In a competition, winner are to be selected in three categories, categ

Question

In a competition, winner are to be selected in three categories, category 1, 2, and 3. The cash price of $ 150, $ 100, and $ 50 is to be given in category 1, 2, and 3 respectively. If one candidate can be selected in one category only but multiple candidates can be selected for one category, then in how many ways winners in each category can be selected from 50 participants?

(1) A total of 9 winners are to be selected.

(2) The ratio of winner in category 1, 2, and 3 is 1: 3: 5.

Show Answer

Official Answer

C

(1) A total of 9 winners are to be selected.

(2) The ratio of winner in category 1, 2, and 3 is 1: 3: 5.

ktzsikka · Answer

Here is the  OE

Step 1: Analyse Question Stem
Total participants = 50.
Winners are to be selected in 3 categories. 
One candidate can be selected in one category only
Multiple candidates can be selected for one category.
We need to find the number of ways in which winners in each category can be selected.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: A total of 9 winners are to be selected.

We know how many winners are to be selected.
However, we don’t know in category how many winners are to be selected.
Thus, we cannot find the number of ways in which winners can be selected in each category.
Hence, statement 1 is not sufficient, we can eliminate answer options A and D.

Statement 2: The ratio of winner in category 1, 2, and 3 is 1: 3: 5.

With this statement we know the distribution of winners in each category.
However, we don’t know the total number of winners that we need to select.
Thus, we cannot find the number of ways in which winners in each category can be selected.
Hence, statement 2 is also not sufficient, we can eliminate answer options B.

Step 3: Analyse Statements by combining.
From statement 1: Total winners = 9

From statement 2: Winners from category 1, 2, and 3 are in ratio 1: 3: 5.

By combining both the statements,

Winner in category 1 = 1.
Number of ways of selecting winner in category = 50C1.
Winner in category 2 = 3.
Number of ways = 49C3.
Winner in category 3 = 5.
Number of ways = 46C5.
Total number of ways = 50C1*49C3*46C5.
Hence, the correct answer is  Option C.

deeptikashyap20 · Answer

ktzsikka : I think that this question's language needs improvement - the info about the number of candidates in each category is really misguiding and is not phrased properly  .

Also, just the way we need the number of winners in each category, we also need the number of candidates in each category. Thus, the answer should be E. 
This question is from the GMATWhiz practice test and I strongly feel that it needs revision.

bb : What do you think?

singhall · Answer

I agree. What I deciphered from the question stem was.. participants would be put into categories and then one winner would be selected from each one of them.
Like from 50participants 10 went into category 1, then from statement 2 I knew the ratio of winners, I would use 10C1. 
What is the point of categories here? and putting some members into each category if at the end we are selecting winners from the total.
It went like selecting 1 person from 50, then 3 from 49, then 3 from 46. Bunuel : could you please help us with this question?

In a competition, winner are to be selected in three categories, categ

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