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