PPT Averages - CSAT Preparation - UPSC

 Page 1


Averages 
Page 2


Averages 
Introduction to Averages
Why It Matters
Core concept in Quantitative Aptitude & Data Interpretation.
Quick-solving saves time.
Definition
Example
First five natural numbers (1, 2, 3, 4, 5):
Sum = 15, Count = 5, Average = 15 / 5 = 3
Page 3


Averages 
Introduction to Averages
Why It Matters
Core concept in Quantitative Aptitude & Data Interpretation.
Quick-solving saves time.
Definition
Example
First five natural numbers (1, 2, 3, 4, 5):
Sum = 15, Count = 5, Average = 15 / 5 = 3
Key Properties of Averages
Property 1
Each number ± ( n ) ³ 
Average ± ( n ).
Example: 
Avg age 39 (5 people), after 1 
year ³ New avg = 39+1 = 40.
Property 2
Each number × or ÷ ( n ) ³ 
Average × or ÷ ( n ).
Example: 
Avg of 10, 20, 30 = 20 
if every number is ×2 
New avg = 20 × 2 = 40.
Property 3
Add value to half, subtract 
from other half ³ No change 
in avg.
Example: 
{10, 20, 30, 40} ³ add 5 to 
10, 20 and subtract 5 from 
30, 40 
Avg stays 25.
Page 4


Averages 
Introduction to Averages
Why It Matters
Core concept in Quantitative Aptitude & Data Interpretation.
Quick-solving saves time.
Definition
Example
First five natural numbers (1, 2, 3, 4, 5):
Sum = 15, Count = 5, Average = 15 / 5 = 3
Key Properties of Averages
Property 1
Each number ± ( n ) ³ 
Average ± ( n ).
Example: 
Avg age 39 (5 people), after 1 
year ³ New avg = 39+1 = 40.
Property 2
Each number × or ÷ ( n ) ³ 
Average × or ÷ ( n ).
Example: 
Avg of 10, 20, 30 = 20 
if every number is ×2 
New avg = 20 × 2 = 40.
Property 3
Add value to half, subtract 
from other half ³ No change 
in avg.
Example: 
{10, 20, 30, 40} ³ add 5 to 
10, 20 and subtract 5 from 
30, 40 
Avg stays 25.
PYQ
There are four numbers such that average of first two numbers is 1 more than the first number, average 
of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 
more than average of first three numbers. Then, the difference between the largest and the smallest 
numbers, is                                                                                                                                                                                                    
Ans: 15
Sol: Let the four numbers be
 a, a+2, a+7, and a+15
 Clearly, the above four numbers satisfy all the conditions given in the question.
 So, the required difference
 = (a+15) - (a)
 = 15
Page 5


Averages 
Introduction to Averages
Why It Matters
Core concept in Quantitative Aptitude & Data Interpretation.
Quick-solving saves time.
Definition
Example
First five natural numbers (1, 2, 3, 4, 5):
Sum = 15, Count = 5, Average = 15 / 5 = 3
Key Properties of Averages
Property 1
Each number ± ( n ) ³ 
Average ± ( n ).
Example: 
Avg age 39 (5 people), after 1 
year ³ New avg = 39+1 = 40.
Property 2
Each number × or ÷ ( n ) ³ 
Average × or ÷ ( n ).
Example: 
Avg of 10, 20, 30 = 20 
if every number is ×2 
New avg = 20 × 2 = 40.
Property 3
Add value to half, subtract 
from other half ³ No change 
in avg.
Example: 
{10, 20, 30, 40} ³ add 5 to 
10, 20 and subtract 5 from 
30, 40 
Avg stays 25.
PYQ
There are four numbers such that average of first two numbers is 1 more than the first number, average 
of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 
more than average of first three numbers. Then, the difference between the largest and the smallest 
numbers, is                                                                                                                                                                                                    
Ans: 15
Sol: Let the four numbers be
 a, a+2, a+7, and a+15
 Clearly, the above four numbers satisfy all the conditions given in the question.
 So, the required difference
 = (a+15) - (a)
 = 15
PYQ
If a certain amount of money is divided equally among n persons, each one receives Rs 352. However, if 
two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, 
each of them receive less than or equal to Rs 330. Then, the maximum possible value of n is                      
Ans: 16
Sol: Let the total amount be equal to T.
T = n × 352
<However, if two persons receive Rs 506 each and the remaining amount is divided equally among the 
other persons, each of them receive less than or equal to Rs 330=
So, the maximum value that n can take is 16.