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

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

Final Answer:

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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]
Have to be cautious to not overthink the prompt. Take into account what the prompt tells you:

1) Consecutive order of steps (Step 1 - Step 8)
2) Points able to achieve; 1 (min) - 5 (max)
3) she gets 1,2,3,4,5 - so that is concrete and 5 steps are already completed & never gets the same score in order.

Now, you have to max the score, but recall 5 is the highest possible score, so have to think, is there any pattern to incorporate that is within the given constraints?

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


why is the answer not 36 i.e., 5+4+5+4+5+4+5+4=36
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]
Expert Reply
Ayushmnitj wrote:
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


why is the answer not 36 i.e., 5+4+5+4+5+4+5+4=36


Because of the highlighted part: Andrea got at least one score of each of 1, 2, 3, 4, and 5.
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]
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