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Data Sufficiency - Probability

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Data Sufficiency - Probability

by beatgmatny1 » Mon Mar 10, 2014 4:14 pm
The following question is from GMAT PREP EXAM 2. I couldn't find an explanation in relates to this problem. Please assist.

A certain bag contains only red balls, blue balls, and green balls. what percent of all the balls in the bag are red?

1. The ratio of the number of red balls to the number of blue balls in the bag is 1:3
2. There are 2 green balls in the bag.

My analysis:

Since the question asks you to find the % of red balls in the bag, you need total number of balls and the balls that are red.

Statement 1 is not sufficient since it only provides a ratio. moreover, it doesn't provide any information on green balls.

Statement 2 is not sufficient since it doesn't provide any information on blue or red balls.

Combined: I thought this was sufficient since there are only 2 green balls in the bag and that means that the ratio is 1:3:2. which means there is 1 red ball 3 blue ball, and 2 green balls, a total of 6 balls. % red = 1/6 = .167 = 16.7%.

Please tell me where I went wrong with my analysis and provide explanation.

Correct Answer is E
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by Patrick_GMATFix » Mon Mar 10, 2014 6:10 pm
You've made the mistake of mixing a ratio number with a real number. When (1) gives ratio of red:blue = 1:3, you cannot take that to mean that there are 1 red and 3 blue. there may be 10 and 30, or infinitely many other possibilities.

When the statements are combined, we know that there are 2 green balls but we have no way to know how many red or blue. The numbers could be (red, blue, green) = (1, 3, 2) as you suggested, but they could also be (10, 30, 2). In both cases, the ratio red:blue = 1:3 and there are 2 green balls so both statements are respected. Since we end up with different % of red, we still don't have enough info. The answer is E.

In general, the safest way to work with ratio numbers is to express them as multiples of the same variable. red:blue=1:3 should be written as red=x, blue=3x.

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by beatgmatny1 » Mon Mar 10, 2014 6:27 pm
Thank you for your response. I get it now. I have to be careful with these kinds of questions in near future.
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