“user-friendly” and “fast response time”

[apoorva_srivastva]

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

[hunkysden]

is the answer A i.e, 312?

if that is correct then I can post the method I've used.

[tomslawsky]

anyone??

[jonathanc]

I' say 312 too.

I did it using the Venn Diagramm (I like this trick found in MGMAT bbook because it 's very fast to use like the Prime box) unfortunately I dont find how to paste image here so I will use the text but if you trace the circles it is easy to follow.

I did my diagramm with 100 people to not waste time on calculation but you can do it with 1200 I think i guess it 's just longer.
You Know that the total of people in the User Friendly (UF) circle is 56 and the total in the Fast Response (FR) time is 48. The overlapping area between both including the overlapping with Bargain Prices (BP) is 30. So the Min and the Max people of UF + FRT (forget about BP circle now , dont even trace it if you want) is (56-30) + (48-30) +30 = 74. (with the circle it is easy to see). Means that you have 26 persons NOT UF and NOT FRT and the remaining 16 (42-26) have to be in an Overlapping area UF-BP or FRT-BP.

Thus 26 % is the number of people citing BP but not UF and not FRT ( I dont think there is a min and a max , it can only be this number.) and 26% of 1200 = 25%+ 1% = 300+12=312 (it s the way i do my calculation to go faster).

Hope it s the right method?

John

[tomslawsky]

amazing response, thank you

[Ben Ku]

John, great response and approach. Let me know if there are other questions here.

[kr.prateek]

Hi Ben / Staff,

If we solve this question using Venn Diagram, i get that remain 16% as only that common between BP and either of UF or FRT and not both since one of those will be also part of the 30% which is already excluded. Is that correct?

regards,
Kumar

[mithunsam]

You can solve using Venn diagram (mentioned above) or as below... (To get the maximum, we have to assume that no respondent chose userfriendly & bargain price or fast response & bargain price... )

[Consider the total respondents are 100 for the time being. We would convert back to 1200 later]

[Using formula P(AuB) = P(A) + P(B) - P(AnB)]

100 = (56 + 48 + 42) - 30 - Bargain Price
100 = 116 - Bargain Price
Bargain Price = 26

Now converting back to 1200 respondents
Bargain Price = 1200 * 26/100 = 312

[tim]

thanks; let us know if you have any more questions on this one, Kumar..

[kr.prateek]

thanks mithunsam.
That was helpful.

No questions Tim. thanks.

regards,
Kumar

[RonPurewal]

good stuff

[reagan88]

I am sorry, i dont quite get the venn-diagram explanation by John.. Are there any diagrams please??

[jnelson0612]

I am sorry, i dont quite get the venn-diagram explanation by John.. Are there any diagrams please??

Reagan, not that I know of. Were you able to draw a diagram based on the information given?

[rachelhong2012]

I' say 312 too.

I did it using the Venn Diagramm (I like this trick found in MGMAT bbook because it 's very fast to use like the Prime box) unfortunately I dont find how to paste image here so I will use the text but if you trace the circles it is easy to follow.

I did my diagramm with 100 people to not waste time on calculation but you can do it with 1200 I think i guess it 's just longer.
You Know that the total of people in the User Friendly (UF) circle is 56 and the total in the Fast Response (FR) time is 48. The overlapping area between both including the overlapping with Bargain Prices (BP) is 30. So the Min and the Max people of UF + FRT (forget about BP circle now , dont even trace it if you want) is (56-30) + (48-30) +30 = 74. (with the circle it is easy to see). Means that you have 26 persons NOT UF and NOT FRT and the remaining 16 (42-26) have to be in an Overlapping area UF-BP or FRT-BP.

Thus 26 % is the number of people citing BP but not UF and not FRT ( I dont think there is a min and a max , it can only be this number.) and 26% of 1200 = 25%+ 1% = 300+12=312 (it s the way i do my calculation to go faster).

Hope it s the right method?

John

I tried to draw a venn diagram based on this but still cannot follow all the steps and visualize it, can an instructor please draw the image? Thanks a lot!

[rachelhong2012]

I managed to arrive at the same conclusion without using the venn diagram. Can any of the instructors let me know if my method can be applied to nearly all problems involved three parts in overlapping set?

User friendly (U) ---56%
fast response time (F)---48%
bargain price (B)---42%

Without drawing venn diagram I know there are 8 cases:
UFB----unknown
UF----30%
FB----unknown
UB---unknown
NONE----unknown
U only----56%-30% = 26%
F only---48% - 30% = 18%
B only ---? max.
B---42%

altogether U + UF + F = 30 + 26 + 18 = 74 %
100-74 = 26 % left

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

Thanks!