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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 ?"

Answer Choices 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!

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 ?"

Answer Choices 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 _________________

Your attitude determines your altitude Smiling wins more friends than frowning

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. _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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. _________________

Your attitude determines your altitude Smiling wins more friends than frowning

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.

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.

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.

Re: Permutation/Combination question [#permalink]
04 Oct 2008, 21:12

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 ?"

Answer Choices 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.... _________________

Re: Permutation/Combination question [#permalink]
04 Oct 2008, 21:57

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 ?"

Answer Choices 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?