The number of 3 -digit numbers, that are divisible by either 2 or 3 but not divisible by 7 is _____ .

Step-by-step solution

We know that total number of three-digit number will be 900 , Now let n A be number of three-digit number which are divisible by 2 , i.e, A = 100 , 102 , . . . , 998 ⇒ n A = 450 n B be number of three-digit number which are divisible by 3 , i.e, B = 102 , 105 , . . . , 999 n B = 300 Numbers divisible by both 2 and 3 is 102 , 108 , . . . 996 i.e, 150 Numbers divisible by both 2 and 7 are 112 , 126 , . . . , 994 i.e., 64 numbers. Numbers divisible by both 3 and 7 is 105 , 126 , . . . 987 i.e, 43 numbers. Number