The number of numbers lying between 100 and 500 that are divisible by 7 but not by 21?
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Answer:
Two ways to do it, the long way is to start listing them:
Two ways to do it, the long way is to start listing them:105
Two ways to do it, the long way is to start listing them:105112
Two ways to do it, the long way is to start listing them:105112119
Two ways to do it, the long way is to start listing them:105112119126
Two ways to do it, the long way is to start listing them:105112119126133
Two ways to do it, the long way is to start listing them:105112119126133etc
Two ways to do it, the long way is to start listing them:105112119126133etc
Two ways to do it, the long way is to start listing them:105112119126133etc and then finding the first one divisible by 21 (hint, it's 105) and then crossing out every third one.
Two ways to do it, the long way is to start listing them:105112119126133etc and then finding the first one divisible by 21 (hint, it's 105) and then crossing out every third one.
Two ways to do it, the long way is to start listing them:105112119126133etc 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
Two ways to do it, the long way is to start listing them:105112119126133etc 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, so400/7 = 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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