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# Permutation/Combination question

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Intern
Joined: 18 Sep 2008
Posts: 5

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26 Sep 2008, 23:41
Hi all,

Just came across this question from of the questions banks I found on the internet for counting related problems for the GMAT.
The question reads :
" A computer game has 5 difficulty levels.In each level you can choose among 4 different scenarios, except for the first level, where you can choose among three scenarios only.How many different games are possible ?"

a)18
b)19
c)20
d)21
e)None of the above.

I thought the answer is e)None of the above.

How did I get to this ?
I thought the solution was pretty simple
Number of possibilities for Level 1 : 3
" Level 2 = 4
" Level 3 =4
" Level 4 = 4
" Level 5= 4

Different number of games possible = 4*4*4*4*3

But, the Answer key says option b)19

Am I missing something here ?
Appreciate any help!

Regards,
dhegde

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
SVP
Joined: 07 Nov 2007
Posts: 1728
Location: New York
Re: Permutation/Combination question  [#permalink]

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26 Sep 2008, 23:57
dhegdex wrote:
Hi all,

Just came across this question from of the questions banks I found on the internet for counting related problems for the GMAT.
The question reads :
" A computer game has 5 difficulty levels.In each level you can choose among 4 different scenarios, except for the first level, where you can choose among three scenarios only.How many different games are possible ?"

a)18
b)19
c)20
d)21
e)None of the above.

I thought the answer is e)None of the above.

How did I get to this ?
I thought the solution was pretty simple
Number of possibilities for Level 1 : 3
" Level 2 = 4
" Level 3 =4
" Level 4 = 4
" Level 5= 4

Different number of games possible = 4*4*4*4*3

Why are you multiplying.. you need to add.
= 4+4+4+4+3=19

But, the Answer key says option b)19

Am I missing something here ?
Appreciate any help!

Regards,
dhegde

Possible ways for L1 + possible ways for other levels
= 1*3+4*4=19
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Joined: 24 Jun 2008
Posts: 1345
Re: Permutation/Combination question  [#permalink]

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27 Sep 2008, 00:12
1
Clearly they've added to get the answer 19, but I don't see any reason why you'd add here. By my reading of the question, this is a straightforward Fundamental Counting Principle question, and the answer should be 4*4*4*4*3. The wording of the question isn't great, however, and they either have a completely different interpretation of their question that I just don't see, or they've made a fundamental mathematical error in their solution - hard to know which without seeing their explanation. Where specifically is the question from, by the way?

Edit- Actually, rereading the question, and knowing what answer they give, I can guess what they mean. In my reading, I was assuming a player would progress from level one through to level five, choosing one scenario each time. Then there would be 3*4*4*4*4 different games. If instead you simply choose one level and one scenario, and then it's game over, there would be exactly 3+4+4+4+4 = 19 different games. It's a very poorly worded question, open to multiple interpretations, because they never explain just what makes up a 'game'. It's not like anything you'd see on the real GMAT.
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SVP
Joined: 07 Nov 2007
Posts: 1728
Location: New York
Re: Permutation/Combination question  [#permalink]

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27 Sep 2008, 00:17
IanStewart wrote:
Clearly they've added to get the answer 19, but I don't see any reason why you'd add here. By my reading of the question, this is a straightforward Fundamental Counting Principle question, and the answer should be 4*4*4*4*3. The wording of the question isn't great, however, and they either have a completely different interpretation of their question that I just don't see, or they've made a fundamental mathematical error in their solution - hard to know which without seeing their explanation. Where specifically is the question from, by the way?

Edit- Actually, rereading the question, and knowing what answer they give, I can guess what they mean. In my reading, I was assuming a player would progress from level one through to level five, choosing one scenario each time. Then there would be 3*4*4*4*4 different games. If instead you simply choose one level and one scenario, and then it's game over, there would be exactly 3+4+4+4+4 = 19 different games. It's a very poorly worded question, open to multiple interpretations, and unlike anything you'd see on the real GMAT.

agree with you.. (poorly worded question)
I choose one level and one scenario.
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VP
Joined: 17 Jun 2008
Posts: 1474
Re: Permutation/Combination question  [#permalink]

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28 Sep 2008, 04:46
Not sure whether this is a GMAT question. It expects you to apply real world understanding. In a computer game, difficulty level is typically chosen before starting the game, hence multiplication is not correct.
Intern
Joined: 18 Sep 2008
Posts: 5
Re: Permutation/Combination question  [#permalink]

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29 Sep 2008, 09:53
Hey Everyone,
Thanks for the replies.Probability and the like are my weakest areas and hence was practicing stuff from all possible sources .
I imagined that the user would progress from each difficulty level to the next and hence multiplied the possibilities.

