## â€œuser-friendlyâ€ and â€œfast response timeâ€

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RonPurewal
Students

Posts: 19747
Joined: Tue Aug 14, 2007 8:23 am

### Re: â€œuser-friendlyâ€ and â€œfast response timeâ€

rachel, your mistake was in writing "UF = 30%". the problem states that 30% is the percentage of users who cited both U and F -- but that is a group that encompasses both your "UF" and your "UFB".

if B is given as 42%, this just means that a certain part of that 30% has to be in the "UFB" region.

i could be wrong about this, but it seems to me that you would have an easier time seeing these things if you drew the venn diagram -- it's quite a task to deal with eight different "regions" without a diagram.

rachelhong2012 wrote:My question is: how can B (including B only, FB, UB, UFB) be 42% if our capacity is only 26% for the remainder?

Thanks!
jp.jprasanna
Students

Posts: 200
Joined: Thu Nov 03, 2011 3:48 am

### Re: â€œuser-friendlyâ€ and â€œfast response timeâ€

RonPurewal wrote:rachel, your mistake was in writing "UF = 30%". the problem states that 30% is the percentage of users who cited both U and F -- but that is a group that encompasses both your "UF" and your "UFB".

if B is given as 42%, this just means that a certain part of that 30% has to be in the "UFB" region.

i could be wrong about this, but it seems to me that you would have an easier time seeing these things if you drew the venn diagram -- it's quite a task to deal with eight different "regions" without a diagram.

rachelhong2012 wrote:My question is: how can B (including B only, FB, UB, UFB) be 42% if our capacity is only 26% for the remainder?

Thanks!

Hi Ron and all - I have posted the images in the below link.

http://postimage.org/image/3v2fcqblp/ - Is this the correct interpretation ?

Calc for above dia (56-30) + (48-30) +30 = 74 ; 100 -74 =26 %

26% of 1200 = 312
OR

http://postimage.org/image/4xnolrw39/ - Is this the correct
interpretation ?

Cal for the above dia - Now as we know 56 + 42 + 48 - 30 - X - Y - Z = 100
116 - ( X + Y + Z )= 100 or 16 = X + Y + Z
From the question stem we also know that X + Y + Z + A = 42 Hence A = 26 %

1200 x 26 /100 = 312

The statement says "If 30 percent of the respondents cited
both "user-friendly" and "fast response time"" So the latter interpretation is correct ?

Even If I interpret it wrongly,(which ever one that is!), I still get 26%! How come!? :-(
jlucero
ManhattanGMAT Staff

Posts: 1102
Joined: Wed May 12, 2010 1:33 am

### Re: â€œuser-friendlyâ€ and â€œfast response timeâ€

Both of these are correct ways of looking at these 3-group Venn Diagram problems.

The first method includes adding 7 distinct sections of the diagram- 3 parts are only 1 category, 3 parts overlap 2 categories, and 1 part overlaps all 3 categories.

The second method includes adding up all of the people in three different groups and then subtracting the people you've counted more than once. For example, if someone has been counted as "User-Friendly" and as "Fast Response Time" we want to subtract the overlap (30%) so that we aren't counting them twice.

This means that you could use either formula with one important change: If you've counted someone in user-friendly, fast response time, and bargaining power- you've counted them three times, so you need to subtract the "all three categories" group twice in order to only count them once in your total calculations. Here's the two formulas:

(1) only A + only B + only C + only AB + only AC + only BC + only ABC = total

OR

(2) any A + any B + any C - AB - AC - BC - 2ABC = total
Joe Lucero
Manhattan GMAT Instructor