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18 Jun 2008, 02:39
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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
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
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18 Jun 2008, 03:09
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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
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
18 Jun 2008, 04:29
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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
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
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
