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Data Sufficiency Pack 3, Question 1) A survey of 72 people...

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Data Sufficiency Pack 3, Question 1) A survey of 72 people... [#permalink]

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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.


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[Reveal] Spoiler: OA

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Re: Data Sufficiency Pack 3, Question 1) A survey of 72 people... [#permalink]

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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.


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Earn KUDOS! Post your answer and explanation.
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Need to find the number of people who like soda C =x ?

Per statement 1, number of people who like just D = 2/9*72 = 16. As there are 0 people who do not like either, you can clearly calculate 'x' (x=72-16=56. Sufficient.

Per statement 2, clearly not sufficient.

A is the correct answer.

This question is straightforward with the 2X2 matrix method.
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Re: Data Sufficiency Pack 3, Question 1) A survey of 72 people... [#permalink]

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New post 08 Nov 2015, 18:55
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IMO A is correct

We need to find people who like Soda
I]It's given number of people who like just D = (2/9)*72 = 16.

Further no one dislike both the drinks

So deducting no of people who just like soda D from total no of people will give us people who like Soda c
= 72-16
=56

II] no of people who like both sodas is given , but this information is clearly insufficient as we don't know about people who like just one of the two drinks

A is correct

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Re: Data Sufficiency Pack 3, Question 1) A survey of 72 people... [#permalink]

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New post 10 Nov 2015, 17:49
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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:
[Reveal] Spoiler:
A


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Re: Data Sufficiency Pack 3, Question 1) A survey of 72 people... [#permalink]

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New post 24 Jan 2017, 20:44
This question stumpted me with words that it chooses to describe the situation. The key is that since each liked soda just C or just D or both , this implies that there are none who didnt like any.

Choice A says how many like just D and in doing so tells how many like C (assuming that there are none who like neither)
Choice B only tells us how many people like both, but to know how many like soda C, we need to know how many like just C.

Choice B adds no information at all. I didnt understand that there are none who liked neither and ended up with E. Lesson learnt is to consider the choice of words carefully. :)

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Re: Data Sufficiency Pack 3, Question 1) A survey of 72 people... [#permalink]

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New post 03 Aug 2017, 22:46
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Re: Data Sufficiency Pack 3, Question 1) A survey of 72 people...   [#permalink] 03 Aug 2017, 22:46
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