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population reads

by sanju09 » Sat Apr 04, 2009 2:13 am
In a certain city X, only two newspapers A and B are published. It is known that 25% of the city population reads A and 20% reads B, while 8% read both A and B. It is also known that 30% of those who read A but not B, look into advertisements and 40% of those who read B but not A, look into advertisements while 50% of those who read both A and B, look into advertisements. What percentage of the population of city X reads an advertisement?
A. 8.1
B. 10.8
C. 13.9
D. 15.4
E. 16.5
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by truplayer256 » Sat Apr 04, 2009 5:10 am
Let's assume that City X has a population of x people.

(.25)(x) people read newspaper A.
(.20)(x) people read newspaper B.
(.08)(x) people read both.
(.30)(.25x-.08x)=(.30)(.17x)=People who read newspaper A but not newspaper B and look into advertisements section.
(.40)(.20x-.08x)=(.40)(.12x)= People who read newspaper B but not newspaper A and look into the advertisements section.'
(.50)(.08x)=.04x= People who read both newspapers and look into the advertisements section.
Answer:.139 or 13.9% C
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Re: population reads

by dtweah » Sat Apr 04, 2009 8:10 am
sanju09 wrote:In a certain city X, only two newspapers A and B are published. It is known that 25% of the city population reads A and 20% reads B, while 8% read both A and B. It is also known that 30% of those who read A but not B, look into advertisements and 40% of those who read B but not A, look into advertisements while 50% of those who read both A and B, look into advertisements. What percentage of the population of city X reads an advertisement?
A. 8.1
B. 10.8
C. 13.9
D. 15.4
E. 16.5
Avoid algebra on such questions. Say there are 100 people.

A= 25

B = 20

A n B = 8

People who read A but not B = 17 (25- 8)

People who read B but n0t A = 12 (20-8)

A only who read Ads = 17 (30%) = 5.1
B only who read Ads = 12* (40%) =4.8
A and B who read Ads 8 (50%) =4

4+4.8+5.1= 13.9. 13.9/100 is 13.9 %. You are done. Algebra is wonderful but it can be a problem some times if time is of the essence. Choosing 100 is like choosing X=100, so why choose X and not just throw in the 100!!
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