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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]  02 Dec 2018, 08:40
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Question Stats:

30% (00:35) correct 69% (00:35) wrong based on 13 sessions
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
[Reveal] Spoiler: OA

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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]  03 Dec 2018, 07:59
1
KUDOS
There are 8 slots for the numbers.
Numbers cannot occur consecutively.
We want the greatest sum of the number.
We know this occurs when we have maximum number of 5's
Hence if the number occurred in the following pattern the sum would be greatest
54535251 These digits add to 30
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]  28 Dec 2018, 04:12
amorphous wrote:
There are 8 slots for the numbers.
Numbers cannot occur consecutively.
We want the greatest sum of the number.
We know this occurs when we have maximum number of 5's
Hence if the number occurred in the following pattern the sum would be greatest
54535251 These digits add to 30

We can also have 54545454. This adds up to 36. Why this is not considered kindly explain.
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]  28 Dec 2018, 05:13
sumarch2002 wrote:
amorphous wrote:
There are 8 slots for the numbers.
Numbers cannot occur consecutively.
We want the greatest sum of the number.
We know this occurs when we have maximum number of 5's
Hence if the number occurred in the following pattern the sum would be greatest
54535251 These digits add to 30

We can also have 54545454. This adds up to 36. Why this is not considered kindly explain.

This is not possible because 1,2 and 3 should at least feature once
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Post in BookmarksDeleteBookmark [#permalink]  28 Dec 2018, 05:31
I apologise, but, in my opinion, you are not right. I am assured. I can prove it. Write to me in PM, we will talk.
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]  28 Dec 2018, 06:21
Expert's post
There is no need to keep a conversation private.

The forum exists just for this reason: anyone might have benefited from a discussion.

thank you so much
Regards
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]  28 Dec 2018, 08:57
Expert's post
Carcass 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

Hi...

The s ores consist of atleast one of each of 1, 2, 3, 4, 5, so 1+2+3+4+5=15 in 5 steps..
Now there are 8-5=3 steps left and let us give them the maximum that is 5, so 15+3*5=30..

We can check for having different score in consecutive steps..
We can have 5,1,5,2,5,3,5,4...1,5,2,5,4,5,3,5.....5,1,2,5,3,5,4 and so on..

C
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]  01 Apr 2019, 08:41
Maybe it's my ineptitude in English. But so far my knowledge in English goes, I find many math questions in this forum are incorrectly framed ( Leaving lots of confusion-maybe my folly). For example- in the above math, the question could have been put like- she had 'each of the scores at least once' ...
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]  01 Apr 2019, 09:22
Expert's post
Sorry, jelal123 but your reflection on the question above and how it has been formatted (not to mention the, and I quote,

Quote:
I find many math questions in this forum are incorrectly framed
) is meaningless.

The reasons why are

• the questions come from well-established prep company such as Kaplan, Princeton, Manhattan and so forth. I do think a typo is always possible. what is NOT possible is a question is badly written in its entirety or part of the stem.
• This is a test of standard English in an academic environment.
• If the question is framed that way is because of a valid reason: logic, math concepts tested behind.

Put like instead of at least one score has no sense in the economy of the sentence.

My opinion.

Regards
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]  01 Apr 2019, 09:42
Awesome question!
Re: In a certain game there are 8 steps, referred to as step 1,   [#permalink] 01 Apr 2019, 09:42
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# In a certain game there are 8 steps, referred to as step 1,

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