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Venn diagrams - help needed

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Venn diagrams - help needed

by praveen_gmat » Wed Oct 12, 2011 3:23 am
User-friendly 56%
Fast response time 48%
Bargain prices 42%

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
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by CappyAA » Wed Oct 12, 2011 4:37 am
This is a tough one that takes a lot of work. Is this a GMAT problem or did you get this somewhere else?

Anyways, IMO it is A: 312

Let:

User Friendly = U
Fast Response Time = F
Bargain Prices = B
User Friendly & Fast Response Time = UF
User Friendly & Bargain Prices = UB
Fast Response Time & Bargain Prices = FB
All 3 = ALL

Doing a quick calculation to convert percentages to people with information we know:

Total set = 1200
U = 0.56*1200 = 672
F = 0.48*1200 = 576
B = 0.42*1200 = 504
UF = 0.3*1200 = 360

We know from venn diagram formulas that:

U + F + B - UF - UB - FB - 2*ALL + NONE = 1200

Plugging in for what we know:

672 + 576 + 504 - 360 - UB - FB - 2*ALL + NONE = 1200
- UB - FB - 2*ALL + NONE = -192
-(UB + FB + 2*ALL) + NONE = -192

We are looking for those that responded with Bargain Prices but not user friendly or fast response time. This is just the value of B - UB - FB - 2*ALL, which can also be written as B - (UB + FB + 2*ALL). We already know B. We are looking for the maximum value so assume that NONE = 0. We can solve for (UB + FB + 2*ALL) and we find find that this group is 192. We can then subtract this value from B in the equation above to get 504-192 = 312.
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by praveen_gmat » Wed Oct 12, 2011 4:42 am
Yes its a real GMAT problem. your answer is right.
But all questions will be solvable in 2 or 3 mins.
There should be a better way to do it.
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by CappyAA » Wed Oct 12, 2011 4:50 am
The only other way you can do it is by keeping the percentages in.

U + F + B - UF - UB - FB - 2*ALL + NONE = 1200

can also be written as:

U + F + B - UF - UB - FB - 2*ALL + NONE = 100

where they are all percentages. Plugging in our values that we are given we get:

56 + 48 + 42 - 30 -(UB + FB + 2*ALL) + NONE = 100
-(UB + FB + 2*ALL) + NONE = -16

Again, we assume NONE is 0 and find that (UB + FB + 2*ALL) = 16 which is 16%.

We can subtract the 16 from 42 to get a total of 26% that responded for Bargain Prices but not the other two. Then we can multiply 1200 by the 0.26 to get 312. Either way works.
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by praveen_gmat » Wed Oct 12, 2011 6:20 am
This is cool !
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by leonswati » Wed Oct 12, 2011 7:14 am
User friendly = U = 672

Fast Response = F = 576

Best Bargain = B = 504

Both User friendly and Best bargain = UB = 360

therefore

only U = 672-360 = 312

Only F = 576-360 = 216

Therefore Only B = 1200-312+216+360
= 312

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by [email protected] » Tue Nov 01, 2011 10:13 pm
One of the easy way i found is :

Take total as 100
User friendly - 56
Fast response - 48
Best Bargain - 42

Both User friendly and Fast response - 30

so total number of either user friendly or fast response is
User friendly + Fast response - Both = Total
56+48-30=74

so neither user friendly nor best bargain is 100-74 =26

as out of 100 it is 26
so out of 1200 it is 26*12 = 312

hence answer is A
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