Question

How many numbers between 400 to 700 (both exclusive) are divisible by either 9, or 11? A 55 B 58 C 62 D 51

Answer 1

Greatest number below 700 which is divisible by 9 = 693

Smallest number above 400 which is divisible by 9 (a)= 405

d=9

numbers = n

405 + (n-1)9 = 693

(n-1)9 = 288

n-1 = 32

n = 33

Greatest number below 700 which is divisible by 9 = 693

Smallest number above 400 which is divisible by 9 (a)= 407

d=9

numbers = n

407 + (n-1)11 = 693

(n-1)11 = 286

n-1 = 26

n = 27

32 + 27 = 59

We should reduce the numbers which are divisible by both 9 and 11

So let use check the numbers which are divisible by both 9 and 11

Greatest number below 700 which is divisible by 9 and 11 = 693

Smallest number above 400 which is divisible by 9 and (a)= 495

d=99

numbers = n

495 + (n-1)99 = 693

(n-1)99 = 198

n-1 = 2

n = 3

58 - 3 = 55