PROBLEMS ON NUMBERS -> DESCRIPTION

In this section, questions involving a set of numbers are put in the form of a puzzle. You have to analyse the given conditions, assume the unknown the numbers and form equations accordingly, which on solving yield the unknown numbers.

AVERAGE -> IMPORTANT FACTS AND FORMULAE 

I. Average = [Sum of observations / Number of observations] 

II. Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is [2xy / x + y] kmph.

Numbers -> IMPORTANT FACTS AND FORMULAE 

1. Natural Numbers : Counting numbers 1, 2, 3, 4, 5, .. are called natural numbers. 

II. Whole Numbers : All counting numbers together with zero form the set of whole numbers. 

Thus, I. 0 is the only whole number which is not a natural number.  

II. Every natural number is a whole number. 

III.Some Important Formulae :

 I. ( 1 + 2 + 3 + .....+ n) = n (n + 1 ) / 2 

II. (1 2 + 22 + 32 + ..... + n2) = n ( n + 1 ) (2n + 1) / 6 

III. (1 3 + 23 + 33 + ..... + n3) = n2 (n + 1)2 / 4 

Average

1. In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
A. 6.25	B. 5.5
C. 7.4	D. 5

Answer : Option A

Explanation :

Runs scored in the first 10 overs = 10×3.2=32

Total runs = 282

remaining runs to be scored = 282 - 32 = 250

remaining overs = 40

Run rate needed = 25040=6.25

2. A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
A. 4800	B. 4991
C. 5004	D. 5000

Answer : Option B

Explanation :

Let the sale in the sixth month = x

Then 6435+6927+6855+7230+6562+x6=6500

=> 6435 + 6927 + 6855+ 7230 + 6562 + x = 6 × 6500 = 39000

=> 34009 + x = 39000

=> x = 39000 - 34009 = 4991