PS Sets Ques

Question

Hello Everyone, Another one of the Venn diagram Sets ques where I get stuck.

Q- In survey of potential presidential candidates A and B, 30 percent liked A and 48 percent liked B. If the percentage of people who liked only one candidate is two times the percentage of people who liked both candidates then what is percentage of people who liked neither candidate ? (A) 27.5% (B) 35.5% (C) 41.5% (D) 58.5% (E) 64.5% OA is C. I tried solving it using formula - AUB = A + B - (A INT B) + none A = 30% & B = 48% None = what we need to find out so far it seems okay, now...% who like one is 2 twice who liked both then we can rewrite it as - 2(A IN B)= A or B.. i mean twice a intersection b is = a or b.. I mean got stuck here...how do I go ahead ? Cheers, GR

durgesh79 · Answer

you are almost there.

Question says that A+B - 2x = 2x
where x is number (%) of people who liked both. 
30+48=4x
x=19.5

total = A + B - x + none
100 = 30+48-19.5+ none
none = 41.5

greatchap · Answer

I know the ques says the % of people who like both the candidates is twice those who like one.
But how did you get -
A+B - 2x = 2x

A + B - 2x = 2x
---OK---- = ??

can you explain a bit please.

Thanks.

durgesh79 · Answer

if x is the number of people common in A and B 
then people who like only A = A -x
people who like only B = B - x

People who like only one candiddate = A-x + B -x = A+B - 2x
this is double than x.

The best way to solve these questions is to make diagram.

greatchap · Answer

Thanks a lot durgesh, kinda getting a bit of hang.

aaron22197 · Answer

This is an overlapping sets problem. I use the following strategies for such problems.

For questions with 2 variables, I use tables
For questions with 3 variables, I use circular Venn diagrams.

If we represent the question in the form of a table, we get the following.

LikeA Not-LikeA Total

LikeB 48

Not-likeB 52

Total 30 70 100

Let us also use variables to fill other areas.

LikeA Not-LikeA Total

LikeB p x 48

Not-likeB y q 52

Total 30 70 100

HOW DO I DISPLAY TABLES CORRECTLY ON THIS PAGE

Our goal is to find q. We also know from the question that  x+y=2p

write two other equations

P+x= 48
P+y=30

Adding both equations we get p=19.5... rest of it follows q=41.5.

This is the easiest approach to solve such problems. I have shown the detailed steps here. However, it takes less than 2 mins to solve the problems using the above strategy.

Hope this helps

PS Sets Ques

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