CAT Average Questions

Average Questions on CAT: The questions based on averages are quite frequent in the quantitative section of the CAT. These questions are generally related to basic and elementary maths skills and so, most of the candidates can easily solve the given average questions on CAT. But, as the CAT exam is all about time, being able to quickly solve CAT quantitative aptitude questions is very crucial. Please refer BYJU’S CAT College Predictor tool.

To help the CAT aspirants prepare average questions on CAT more effectively, detailed lessons on averages are given here. Also, some useful shortcut techniques are explained which can help to find the average along with various illustrations.

What are CAT Average Questions?

Averages can be defined as the central value in a set of data. The average can be calculated simply by dividing the sum of all values in a set by the total number of values. In other words, an average value represents the middle value of a data set. The data set can be of anything like age, money, runs, etc.

The Average Questions for CAT is an important chapter and it comes under CAT quants. The candidates who are appearing in the upcoming exam must practice CAT average questions to score a good rank in this section.

Average = [ Sum of Data (or observations) in a set / Number of data (or observations) in that set]

Average Questions on CAT – Example

Below are some important examples of average questions that you can follow to complete your CAT Preparation.

Example:

What is the average of the first five consecutive odd numbers?

Solution:

The first five consecutive odd numbers are 1, 3, 5, 7, 9.

Here, the number of data or observations is 5 and the sum of these 5 numbers is 25.

So, average = 25 / 5 = 5.

Also Check:

For More Information On Average, Ratio and Proportions, Watch The Below Videos:

Average Questions for CAT – Shortcut Techniques in Averages

Questions based on averages can be easily solved using shortcuts. By using shortcuts, any question can be solved quickly and efficiently which can save a lot of time. So, some shortcuts to solve average questions are explained below along with illustrations.

• Shortcut to find average or change in average from a set of values

Example 1:

The average of a batsman in 16 innings is 36. In the next innings, he is scoring 70 runs. What will be his new average?

1. a) 44
2. b) 38
3. c) 40
4. d) 48

Solution:

Conventionally solving:

New average = (old sum+ new score)/(total number of innings) = ((16 ×36)+70)/((16+1)) = 38

Shortcut technique:

Step 1) Take the difference between the new score and the old average = 70 – 36= 34

Step 2) This is 34 extra runs which are spread over 17 innings. So, the innings average will increase by 34/17 = 2

Step 3) Hence, the average increases by => 36+2 = 38.

Here are a few more average questions and their solutions using the same technique.

Example 2:

The average mark of 19 children in a particular school is 50. When a new student with marks 75 joins the class, what will be the new average of the class?

Solution:

Step 1) Take the difference between the old average and the new marks = 75-50=25

Step 2) This score of 25 is distributed over 20 students => 25/20 = 1.25

Step 3) Hence, the average increases by 1.25=> 50+1.25 = 51.25.

Here is another question where the average dips.

Example 3:

The average age of Mr. Mark’s 3 children is 8 years. A new baby is born. Find the average age of all his children.

Solution:

The new age will be 0 years. The difference between the old average and the new age = 0-8= -8

This age of 8 years is spread over 4 children => (-8/4= -2) Hence, the average reduces to 8-2= 6 years.

• Shortcut to find new value when the average is given

Now here is a technique that will help to compute the new value when the average is given. Take this question for example:

Example 1:

The average age of 29 students is 18. If the age of the teacher is also included the average age of the class becomes 18.2. Find the age of the teacher.

1. a) 28
2. b) 32
3. c) 22
4. d) 24

Solution:

Conventionally solving,

Let the average age of the teacher = x

(29 × 18 + x × 1)/30

Solving for x, we get x = 24.

Shortcut Technique

Using the shortcut, based on the same method used previously:

Step 1: Calculate the change in average = 18.2 – 18 = 0.2.

This change in 0.2 is reflected over a sample size of 30.

The new age is increased by 30 × 0.2 = 6 years above the average i.e. 18 + 6 = 24; which is the age of the teacher.

Thinkquest- The average age of 26 students in an MBA school is 30. One student among these quits school in between. Can you find the age of that student if the new average is 29.8?

Illustrations On CAT Averages

Question 1:

The average number of goals scored by 15 selected players in EPL is 16. The maximum number of goals scored by a player is 20 and the minimum is 12. The goals scored by players is between 12 and 20. What can be the maximum number of players who scored at least 18 goals?

1. a) 10
2. b) 5
3. c) 9
4. d) 6
5. e) None of these

Solution: Option (c)

To maximize the number of players who scored 18 goals or more, one should assume that only one person has scored 20. To counter him, there will be one person who will score 12 goals.

i.e. 15 – 2 = 13 players left.

Now to maximize the 18 and above goals for every two players who are scoring 18, there will be one player scoring 12. This is done, to arrive at an average of 16. We will have 8 players with a score of 18 and 4 players with a score of 12. The last player will have a score of 16 Thus, the maximum number of people with 18 and more goals = 9.

Question 2:

The average weight of a group of 8 girls is 50 kg. If 2 girls R and S replace P and Q, the new average weight becomes 48 kg. The weight of P= Weight of Q and the weight of R= Weight of S. Another girl T is included in the group and the new average weight becomes 48 kg. Weight of T= Weight of R. Find the weight of P.

1. a) 48 kgs
2. b) 52 kgs
3. c) 46 kgs
4. d) 56 kgs

Solution: Option (d)

8 x 50 +R+S-P-Q= 48×8 R+S-P-Q=-16

P+Q-R-S= 16 R=S and P=Q

P-R=8

One more person is included and the weight = 48 kg

Let the weight be a = (48 × 8 + a)9/9 = 48

A = 48 kg= weight of R

=> Weight of P= 48+8= 56 kg.

Tips to Prepare CAT Average Questions

The candidates may know that average questions are one of the most important chapters of the CAT Syllabus of QA. Candidates must focus on their mental calculating abilities as well as practise the fundamental ideas and formulas. Here are a few pointers that the candidates must follow at the time of preparation.

• The chapters from average questions for CAT should be practised as much as possible by aspirants.
• Keep notebooks where you can record all the key theorems and formulas. Spend your free time editing them.
• After finishing the curriculum, work through the previous years’ question paper to gain an understanding of the level of complexity of the CAT Average Questions.
• Take CAT mock tests, then review your errors.

To know more about such shortcut tricks and methods for average questions for CAT, stay tuned with BYJU’S. Also, get the latest exam pattern and CAT sample papers along with various engaging videos to effectively prepare for the exam.