Find the smallest number such that if its rightmost digit is placed at its left end, the new number so formed is precisely 50% larger than the original number.

ans: 285714

can get it by solving :

10*m+c= 2/3*( c*10^k+m)
which transforms into:
28m=2c*10^k-3c
which leads to :

28*m=c*199....97

hence c=4 m=28571
and the combined number 428571

OR c=8 m=57142
and the combined number 571428




Another method is by looking at the multiples of the periodic decimal representation of 1/7:
1 142857
2 285714
3 428571
4 571428
5 714285
6 857142

HERE YOU CLEARLY SEE BOTH ANSWERS
i.e. 2/7=>3/7 and 4/7=>6/7

since the problem requested the smallest number
the answer is 285714 .
ady

Posted by Ady TZIDON on 2004-01-25 15:16:14