Asked by William Bent
A number rounded up to the next thousand is 8000. It is divisible by 6 and 10 but not by 9. The hundreds digit is three more than the tens digit. What is the number?
Answers
Answered by
drwls
Rather than use algebra, I would use trial and error. The number is between 7500 and 8499 and ends with zero. Possibilities that are also divisible by 6 are:
7500, 7530, 7560, 7590, 7620, 7630, 7680, 7710, 7740, 7770, 7800, 7830, 7860, 7890, 7920, 7950, 7980, 8010, 8040, 8070, 8100, 8130, 8160, 8190, 8220, 8250, 8280, 8310, 8340, 8370, 8400, 8430, and 8460.
The only ones that meet the last requirement -- about the hundreds and tens digits -- are 7630 and 7740. Only 7740 is not evenly divisible by 9; so that is the answer.
7500, 7530, 7560, 7590, 7620, 7630, 7680, 7710, 7740, 7770, 7800, 7830, 7860, 7890, 7920, 7950, 7980, 8010, 8040, 8070, 8100, 8130, 8160, 8190, 8220, 8250, 8280, 8310, 8340, 8370, 8400, 8430, and 8460.
The only ones that meet the last requirement -- about the hundreds and tens digits -- are 7630 and 7740. Only 7740 is not evenly divisible by 9; so that is the answer.