EMPOWERgmatRichC wrote:

QUANT 4-PACK SERIES Data Sufficiency Pack 3 Question 1 A survey of 72 people...

A survey of 72 people showed that each liked Soda C, Soda D or both. How many of the people surveyed liked Soda C?

1) 2/9 of the people surveyed liked just Soda D.

2) 5/18 of the people surveyed liked both Soda C and Soda D.

Hi All,

This DS question is a variation on a typical Overlapping Sets question - the difference is that there is NO group that likes neither soda. These types of prompts can be solved in a number of different ways, depending on how you choose to organize your data. For this prompt, some basic arithmetic is all that is needed.

We're told that a total of 72 people were surveyed about whether they liked Soda C, Soda D or both. We're asked for the number of people surveyed who liked Soda C. With the information in the prompt, we can construct an initial equation:

(Like Just Soda C) + (Like Just Soda D) + (Like BOTH Sodas) = 72

1) 2/9 of the people surveyed liked just Soda D.

With this Fact, we know that (2/9)(72) = 16 people liked JUST Soda D. The remaining two groups must total 72 - 16 = 56. Since those two groups combined account for ALL of the people surveyed who like Soda C, we have enough information to answer the question (and the answer IS 56).

Fact 1 is SUFFICIENT

2) 5/18 of the people surveyed liked both Soda C and Soda D.

With this Fact, we know that (5/18)(72) = 20 people liked BOTH Sodas, so we know that there are at least 20 people who like Soda C. The remaining two groups must total 72 - 20 = 52, BUT we don't know how many of those 52 people liked JUST Soda C.

Fact 2 is INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,

Rich

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