Unfortunately the answer key does not provide any explanation.

Regards,
dhegde
Intern
Joined: 19 Apr 2008
Posts: 31
Re: Permutation/Combination question  [#permalink]

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30 Sep 2008, 04:29
dhegdex wrote:
Hey Everyone,
Thanks for the replies.Probability and the like are my weakest areas and hence was practicing stuff from all possible sources .
I imagined that the user would progress from each difficulty level to the next and hence multiplied the possibilities.

Unfortunately the answer key does not provide any explanation.

Regards,
dhegde

What source did you get the question from?
Intern
Joined: 18 Sep 2008
Posts: 5
Re: Permutation/Combination question  [#permalink]

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01 Oct 2008, 01:24
1
FYI
Attachments

File comment: Attaching the source
Probability and Combinations.doc [99 KiB]

Intern
Joined: 19 Apr 2008
Posts: 31
Re: Permutation/Combination question  [#permalink]

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04 Oct 2008, 16:25
Thanks for the file. These questions remind me of my Business Algebra class.
SVP
Joined: 29 Aug 2007
Posts: 2419
Re: Permutation/Combination question  [#permalink]

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04 Oct 2008, 22:12
dhegdex wrote:
Hi all,

Just came across this question from of the questions banks I found on the internet for counting related problems for the GMAT.
The question reads :
" A computer game has 5 difficulty levels.In each level you can choose among 4 different scenarios, except for the first level, where you can choose among three scenarios only.How many different games are possible ?"

a)18
b)19
c)20
d)21
e)None of the above.

I thought the answer is e)None of the above.

How did I get to this ?
I thought the solution was pretty simple
Number of possibilities for Level 1 : 3
" Level 2 = 4
" Level 3 =4
" Level 4 = 4
" Level 5= 4

Different number of games possible = 4*4*4*4*3

But, the Answer key says option b)19

Am I missing something here ?
Appreciate any help!

Regards,
dhegde

so it is always important to make sure about the resources and their sources. if you have such question as this one, you would be wasting your time and putting yourself in big confusion. Unreliable sources confuse you easily. so some selective sources such as OG, OG Old test materials, Manhattan, Gmat Club forum, and few others are enough for the understanding of whole gmat test....
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Manager
Joined: 30 Sep 2008
Posts: 111
Re: Permutation/Combination question  [#permalink]

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04 Oct 2008, 22:57
dhegdex wrote:
Hi all,

Just came across this question from of the questions banks I found on the internet for counting related problems for the GMAT.
The question reads :
" A computer game has 5 difficulty levels.In each level you can choose among 4 different scenarios, except for the first level, where you can choose among three scenarios only.How many different games are possible ?"

a)18
b)19
c)20
d)21
e)None of the above.

I thought the answer is e)None of the above.

How did I get to this ?
I thought the solution was pretty simple
Number of possibilities for Level 1 : 3
" Level 2 = 4
" Level 3 =4
" Level 4 = 4
" Level 5= 4

Different number of games possible = 4*4*4*4*3

But, the Answer key says option b)19

Am I missing something here ?
Appreciate any help!

Regards,
dhegde

If you think this question is not about probability, the answer will be very clear.

"How many different games are possible ?" = How many different games at least?
Manager
Joined: 10 Aug 2008
Posts: 72
Re: Permutation/Combination question  [#permalink]

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05 Oct 2008, 01:12
Here Games means of 1 scenario of 1 level. (Yes language of level is not clear, by the lang it seems i game is consist to cross all the 5 levels)

3 + 4*4 = 19

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: Permutation/Combination question &nbs [#permalink] 05 Oct 2008, 01:12
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# Permutation/Combination question

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