How many integers in the set {500, 501 , 502, ,,, , 1385, 1386 } are:

Question

a) divisible by 3?

b) divisible by 4?

c) divisible by 5?

d) divisible by 3 and 5?

e) divisible by either 3, 4, or 5?

f) not divisible by neither 3, 4, nor 5?

Answer 1

How many integers in the set {500, 501 , 502, ,,, , 1385, 1386 } are:

There are 887 integers in the specified set.

a) divisible by 3? 501, 504, ...1386 ...... 296 integers (1386-501)/3 + 1

b) divisible by 4? 500, 504, ... 1384 ...... 222 integers (1384-500)/4 + 1

c) divisible by 5? 500, 505, ... 1385 ...... 178 integers (1385-500)/5 + 1

d) divisible by 3 and 5? 510, 525, ... 1380 ...... 59 integers

e) divisible by either 3, 4, or 5? 500, 501, 504, ... 1386 ...... 533 integers

f) not divisible by neither 3, 4, nor 5? 502, 503, 506, ... 1382 ...... 354 integers