A game is played with a six sided, regularly numbered fair

[BTGmoderatorDC]

A game is played with a six sided, regularly numbered fair die. A player starts with a number equal to 0.1n, where n is an integer between 1 and 6 inclusive. On each of 20 subsequent rolls, if the number rolled times 0.1 is greater than or equal to the players current number, the players current number is incremented by 0.1; if the number rolled times 0.1 is less than the player's current number and is odd, the players number is decremented bu 0.1; if the number rolled times 0.1 is less than the player's current number and is even, the players number is unaffected. If 55% of the die rolls in a particular game are even, which of the following is a possible final value of that game

i. 0.8
ii. 0.5
iii. 0.1

A. i only
B. i and ii only
C. i and iii only
D. ii and iii only
E. i, ii and iii

OA D

Source: GMAT Prep

[deloitte247]

Consider the following scenarios;
1* If the number rolled multiplied by 0.1 is greater than or equal to the players current number, The players current number is increased by 0.1

2* If the number rolled * 0.1 is less than the player's current number and it's odd, the players current number is decreased by 0.1.

3* If the number rolled multiplied by 0.1 is less than the player's current number and it's even, the player's number is unaffected.

Remember that a dice has 6 possibilities.
After a person has 0.6 the only value that can increase it is to throw 6 this will increase it to 7 but will not increase any further because there is no 7 on the dice, so 0.8 is out of it.
Hence, we have 0.7 as the maximum value and it is possible to obtain a final value of 0.5 and 0.1.
Option D the correct answer.