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In a certain game there are 8 steps, referred to as step 1,

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In a certain game there are 8 steps, referred to as step 1,  [#permalink]

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New post Updated on: 13 Oct 2013, 11:35
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Question Stats:

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In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Andrea played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Andrea could have gotten?

A. 28
B. 29
C. 30
D. 36
E. 40

OE to follow

Originally posted by avohden on 13 Oct 2013, 11:24.
Last edited by Bunuel on 13 Oct 2013, 11:35, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In a certain game there are 8 steps, referred to as step ...  [#permalink]

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New post 13 Oct 2013, 11:37
1
avohden wrote:
In a certain game there are 8 steps, referred to as step 1, step 2,
and so on with the final step being step 8. The steps are played
one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained.
Andrea played the game, getting at least one score of each of 1, 2, 3, 4,
and 5, and never getting the same score in consecutive steps. What is
the greatest possible score that Andrea could have gotten?

A. 28
B. 29
C. 30
D. 36
E. 40

OE to follow


I go with C.

Here we need to get atleast one of 1,2,3,4,5...in each step.

To get greatest possible value and also no same score in consecutive steps. we can use 5 as many times as possible.

So 5+4+5+3+5+2+5+1= 30
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Re: In a certain game there are 8 steps, referred to as step 1,  [#permalink]

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New post 13 Oct 2013, 11:37
avohden wrote:
In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Andrea played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Andrea could have gotten?

A. 28
B. 29
C. 30
D. 36
E. 40

OE to follow


There are two conditions:
1. Andrea got at least one score of each of 1, 2, 3, 4, and 5.
2. She never got the same score in consecutive steps.

Taking that into account, the greatest possible score that Andrea could have gotten is 5 + 1 + 5 + 2 + 5 + 3 + 5 + 4 = 30.

Answer: C.
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Re: In a certain game there are 8 steps, referred to as step ...  [#permalink]

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New post 22 Oct 2013, 10:43
Official Explanation

Answer C
- To maximize the score, we want to maximize the number of steps where a score of 5 was obtained. Let's alternate the score of 5 with a score other than 5, each time the other score being a different number from among the scores 1, 2, 3, and 4. Since there are 8 steps, we will be able to maximize the number of steps where a 5 was obtained and also have at least one score of each of the scores 1, 2, 3, 4, and 5.
This is a sequence of scores for steps 1 through 8, respectively, which will lead to the greatest possible score.
The greatest possible score that Andrea could have obtained is 5 + 4 + 5 + 3 + 5 + 2 + 5 + 1 = 30. (C) is correct.

Hope this helps.
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In a certain game there are 8 steps, referred to as step 1,  [#permalink]

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New post 03 Feb 2015, 05:36
Our conditions are:
1. Andrea got at least one score of each of 1, 2, 3, 4, and 5.
2. She never got the same score in consecutive steps.

Just using a visual aid: I started adding the 5 points (5 as we need the greatest score), because they had to have at least one point of a different value between them.

A_B_C_D_E_F_G_H --> 8 games
5_1_5_2_5_3_5_4 --> addition gives 30 points, ANS C

So, both conditions are met: all numbers from 1-5 exist at least once and no number is the same as the 2 numbes next to it.
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In a certain game there are 8 steps, referred to as step 1,  [#permalink]

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New post 13 Dec 2015, 11:10
picked C
she might have gotten:
5, 4, 5, 1, 5, 2, 5, 3, 5
this satisfies the condition: 1,2,3,4,5 - present. 8 steps, never a score is repeated in consecutive steps.

total - 30
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Re: In a certain game there are 8 steps, referred to as step 1,  [#permalink]

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New post 02 Jan 2017, 04:02
Here is my answer 5 + 1 +5 + 2 + 5 + 3 + 4 + 5 = 30
Easy :D
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Re: In a certain game there are 8 steps, referred to as step 1,  [#permalink]

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New post 05 Feb 2018, 12:25
Hi All,

To answer the given question, you have to think about how to maximize the number of 5s that Andrea could have scored (keeping in mind that she scored each of the five numbers at least once AND she never got the same score back-to-back). There are a variety of different orders to maximize the score, but they all include the maximum possible number of 5s (which would be four):

5, 1, 5, 2, 5, 3, 5, 4
Sum = 30

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Re: In a certain game there are 8 steps, referred to as step 1, &nbs [#permalink] 05 Feb 2018, 12:25
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