Question 1178646: A four-digit number abcd is called cool if a is divisible by 4, the two-digit number ab is divisible by 5, the three-digit number abc is divisible by 6 and abcd is divisible by 7. How many cool numbers are there where 8 is not one of the digits?
Answer by greenestamps(13203)   (Show Source):
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(1) a is divisible by 4. What are the possible values of a?
(2) ab is divisible by 5, so a is either 0 or 5. From (1) and (2), what are the possibilities for the string ab?
(3) abc is divisible by 6. For each of the possible strings ab, what digit(s) c make abc divisible by 6?
(4) For the possible strings abc from steps (1) to (3), what digit(s) make abcd divisible by 7?
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