Matho

[d]

I am thinking of three numbers. One number contains 2 digits, one 3digits, and one 5 digits. The numbers 0-9 are each used only once in all three numbers. If I label these three numbers x,y, and z, then y=22x and x y=z. What are the three numbers?

 

[Denis]

27, 594, 16038

 

[TchrWill]

I am thinking of three numbers. One number contains 2 digits, one 3digits, and one 5 digits. The numbers 0-9 are each used only once in all three numbers. If I label these three numbers x,y, and z, then y=22x and x y=z. What are the three numbers?

1--x = the 2 digit number, y the 3 digit number and z the 5 digit number.
2--y must end in 6,, 7, 8 or 9 or duplicate digits result from y = 22x.
3--y < 999 making x < 999/22 = 45+ or less than 40.
4--Therefore, x must be one of
....16, 17, 18, 19
....26, 27, 28, 29
....36, 37, 38,39
5--The resulting x, y possibilities become
....x.....16.....17.....18.....19
....y....352...374...396....418

...x.....26.....27.....28.....29
...y....572...584....616...638

...x.....36.....37.....38.....39
...y....792...814...836....858

6--26x572 produces the first 5 digit number as 14872.
7--Therefore, z lies between 26 and 39
8--26x572, 28x818, 29x638, 36x792, 37x81438x835 and 39x858 can be eliminated as they produce duplicate digits in either the two or five digit result.
9--Connsequently, x = 27, y = 594 and z = 16,038 is the only solution.

 

[d]

Thank you so much I appreciate your help