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DS problem involving overlapping sets

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DS problem involving overlapping sets

by Osirus@VeritasPrep » Mon Nov 30, 2009 1:11 pm
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.


OA C

I am not interested in the answer per se, I am more interested in seeing someone solving this problem. When I try to solve it I get non integer numbers.
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by quantfunda » Tue Dec 01, 2009 9:07 am
osirus0830 wrote: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.


OA C

I am not interested in the answer per se, I am more interested in seeing someone solving this problem. When I try to solve it I get non integer numbers.
Lets take 1)

Given 27% purchases neither X nor Y, Hence 73% purchases either X , Y and both.
Now from the initial statement, given X/Y = 7/1 = k(say)
hence X=7k and Y =k
n(X U Y) = n(X) + n(Y) - n(X intersection Y)
Now we can't proceed further from here since reqd info not there.

Lets take 2)

X=7k and Y =k , Now it says 70% of Y is equal to the intersection of X and Y.

again taking individual statement like 2, wont give us the result.

So lets see if we can solve it by taking both statement into account.

73 = 7k+k+0.7k
=> k = 73/8.7
Hence C

PS* Do post your solution too and let me know if i made any error here. Thanks
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by Osirus@VeritasPrep » Tue Dec 01, 2009 1:07 pm
quantfunda wrote:
osirus0830 wrote: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.


OA C

I am not interested in the answer per se, I am more interested in seeing someone solving this problem. When I try to solve it I get non integer numbers.
Lets take 1)

Given 27% purchases neither X nor Y, Hence 73% purchases either X , Y and both.
Now from the initial statement, given X/Y = 7/1 = k(say)
hence X=7k and Y =k
n(X U Y) = n(X) + n(Y) - n(X intersection Y)
Now we can't proceed further from here since reqd info not there.

Lets take 2)

X=7k and Y =k , Now it says 70% of Y is equal to the intersection of X and Y.

again taking individual statement like 2, wont give us the result.

So lets see if we can solve it by taking both statement into account.

73 = 7k+k+0.7k
=> k = 73/8.7
Hence C

PS* Do post your solution too and let me know if i made any error here. Thanks
Thanks, I appreciate you taking the time to reply. I didn't do it the way you did, I used MGMATs approach and I put the wrong info in the tables.
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