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Take the task of selecting or not selecting questions and break it into stages.RBBmba@2014 wrote:In a test of 8 questions, each question has an alternative.What is the number of ways in which one can select one or more questions ?
(A) 2^8-1
(B) 2^8
(C) 2^8*3
(D) 3^8-1
(E) 3^8
Hi Brent,Brent@GMATPrepNow wrote:Take the task of selecting or not selecting questions and break it into stages.RBBmba@2014 wrote:In a test of 8 questions, each question has an alternative.What is the number of ways in which one can select one or more questions ?
(A) 2^8-1
(B) 2^8
(C) 2^8*3
(D) 3^8-1
(E) 3^8
Stage 1: Select or don't select question #1
We have 2 options: select the question or don't select the question.
So, we can complete stage 1 in 2 ways
Stage 2: Select or don't select question #2
We have 2 options: select the question or don't select the question.
So, we can complete stage 2 in 2 ways
Stage 3: Select or don't select question #3
We have 2 options: select the question or don't select the question.
So, we can complete stage 3 in 2 ways
.
.
.
.
Stage 8: Select or don't select question #8
We have 2 options: select the question or don't select the question.
So, we can complete stage 8 in 2 ways
By the Fundamental Counting Principle (FCP), we can complete all 8 stages (and thus deal with all 8 questions) in (2)(2)(2)(2)(2)(2)(2)(2) ways (= 2^8 ways)
So, the correct answer is E . . . . NOPE!
Included in those 2^8 ways is a single case in which NONE of the questions are selected. HOWEVER, the question tells us that we must select one or more questions. So, we should not have counted that 1 case in which NONE of the questions are selected.
So, we must subtract 1 from our answer to get [spoiler]2^8 - 1[/spoiler]
Answer: D
--------------------------
Cheers,
Brent
The wording is strange, but I think it means that the test has two options for each of the eight questions (almost like a primitive CAT), but each of those options can ONLY be assigned to that specific number. In other words, we have questions {A, B, C, ..., P}, and Question 1 can be (A or B), Question 2 can be (C or D), ..., and Question 8 can be (O or P).RBBmba@2014 wrote:As for the question, I'd request you to clarify what does this mean - " each question has an alternative " ?
Look forward to your reply.
As Matt points out, the question is poorly worded (what's the source?).RBBmba@2014 wrote: Hi Brent,
Thanks for your reply. But I think, per your explanation the OA should be A (i.e. 2^8 - 1). Not the option D (I also marked it wrong unfortunately in my post!). Correct me please if wrong.
As for the question, I'd request you to clarify what does this mean - " each question has an alternative " ?
Look forward to your reply.
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