The table gives three factors to be considered when...

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The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,200 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both "user-friendly" and "fast response time", what is the maximum possible number of respondents who cited "bargain prices", but neither "user-friendly" nor "fast response time"?

A. 312
B. 336
C. 360
D. 384
E. 420

The OA is A.

I'm really confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
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by [email protected] » Sun Feb 25, 2018 5:42 pm
Hi LUANDATO,

We're told that the table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,200 respondents to a survey who cited that factor as important. We're asked if 30 percent of the respondents cited both "user-friendly" and "fast response time", what is the MAXIMUM possible number of respondents who cited "bargain prices", but NEITHER "user-friendly" nor "fast response time."

While this prompt looks like some version of an Overlapping Sets question, you do not have to do too much work to organize the given information and answer the question (although some arithmetic will be required).

To start, we want to MAXIMIZE the number of people who chose JUST "bargain prices" (and neither of the other 2 reasons). To do that, we need to MINIMIZE the percents that cover the other two reasons.

According to the table:
56% chose 'user friendly'
48% chose 'fast response time'

IF... 30% of the people surveyed chose BOTH of those two reasons, then that 'group' of people is included in BOTH percents - but we're only supposed to include each person once. Thus, we have to remove one of those 'counts' for each person that shows up twice...

56% + 48% - 30% = 74%

This 74% would be the MINIMUM percent (of the group of 1200) who didn't choose JUST 'bargain prices'; this would leave 100% - 74% = 26% as the MAXIMUM percent that could have chosen JUST 'bargain prices'

(.26)(1200) = 312 people

Final Answer: A

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Rich
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by Scott@TargetTestPrep » Tue Feb 27, 2018 11:00 am
LUANDATO wrote:Image

The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,200 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both "user-friendly" and "fast response time", what is the maximum possible number of respondents who cited "bargain prices", but neither "user-friendly" nor "fast response time"?

A. 312
B. 336
C. 360
D. 384
E. 420
Since 30% of the respondents cited both "user-friendly" and "fast response time," then the percentage of respondents who cited "user-friendly" and/or "fast response time" is 56% + 48% - 30% = 74%.

Thus, we have 100% - 74% = 26% of the respondents who cited "bargain prices" but neither "user-friendly" nor "fast response time," and the number of such respondents is 1,200 x 0.26 = 312.

Answer: A

Scott Woodbury-Stewart
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