Number of 4 -digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to _____ .

Step-by-step solution

Four-digit numbers that are less than or equal to 2800 are 1000 , 1001 , 1002 , . . . . , 2800 Numbers divisible by 3 are 1002 ,   1005 ,   . . . . , 2796 , 2799 Let total numbers be n , then 1002 + n - 1   3 = 2799 ⇒ n = 600 Numbers divisible by 11 are 1001 ,   1012 ,   . . . ,   2794 Let total numbers be m , then 2794 = 1001 + m - 1 11 ⇒ m = 164 Numbers divisible by 33 are 1023 , 1056 , . . . , 2772 Let total numbers be r , then 2772 = 1023 + r - 1 33 ⇒ r = 54 Numbe