Question

How many integers from 1 to 500 are divisible by 3 but not 5 or 6?

Answer 1

Answer:

N= n1-n2-n3 = 50

Step-by-step explanation:

number divisible by 3

l = a + (n-1) d

l is last term divisible

a is first term divisible

n is number of term

d is number of gap between two term

(1-500) number divisible by 3

3,6,9.........498

using above equation

498= 3 + (n-1) 3

solving we get

n= 166 term divisible by 3

similarly number divisible by 5 ( 3-498)

are 15,30,45......495

495= 15+ (n-1)15

solving we get n=33 term divisible by 5

similarly number divisible by 6 (3-498)

are 6,12,18.....498

498= 6+ (n-1)6 solving we get

n= 83 term divisible by 6

subtract equation 2 and 3 from 1

N = n1-n2-n3 = 166-83-33= 50