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by [email protected] » Thu Mar 10, 2016 4:14 pm
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

Hi didieravoaka,

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: C

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by Matt@VeritasPrep » Thu Mar 17, 2016 9:43 pm
I'd think of it as (Necessary scores) + (Maximum optional scores). We know Andrea scored a 1, a 2, a 3, a 4, and a 5, so

Necessary scores = 1 + 2 + 3 + 4 + 5

In the other steps, we want to score as many points as possible, so

Maximum optional scores = 5 + 5 + 5

Summing these gives us 30, so we're done!
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