Question

find the sum of all two digit natural numbers which are neither dividible by 2 nor divisible by 3 ​

Answer 1

Answer:

1223

Step-by-step explanation:

Sum of all 2 -digit number divisible by 3 be Sn

Sn=a+a+d+.....a+(n−1)d

a=12;d=3

First number is 12 and last is 99

So 99=12+(n−1)d==>n=30

HENCE Sn=30×12+29×30×32=360+29×15×3=1665.

The numbers which are divisible by 4 and 3 are 4×3,4×2×3,....,4×8×3

Let Sn1

denote the sum of The numbers which are divisible by 4 and 3

Sn1=4×3+4×2×3......+4×8×3=12(1+2+....+8)=12((9)(8)2)=12(36)=12×36

The sum of numbers divisible by 3 but not by 4 is Sn−Sn1=1665−432=1233.

Answer 1233.