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# The table above shows the results of a survey of 100 customers of a pa

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Math Expert
Joined: 02 Sep 2009
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The table above shows the results of a survey of 100 customers of a pa  [#permalink]

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16 Aug 2019, 02:27
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Difficulty:

55% (hard)

Question Stats:

60% (02:02) correct 40% (02:08) wrong based on 30 sessions

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The table above shows the results of a survey of 100 customers of a particular company, each of whom gave a "Positive," "Negative" or "Neutral" rating of the company's product and its customer service. What was the number of customers who rated both the company's product and its service negatively?

(1) The number of customers who did not rate either product or service "Negative" was 40.

(2) The number of customers who rated both product and service "Positive" was 30.

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Re: The table above shows the results of a survey of 100 customers of a pa  [#permalink]

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16 Aug 2019, 02:29
Bunuel wrote:

The table above shows the results of a survey of 100 customers of a particular company, each of whom gave a "Positive," "Negative" or "Neutral" rating of the company's product and its customer service. What was the number of customers who rated both the company's product and its service negatively?

(1) The number of customers who did not rate either product or service "Negative" was 40.

(2) The number of customers who rated both product and service "Positive" was 30.

Attachment:
image649.png

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Re: The table above shows the results of a survey of 100 customers of a pa  [#permalink]

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17 Aug 2019, 03:40
Bunuel wrote:

The table above shows the results of a survey of 100 customers of a particular company, each of whom gave a "Positive," "Negative" or "Neutral" rating of the company's product and its customer service. What was the number of customers who rated both the company's product and its service negatively?

(1) The number of customers who did not rate either product or service "Negative" was 40.

(2) The number of customers who rated both product and service "Positive" was 30.

Attachment:
image649.png

customers rating negative ; 30+45-x ; 75-x
x = both
#1
The number of customers who did not rate either product or service "Negative" was 40.
total 100 so 100-40 ; 60 is both
75-60 ; 15 sufficient
#2
The number of customers who rated both product and service "Positive" was 30.insufficient
IMO A
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Re: The table above shows the results of a survey of 100 customers of a pa  [#permalink]

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17 Aug 2019, 03:52
Bunuel wrote:

The table above shows the results of a survey of 100 customers of a particular company, each of whom gave a "Positive," "Negative" or "Neutral" rating of the company's product and its customer service. What was the number of customers who rated both the company's product and its service negatively?

(1) The number of customers who did not rate either product or service "Negative" was 40.

(2) The number of customers who rated both product and service "Positive" was 30.

Attachment:
image649.png

Let the number of customers who rated both the company's product and its service negatively be x

30 + 45 - x = 75 - x = Number of customers who rated either product or service "Negative"

(1) The number of customers who did not rate either product or service "Negative" was 40.
75 - x = 100 - 40 = 60
x = 15
SUFFICIENT

(2) The number of customers who rated both product and service "Positive" was 30.
NOT SUFFICIENT

IMO A
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Re: The table above shows the results of a survey of 100 customers of a pa  [#permalink]

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17 Sep 2019, 23:39
Bunuel wrote:

The table above shows the results of a survey of 100 customers of a particular company, each of whom gave a "Positive," "Negative" or "Neutral" rating of the company's product and its customer service. What was the number of customers who rated both the company's product and its service negatively?

(1) The number of customers who did not rate either product or service "Negative" was 40.

(2) The number of customers who rated both product and service "Positive" was 30.

Attachment:
image649.png

Official Explanation

In this question, 30 out of 100 ratings of product were negative, and 45 out of 100 ratings of service were negative, and we want to know the overlap of those ratings--the number of unique people who rated both negatively. The answer could be as high as 30 (in the case of maximum overlap of the negative ratings) or as low as 0 (in the case of no overlap of the negative ratings), based on what we know so far. On to the statements, separately first.

Statement (1) gives us the count of people who fit in neither group. Since we are getting "neither" (N), and we want "both" (B), we can use the overlapping sets formula, which you can recall or derive from a Venn diagram:

T = G1 + G2 - B + N

Note that this formula doesn't describe the whole table, but rather just the "Negative" column of the table. From the table, we know that T = 100, G1 = 30, G2 = 45. From the data statement, we now know N = 40, so we can solve for B. Statement (1) is therefore sufficient.

Statement (2) gives us some information about the "Positive" column. Is it relevant to the number who rated both negative? It's relevant, because it allows us to compute the number of unique people in the "Positive" column. But there is still a range of possibilities. For example, the "Neutral" column could represent 15 unique people or, say, 20 unique people, with a corresponding difference in the number of unique people in the "Negative" column. Statement (2) does not allow us to answer the question definitively, so it's insufficient.

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Re: The table above shows the results of a survey of 100 customers of a pa  [#permalink]

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17 Sep 2019, 23:40
Bunuel wrote:

The table above shows the results of a survey of 100 customers of a particular company, each of whom gave a "Positive," "Negative" or "Neutral" rating of the company's product and its customer service. What was the number of customers who rated both the company's product and its service negatively?

(1) The number of customers who did not rate either product or service "Negative" was 40.

(2) The number of customers who rated both product and service "Positive" was 30.

Attachment:
image649.png

Video Explanation

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Re: The table above shows the results of a survey of 100 customers of a pa   [#permalink] 17 Sep 2019, 23:40
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