The number of numbers lying between 100 and 500 divisible by 7 but not by 21 is? Please give a simple and shortcut method.
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Two ways to do it, the long way is to start listing them:
105
112
119
126
133
etc
and then finding the first one divisible by 21 (hint, it's 105) and then crossing out every third one.
The second way is subtract 500 - 100 = 400, so there are 400 numbers to consider, of which 1/7 is divisible by 7, so
400/7 = 57.1 which means there are 57. Again, 1/3 of those will be divisible by 21 so 57/3 = 19 that are and 38 that are not.
105
112
119
126
133
etc
and then finding the first one divisible by 21 (hint, it's 105) and then crossing out every third one.
The second way is subtract 500 - 100 = 400, so there are 400 numbers to consider, of which 1/7 is divisible by 7, so
400/7 = 57.1 which means there are 57. Again, 1/3 of those will be divisible by 21 so 57/3 = 19 that are and 38 that are not.
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