In today’s article we are going to cover some essential formulae required for solving quantitative section of popular banking exams like SBI PO,IBPS PO among others.


Number systems and Simplification

Divisibility rules of…
2: last digit is even or 0  4: last two digits are divisible by 4  8: last 3 digits are divisible by 8 
3: Sum of digits is divisible by 3  6:Number is simultaneously divisible by 2 &3  9: Sum of digits is divisible by 9 
5: last digit is 5 or 0  10: last digit is 0  15:If the number is divisible by 3 and 5 
7: Unit’s place is multiplied by 2 and subtracted from the remaining digits and no obtained is divisible by 7  17: Unit’s place is multiplied by 5 and subtracted from the remaining digits and the number obtained is divisible by 17  14: If the number is divisible by 2 and 7 
11: Sum of digit’s at odd and even places are subtracted and the result is either 0 or the no obtained is divisible by 11  12: If it is divisible by 4 and 3  18: If it is divisible by 2 and 9 
13: If it’s unit place is multiplied by 4 and added to remaining digits and no obtained is divisible by 13  19: If it’s unit place is multiplied by 2 and added to remaining digits and no obtained is divisible by 19 
Examples:
1)Is 2289 divisible by 7?
Ans: 1st pass: 228 – (9 x 2) = 210
2nd pass: 21 – 0 = 21
21 is divisible by 7, hence 2289 is divisible by 7
2)Is 156 divisible by 13?
Ans: 1st pass: 15 + (4 x 6) = 15 + 24 = 39
39 is divisible by 13, hence 156 is divisible by 13
Sum series:
Sum of first n natural nos =
Sum of first n^{2} natural numbers =
Sum of first n^{3 } natural numbers =
Division Algorithm:
Dividend = (Divisor x Quotient) + Remainder
Total number of different divisors of a number X:
Step 1: Find all the possible prime factors of X
X = a^{x} + b^{y} + c^{z } + …
Step 2: Total number of divisors:
=(x + 1)(y + 1)(z+1)….
Example:
Question:Find total number of divisors of 15:
Ans:16 = 2^{4}
The total number of divisors of 16 = (4+1) = 5
If we check through normal way, divisors of 16 are (1,2,4,8,16) i.e. the count is 5
Average
Average/mean =
When one quantity is added or removed from average:
Sum of added/removed quantities = [Change in number of original quantities x original average] [change in average x final no. of quantities]
Ex. The average weight of 25 apples is 8kg. If 5 new apples are added then average is increased by 0.6kg. Find average of new apples.
Sum of weights added = [5(change in quantity) x 8(original average)] + [0.6(change in average) x 30(final no. of quantities)]
= 40 + 18 = 58kg
Average of 5 new apples =
= 11.6 kg
If a part of journey is covered a kmph and equal distance at b kmph then average speed of whole journey
=
That’s for today’s short article. We will cover more formulae in the next post.
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