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niracha
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30% of U and F does include U and F and B case as well.
niracha
How do we know if BOTH means overlapping two sets or overlapping two sets & three sets?

For example,

In this case, both "user-friendly" and "fast response time" means only the part includes ONLY "user-friendly" and "fast response time" NOT "user-friendly" and "fast response time" and possibly "bargain prices" as well.

In this question https://gmatclub.com/forum/in-a-class-o ... 11487.html,
however, 15 play both cricket and football means "cricket" and "football" and possibly "hockey".
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Even though the total number of respondents is 1,200, this question is easiest to answer if we suppose that there were 100 responders. Then we can find the maximum PERCENTAGE of respondents who cited "bargain prices", and once we do that we can multiply that percentage by 1,200 to get our final answer.

We can break this problem into two parts:

1. Find the number of people who cited "user-friendly" OR "fast response time"

2. Maximize the number of people left over for "bargain prices" only

Let's start with part 1. Based on our pool of 100 people, we have:

56 who cited "User-friendly"

48 who cited "Fast response time"

42 who cited "Bargain prices"

We are also told that 30 people cited BOTH “user-friendly” and “fast response time.”

The GMAT wants you to recognize that you can use the standard group formula to find the total number of individuals who care about at least one of these two features:

Total = User Friendly + Fast Response - (Both)

(You have to subtract "Both" because you can't double count the people who are in both groups.)

Place our numbers into the equation:

Total = 56 + 48 - (30) = 74

So 74 people out of our 100 cited "user-friendly", "fast response time", or both.

Now let's move to part 2. Since there are 100 people in total, the number of people who cited neither of those first two options is:

100 - 74 = 26

We want to maximize the number of people who cited "bargain prices" BUT ONLY bargain prices.

Is 26 the maximum possible value? It is, because 26 is less than 42. It could be that 26 respondents out of 100 cited "bargain prices" and only bargain prices. The remaining 16 bargain seekers (42 - 26 = 16) would just overlap with the other categories.

So the maximum percentage for "bargain prices" only is 26%.

Now we can multiply 26% by the original pool of 1,200 respondents:

(1,200)(.26) = 312

Answer A
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