The first digit of a six-number digit number is 1. This digit 1 is now moved from the first digit position to the end, so it becomes the last digit. The new 6 digit number is now 3 times larger...
The first digit of a six-number digit number is 1. This digit 1 is now moved from the first digit position to the end, so it becomes the last digit. The new 6 digit number is now 3 times larger than the original number. What are the last three digits of the original number?
1 Answer
degeneratecircle | High School Teacher | (Level 2) Associate Educator
Let the original six digit number be `1abcde,` where `a,b,c,d,e` are the unknown digits. Moving the `1` to the end results in the new six digit number `abcde1.` It is given that
`1abcde`
`xx.....3`
`-----`
`abcde1`
` `
` `
` `
` `
` `
` ` The dots are just there for spacing, so don't let them confuse you; I couldn't figure out how to get the 3 on the right without them.
Anyway, we know that `3e` ends in 1, so `e` must be 7 and we can make the replacement to get
`1abcd7`
`xx.....3`
`-----`
`abcd71`
` `
Then, since we carry the 2 from `7xx3=21,` we know that `3d+2` ends in `7,` and the only `d` that works is `5,` so
`1abc57`
`xx.....3`
`-----`
`abc571`
Finally, we must have `3c+1` ends in `5` (remember the `+1` comes from carrying the one from `5xx3+2=17` ). The only `c` that works is `8,` and the last three digits of the original number are 857.
You can continue this process to get the whole number if you wish.