GMAT Weighted Average - Tutorial and Questions

GMAT Weighted AverageAverage Question is an important topic in GMAT problem solving and data sufficiency. Let us start with the Basics.
Average (Arithmetic Mean)

Average of n numbers a1, a2, a3, a4, a5....an

(An) = (a1+a2+.....an) /n

Example: Find the average of 34, 56, 75 and 83


a1 = 34
a2= 56
a4 = 83

Total Number of Elements (n) = 4

Average (An) = (a1+a2+a3+a4)/n
= (34 + 56 + 75 + 83)/4 = 62

Shortcut to Remember:  An x n = a1+a2+.......an

Let us straight away apply this shortcut

Q) The average of four numbers is 20. If one of the numbers is removed, the average of the remaining numbers is 15. What number was removed?

(A) 10
(B) 15
(C) 30
(D) 35
(E) 45


Four Numbers = a1, a2, a3, a4


An = 20

An x n = a1 + a2 + a3 + a4

20 x 4 = a1 + a2 + a3 + a4 -> Statement 1

Let us assume that a4 has been removed

n = 3

15 x 3 = a1 + a2 + a3 -> Statement 2

Statement 1 – Statement 2

A4 = 35

Answer = D

So the point to remember here is Arithmetic Mean and Average are the same.

In GMAT, you are unlikely to encounter easy questions like the one above. A more probable question type is Weighted Average Question.

Weighted Average

When we have groups of numbers whose individual averages are known then Weighted Averages will help us find the average of the entire group.

Boring theory! Let us dive into some formulas.

Suppose we have N groups with averages a1,a2,a3,a4 ....aN and n1,n2,n3.....nN represents the number of elements in each group then

Weighted Average = ( n1*a1 + n2*a2 + n3*a3 + ....nN*aN )/(n1+n2...nN)

Got it?

Shortcut to Remember:  Wn x nN = n1*a1+n2* a2+.......nN*aN

Try this question:

Q) The average rainfall for the week was 2.5cm. The first 2 days was 2.5 cm, the next 4 days was 2cm. What was the average rainfall for the last day of the week?

a)    2.75
b)    2.5
c)    4.5
d)    4.75


Wn x nN = n1*a1+n2* a2+.......nN*aN

Wn = 2.5cm
nN = 7

n1 = 2
a1 = 2.5cm

n2 = 4
a2 = 2cm

n3= 1

2.5 x 7 = 2 x 2.5 + 4 x 2 + 1 x a3

17.5 = 5+8+a3

A3= 4.5

Average rainfall for the last day of the week = 4.5 cm

Want a little more tricky type?

Q) John scored 45 out of 50 in his last two tests. In his first test, he topped the class with 50 out of 50. What is his average percentage score?

Hint: The only tricky part is to convert the scores to percentages before solving the question

GMAT Average Age Question

This is a common question seen in GMAT. You will be given the average age of a group of people, x years ago and another average x – n years ago.

Remember this rule

If average age of a group of people is x years

n years from now the average age of a group of people would be x + n

n years before the average age of a group of people would be x - n

Ready for a Question?

Q) The average age of a husband, his wife and son 3 years ago was 29 years and that of his wife and son 5 years ago was 21 years. What is the husband’s present age?

Answer: We don’t have the value of x but we have x-n

X – 3 = 29

X = 32

Average age of Husband Wife and Son, now is 32 Years

X = (Husband + Wife + Son)/3

A (Husband, Wife and Son) = 32

Husband + Wife + Son = 32 x 3 = 96 --> Statement 1

Let the average age of Wife and Son be Y

Y – 5 = 21

Y = 26

A (Wife, Son) = 26

Wife + Son = 26 x 2 = 52 --> Statement 2

Statement 1 – Statement 2

Husband = 96 – 52 = 44

Shortcut to Solve GMAT Weighted Average

If Leo bought two black shirts for $55 each and three blue shirts for $65 each, what is the average that Leo paid for the 5 shirts?

(A) $62.00
(B) $61.00
(C) $63.00
(D) $65.00
(E) $59.00


Average Leo Paid for the 5 Shirts = (2 x 55 + 3 x 65)/ 5 = 61

Where is the freaking shortcut?  :)

Here is the deal.

In Weighted average question if the first average is lower than the second number, you don't have to do all the calculations.

Put the first average as 0

Second Number is greater than first by 10

Weighted Average (3 x 10)/5 = 6

Actual Weighted Average = Add 6 to 0 (or the first average) = 6 + 55 = 61 (Voila)

Weighted Average or Average Leo Paid for the shirts = 61

Recommended GMAT Course: Veritas Prep Full Course (42 Hours / 7 Weeks)

Recommended Books

Full Study Kit (Comprehensive GMAT Preparation Kit)

1) Includes 12 books used in Veritas Prep GMAT Course.
2) Thousands of practice problems with solutions
3) Five Computer Adaptive practice tests

Essential GMAT Reading Comprehension Guide

After reading F1GMAT’s Essential GMAT Reading Comprehension Guide, you will:

1. Complete GMAT RC Questions in less than 1 minute and 50 seconds
2. Read Faster
3. Take Notes Effectively
4. Collect and Interpret Facts
5. Speed up Summary Creation
6. Remember Information
7. Question the Author   
8. Learn to Answer GMAT Reading Comprehension Title question   
9. Learn to Answer GMAT Reading Comprehension Main Idea Question   

10.Learn to Answer GMAT Reading comprehension Inference question

11. Learn to Answer GMAT Reading Comprehension Detail Question   

12. Learn to Answer GMAT Reading Comprehension Purpose Question
12. Learn to Answer GMAT organization of passage Question
13. Learn to identify the style/tone or attitude of the author

Download Essential GMAT Reading Comprehension Guide (2019 Edition) (100+ New Questions)

Mastering GMAT Critical Reasoning

After you read F1GMAT’s Mastering GMAT Critical Reasoning Guide, you will learn:

How to overcome flawed thinking in GMAT Critical Reasoning?  

How to spot Inconsistencies in Arguments  

How to eliminate out of scope answer choices using Necessary and Sufficient Conditions  

How to Paraphrase GMAT Critical Reasoning Question  

How to Answer Assumption Question Type  

How to Answer Conclusion Question Type  

How to Answer Inference Question Type  

How to Answer Strengthen Question Type  

How to Answer Weaken Question Type  

How to Answer bold-faced and Summary Question Types  

How to Answer Parallel Reasoning Questions  

How to Answer the Fill in the Blanks Question

Download Mastering GMAT Critical Reasoning (2019 Edition) (25+ New Questions)

Navigate F1GMAT

F1GMAT Services (MBA Applicants) 

F1GMAT's Books

MBA Salary(Latest Salary Data)
MBA Admission Interview Tips



MBA Application Essays

MBA Recommendation Letter

GMAT Tutorials

GMAT Question Bank

Top MBA Programs

Get F1GMAT's Newsletters (Best in the Industry)
Included in the Newsletter:

  • Ranking Analysis
  • Post-MBA Salary Trends
  • Post-MBA Job Function & Industry Analysis
  • Post-MBA City Review
  • MBA Application Essay Tips
  • School Specific Essay Tips
  • GMAT Preparation Tips
  • MBA Admission Interview Tips
  • School Specific Interview Tips
  • Funding Guidance and
  • Special Consultation Service (only for Subscribers)

Subscribe to F1GMAT's Newsletter