers =5*30 = 150
Minimum possible sum of remaining 10 integers = 10*6 = 60
(as all remaining 10 integers are greater than 5 so their sum will be minimum when they all are equal and each have value =6)
So some of 20 numbers = 150 – 60 = 90
Thus required avg = 90/20 = 4.5
An average or more accurately an arithmetic mean can be defining as the sum of n different data divided by n.
Averages of a group is defined as the ratio of sum of all the items in the group to the number of items in the group.
Average = (Sum of all items in the group)/ Number of items in the group
Find the Average Speed
When a person leaves the group, and another person joins the group in place of that person then-
When a person joins the group-
While solving Averages Questions of arithmetic, for the understanding of the candidate, we have divided the preparation into 3 levels for the upcoming CAT 2021.