Hi vinni.k,

We're told that a market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y and that each person contacted reported that they used AT LEAST ONE of the two brands. We're asked for the percent of respondents who reported that they ONLY use Brand Y. This question can be approached in a number of different ways (including TESTing VALUES), but it ultimately comes down to determining the percentages of 3 groups: Those who use JUST X, those who use JUST Y and those who use BOTH. Those sum of those 3 percentages MUST total 100%.

1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was 3:2

The information in Fact 1 is 'tricky' because there's no way to define the exact percents involved. The ratio of 3:2 means that for every 3 people who use Y, 2 people use X. However, this information does NOT account for those who use BOTH.

IF....
60% of the respondents use Brand Y
40% of the respondents use Brand X
then there is NO "overlap", 0% of people use both. and the answer to the question is 60% - 0% = 60%.
IF....
75% of the respondents use Brand Y
50% of the respondents use Brand X
then 25% of the people use both (since the total can't be greater than 100%, some of these people have been counted 'twice' and appear in both groups) and the answer to the question is 75% - 25% = 50%.
Fact 1 is INSUFFICIENT

2) Among the respondents who reported that they use Brand X, one half also use Brand Y.

Fact 2 defines the "Both" group - it's equal to HALF of the total number of people who use Brand X. This does not give us the actual percentages though...

IF....
75% of the respondents use Brand Y
50% of the respondents use Brand X
then 25% of the people use both and the answer to the question is 75% - 25% = 50%.
IF....
70% of the respondents use Brand Y
60% of the respondents use Brand X
then 30% of the people use both and the answer to the question is 70% - 30% = 40%.
Fact 2 is INSUFFICIENT

Combined, we have a ratio comparing those who use Y to those who use X to those who use BOTH (re: 3:2:1). The only possible option is:
75% of the respondents use Brand Y
50% of the respondents use Brand X
then 25% of the people use both and the answer to the question is 75% - 25% = 50%.

Final Answer: C

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