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CAT Questions| CAT Arithmetic Questions | Averages

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.

CAT Exam

YearNo of QuestionsGood attemptDifficulty
Slot 111Easy to Moderate
Slot 211Easy to Moderate
Slot 121 to 2Moderate
Slot 221Moderate to Difficult
Slot 111Moderate
Slot 211Moderate

CAT 2021 is expected to follow a similar difficulty level and paper pattern like previous years.

CAT Quantitative Aptitude questions | CAT Arithmetic: Averages

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.  

[CAT 2020]

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

 [CAT 2020] 

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

Basic concepts on averages

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

  • If a person travels a distance at a speed of x km/hr and the same distance at a speed of y km/hr then the average speed during the whole journey is given by-
  • If a person covers P km at x km/hr and Q km at y km/hr and R km at z km/hr, then the average speed in covering the whole distance is- {(P+Q+R) / ( [P/x] + [Q/y] + [R/z] ) }

When a person leaves the group, and another person joins the group in place of that person then-

  • If the average age is increased: Age of new person = Age of separated person + (Increase in average × total number of persons)
  • If the average age is decreased: Age of new person = Age of separated person – (Decrease in average × total number of persons)

When a person joins the group-

  • In case of increase in average: Age of new member = Previous average + (Increase in average × Number of members including new member)
  • In case of decrease in average: Age of new member = Previous average – (Decrease in average × Number of members including new member)
  • Average of n natural no’s=(n+1)/2
  • Average of even No=(n+1)
  • Average of odd No= n
  • General Formula = (1st number +Last number)/2

How to deal with preparation on Arithmetic Averages Questions

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.

Level 1

  • If a candidate is in the initial stages of preparation, he should follow the following steps:
  • Attempt and understand the basic concepts and formulas coming under averages questions and weighted average as well. Learn the basic concepts from MBAP CAT E Book (Concept Theory) study material, lecture notes.
  • Further understand in detail the differences between each concept of average and their efficient application by using live lectures
  • As of now do not go to shortcut methods for solving averages questions because that might hamper the understanding of the concept.
  • Practice beginner-level averages questions from MBAP CAT E Book (Practice Questions).

Level 2

  • This level is for the students who have cleared their concepts and are looking averages shortcuts faster methods like problems tricks and shortcuts to solve questions
  • Solve previous year CAT averages question with applying average short trick from MBAP Topic wise Previous Year CAT Question. Do not get stuck on one question and try to solve easy questions first.
  • This should help you to understand the techniques applicable in the questions on this concept and
  • short cuts that can be used
  • The arithmetic questions on averages often use the “points to remember” mentioned above, hence, they should be memorized
  • At this stage, the student should be comfortable in pointing out where to use average and weighted average respectively

Level 3

  • For advanced level preparation, start practicing problems on averages from the MBAP CAT Advance E books or from average aptitude questions pdf or from the book – How to Prepare for Quantitative Aptitude for the CAT, authored by Arun Sharma.
  • Arithmetic Questions in Arun Sharma are categorized into Level of Difficulty (LOD), based upon your preparation level, start attempting 3 or 4 questions daily.
  • Further solve questions from previous year CAT papers and look for solutions available.
  • At the same time look at the different approaches used to solve the same average question and how can the time be effectively reduced on using a particular approach

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