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]

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?