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In a certain city, the ratio of number of people who [#permalink]

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In a certain city, the ratio of 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) 27% of the population purchases neither newspaper X nor newspaper Y (2) 70% of the people who purchase newspaper Y also purchase newspaper X
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

In a certain city, the ratio of 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) 27% of the population purchases neither newspaper X nor newspaper Y (2) 70% of the people who purchase newspaper Y also purchase newspaper X

A x:y :: 7:1

1. 73% will buy either x or yor both - This is where I feel I could be making the mistake 8a = 73% a = 9.1% Y = 9.1% - Sufficeint

In a certain city, the ratio of 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) 27% of the population purchases neither newspaper X nor newspaper Y (2) 70% of the people who purchase newspaper Y also purchase newspaper X

Thanks Amit for the posting. Now I understand what I was overlooking. Basically, the raio of 7:1 is of numbers and from stmt1: we only know of the percentage of union. Hence, this will not be sufficient to get the desired ratio.

Thanks Amit for the posting. Now I understand what I was overlooking. Basically, the raio of 7:1 is of numbers and from stmt1: we only know of the percentage of union. Hence, this will not be sufficient to get the desired ratio.

how do we calculate using the 2 statements ?
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Thanks Amit for the posting. Now I understand what I was overlooking. Basically, the raio of 7:1 is of numbers and from stmt1: we only know of the percentage of union. Hence, this will not be sufficient to get the desired ratio.

how do we calculate using the 2 statements ?

Suppose, p is the total population then from stmt1: 0.73p = XUY = X + Y + X intersection Y = 8Y + X intersection Y....insufficient.

From stmt2: X intersection Y = 0.7Y.

Combining two, 0.73p = 8.7Y and hence, Y/p can be determined.

Question stem: Let P=population X/Y = 7 Y/P=? _______________

XuY - union of X and Y X_Y - intersection of X and Y

Stmt 1: X_Y/P=0.27 Stmt 2: Y/XuY=0.7

Neither statement alone is suff. So, either C or E. P=X+Y-XuY+X_Y - we need to see if we can make this expression consisting of P and Y only. From stem: X=7Y; from stmt1: X_Y=0.27P from stmt2: XuY=Y/0.7 Replacing for the above we have : P = 7Y + Y- Y/0.7 +0.27P; We can bring the above to Y/P form. So answer should be C. Let me know you spot any mistake.

Statement 1 provides us the total percentage of population who buy newspaper, that is 73% total population. but it is insufficient to conclude that in this 73%, the people buy A:B = 7:1 because many people buy B also buy A.

we put the number who buy B = X, then according to the ratio A:B = 7:1 then number buy A = 7X. So the number who buy newspaper could be X+7X subtract the number of people who buy both A and B = total 73% population

Use the statement 2, we know that 70% people buy B also buy A and we have this number equal to 0.7X. This number should be subtracted from the total.

Then we get X+7X - 0.7X = 7.3X = 73% population => x =10%.

Thanks Amit for the posting. Now I understand what I was overlooking. Basically, the raio of 7:1 is of numbers and from stmt1: we only know of the percentage of union. Hence, this will not be sufficient to get the desired ratio.

how do we calculate using the 2 statements ?

Suppose, p is the total population then from stmt1: 0.73p = XUY = X + Y + X intersection Y = 8Y + X intersection Y....insufficient.

From stmt2: X intersection Y = 0.7Y.

Combining two, 0.73p = 8.7Y and hence, Y/p can be determined.

Why you put X + Y = 8Y, 8Y also include those population which buy both X & Y. SO for me you can't replace it directly.

I still think there is issue in question it self. If question is such that : Find the population which buy ONLY paper Y