NUMBERS – Important Notes/Formulae

(1) Sample Q: Find the min no. of identical square tiles required to cover up a rectangular area of with dimensions ‘x’ and ‘y’ units
Solution: Ans = (Total rectangular area / Area of the square)

(2) Find the number of 5’s present when the numbers from 1-500 are written down on a sheet of paper.
Solution: Instead of counting the number of 5’s totally, spit the no. of 5’s by the place of the digits.
No. of 5’s in unit digit = 5*10 = 50
No. of 5’s in ten’s digit = 5*10 = 50
No. of 5’s in hundred’s digit = 1 = 1 → Ans = 101

(3) Find the minimum no. of standard weights required for measuring any whole number weight upto 38Kg?
This question can also be asked as : Find the minimum no. of positive integers which can produce all numbers between 1-38 by either addition or subtraction.
Solution:
For this type of question add up the power of 3, as shown below
(3^0) + (3^1) + (3^2) + (3^3) = 1+3+9+27=40 (>38)
Hence using 1kg, 3kg, 9kg, 27kg weights alone we can measure any weight between 1-38. → Ans = 4 weights

(4) There are ‘a’ apples, ‘b’ bananas and ‘m’ mangoes, Find the maximum no. of boxes required to arrange the fruits so that no. of fruits in each box is the same and the no. of fruits of each variety in each box is the same.
Ans = HCF (a,b,m)