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Percentage Problem?

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by DCJ » Wed Aug 12, 2009 4:43 pm
Can someone set this up?

In a certain city, the ratio of the number of people who purchase newspaper X to the number of people who purchase newspaper Y is 7:1. What percent of the population purchases newspaper Y?

(1) Twenty-seven percent of the population purchases neither newspaper X nor newspaper Y
(2) Seventy percent of the people who purchase newspaper Y also purchase newspaper X

Answer: BOTH statements together are sufficient
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Source: — Data Sufficiency |
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by tohellandback » Wed Aug 12, 2009 7:12 pm
C

1) we don't know how many people buy BOTH.
not suff

2)we don't know the total population or the percentage of population that buys the newspapers
NOT SUFF

combined
Use the venn diagram
if X be the total population.
we know that 73X/100 is the total pupulation that buys these two newspapers
we know the percentage that buys both
we can find the percentage that buys X. X will cancel out

SUFF
The powers of two are bloody impolite!!
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by prindaroy » Wed Aug 12, 2009 7:41 pm
using the venn diagram you arrive at the following equation;

7x - 0.7x + 0.7x + 0.3x = 0.73p

so we determine that x/p = 0.73/7.3

7y = x

y/p = 0.73/51.1

so both statements are required to solve it because i've used the fact from statement 1 that only 73% accounts for newspaper buying and from statement 2 i used the fact that 70% of newspaper y purchasers also purchase newspaper x
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by shahdevine » Wed Aug 12, 2009 8:10 pm
prindaroy wrote:using the venn diagram you arrive at the following equation;

7x - 0.7x + 0.7x + 0.3x = 0.73p

so we determine that x/p = 0.73/7.3

7y = x

y/p = 0.73/51.1

so both statements are required to solve it because i've used the fact from statement 1 that only 73% accounts for newspaper buying and from statement 2 i used the fact that 70% of newspaper y purchasers also purchase newspaper x
Could you algebraically translate " 70% of people who purchased newspaper x, purchase newspaper y?" Also, are you using the overlap formula, Group1+Group2-Both+Neither=Total?

Thanks
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Answer is C

by mark412 » Mon Aug 17, 2009 3:16 pm
I took the linear equation approach of a Venn Diagram

Set A + Set B- Both (A+B)+N=Total

We do need both bits of info as you can see they are complementary and crucial to creating an equation.

This is what C looks like if you had the info lined up

Denote: Set A=X, Set B=Y, N=Neither

X+Y-.72+.27=1 (remember we cannot have a percentage greater than 1)

X+Y=.65 since we were supplied info in the stem that X=7Y we substitute.

7Y+Y=.65 8Y=.65 Y=.081.

Although you do not need to solve it, it does help to see how it all ties together.

Hope this helps.
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by kumadil2011 » Thu Dec 01, 2011 7:31 am
HOW DID YOU GET 0.65 FOR X+Y?
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