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

Really strange question. Can someone confirm that this is indeed a GMATPrep question?

Hi chetan2u,

I still don't get it why we could eliminate 0.8 and keep the other 2 options.
Below are my reasons:
1. For 0.8: let's say that person starts with 0.6 (the highest point). He then throws the dice 20 times. As 55% of the rolls will be even (given as a condition), 11 of his rolls will be even and the remaining 9 will be odd.
For the even-number rolls, it's possible that all these 11 even rolls, he will get a 6 for each roll (yeah, this is quite extreme but still a possibility). In this case, he will get 1.1 points for all these 11 rolls.
For the odd-number rolls, clearly all of these rolls will be less than 6, so he will get -0.1 for each of these rolls, making the the sub-total of -0.9.
In total, for this scenario, he will get 1.1-0.9 = 0.2 for 20 rolls, making his final score to be 0.2 + 0.6 = 0.8!
How can we eliminate this value?

2. For the other two values (0.5 & 0.1), how can we be sure that there will be a combination of increases/decreases after 20 rolls to arrive at those points? Within a few minutes, I feel puzzled to verify these two values. Just because these two values are within the max-min range of the possible scores, would it be safe to conclude that these two are two 'possible' values? We have some conditions that we must abide by, so I think making such a conclusion would be much of a guess.

Thanks.

Hi. During your GMAT test, did you get questions of this level? This is a really hard question.

I did this problem like this,

20*55/100=11 even and 9 odd.
A dice has 6 possibilities. 1,2,3,4,5,6.
Odd: 1,3,5
Even: 2,4,6

to make it easy, lets assume that for every 20 selections, we only get the same odd number and the same even number.

hence,

1*9=9*.1=.9 2*11=22*.1=2.2
3*9=27*.1=2.7 4*11=44*.1=4.4
5*9=45*.1=4.5 6*11=66*.1=6.6

Using this, since all the odd's are less than the number selected, they are reduced by .1 and since all the even's are more than the number selected, they are increased by .1

we get, .8,2.6,4.5(odd) 2.3,4.5,6.7(even)

Adding all possibilities, we only get a difference of .1,.3,.5,.7 or .9

hence it removes .8 as a possibility.

ans: D

you can use this link as a reference. https://www.gmatquantum.com/og13/218-pro ... ition.html

Hello,

Nice to improve your reading skills and comprehension skills. I spent 1 min on reading this question and got answrer in 10 secs.

Condition says the following

1.Ifnumber on the roll of the dice * 0.1\(\geq{current score}\), then increase the score of player by .1

2. If number on the roll of the dice * 0.1 < current score, then decrease the score of player by .1

3. If number on the roll of the dice * 0.1 is even and is < current score, then no change in score of player.


So lets assume that say initially the score of the player is .1*3= .3
\(S_0\)=.3

On the first throw of the dice we get 2. so this is .1*2 = .2 and is even , So we have condition 3 here hence the score remains unchanged.
So \(S_1\)=.3

Now second throw we have 1, so it will be 0.1*1 = .1 and we see condition 2 coming into effect. So score will decrease by .1 and will be .2
\(S_2\)=.2

Now third throw we have 1, so it will be 0.1*1 = .1 and we see condition 2 coming into effect. So score will decrease by .1 and will be .1
\(S_3\)=.1

Now forth throw we have 1, so it will be 0.1*1 = .1 and we see condition 1 coming into effect. So score will increase by .1 and will be .2
\(S_4\)=.2

Clearly lowest possible is 0.1


Now assume that during some pint in the game the players score was .6, and on the throw of the dice he gets 6 so 6*.1\geq{.6}, so new score will be .7
Now on the next throw what ever number comes on the throw of the dice the score will either decrease or remain unchanged. . Why so? Because for a number to increase the throw of the dice *.1 should be \(\geq{current score}\) . but this is possible only if we get 7 on throw of the dice. and getting 7 is not possible ( fair dice) except even the score will decrease

So maximum score possible is .7



So Max score is .7 and min is .1 so only option D

Hi! This solution looks good, but it appears you did not make any use of the following information:

55% of the die rolls in a particular game are even

Is this information not needed at all or did you just not use it?

Hey guys

It seems that I've misread the information: ..."A player starts with a number equal to 0.1n, where n is an integer between 1 and 6 inclusive..." I assumed that n was a tenths digit. Is it usually written the way it's been written in the question? Or if it doesn't explicitly mention that n is some sort of digit, I need to assume that in that cases it's multiplication what's given?

Thanks

chetan2u Bunuel

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