How many three-digit numbers with a hundreds digit of 1, 2, or 6 are divisible by 7 ?
14
21
42
43
63
Answers
Given : three-digit numbers with a hundreds digit of 1, 2, or 6 are divisible by 7
To Find : How many
Solution:
3 digits numbers with hundreds digit 1 and 2 divisible by 7
105 , 112, __________ 196 , 203 , , 294
Hence
294 = 105 + (n -1 ) 7
=> 189 = (n - 1) 7
=> 27 = n - 1
=> n = 28
Hence 28 numbers
3 digits numbers with hundreds digit 6
602 , 609 , ___________ , 693
693 = 602 + (n - 1) 7
=> 91 = (n - 1) 7
=> 13 = n - 1
=> n = 14
Hence total 42 numbers
three-digit numbers with a hundreds digit of 1, 2, or 6 are divisible by 7 are 42
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