vk_vinayak wrote:Which of the following fractions has the greatest number of unique decimal digits?

A. 1/9
B. 3/11
C. 4/9
D. 5/7
E. 7/8

[spoiler]OA: D[/spoiler]
Any shortcuts (or number properties) that would help us solve this without testing each option?[/i]

My thoughts on this :-

x/9 where x is any integer will give a recurring digits after decimal so only one unique number after it so option A and option C is out...

x/11 will give utmost 2 unique digits after which it will be recurring digits

so left with option D and E

with option E divide by 8 :- Any number when divide by 8 after two iteration after decimal point(max) will come as 40 which is divisible by 8 ..>So max we can get only 3 unique numbers

Option D - Anything which is not a multiple of 7 will give a recurring set of 7 unique digits ....

Not sure if this helps....

Sure, it helps.

x/11 will give utmost 2 unique digits after which it will be recurring digits

Any number when divide by 8 after two iteration after decimal point(max) will come as 40 which is divisible by 8 ..>So max we can get only 3 unique numbers

Anything which is not a multiple of 7 will give a recurring set of 7 unique digits ....

Are these three the general rules or apply only to the options that are given?