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Bunuel
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.
Let the number of people who purchase newspaper X be x

and the number of people who purchase newspaper Y be y

and let t be the total population of the city

Overlapping Sets grid

XX'T
Yy
Y'
Txt


Given x/y = 7/1
or x = 7y
XX'T
Yy
Y't-y
T7yt-7yt


To find: y/t

Statement 1:
Twenty-seven percent of the population purchases neither newspaper X nor newspaper Y.

XX'T
Yy
Y'0.27tt-y
T7yt-7yt

We can't find y/t here.
So Insufficient
AD/BCE

Statement 2:

Seventy percent of the people who purchase newspaper Y also purchase newspaper X.
XX'T
Y0.7y0.3yy
Y'6.3yt-y
T7yt-7yt
We can't find y/t here.
So Insufficient
AD/BCE

Combining Statement 1 and Statement 2:
XX'T
Y0.7y0.3yy
Y'6.3y0.27tt-y
T7yt-7yt

From above
t = 0.7y + 0.3y + 6.3y + 0.27t
7.3y = 0.73t
y/t = 1/10
AD/BCE

Sufficient
Answer C
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"How many of the population of the city", not the total population.
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@Bunel - Ans should be A if we want to find % of Y and C if we want to find only Y. Question is worded incorrectly.
Bunuel
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.
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Hi Bunuel, want to understand why statement 1 is insufficient.

If we take the total as 'T' and from statement 1 - then those who buy at least one newspaper = 0.73T

No. who buy Y = 0.73T/8

Y/T = 0.73T/8 / T

Can you please confirm the error in splitting the 'at least one' number of 0.73T in the given ratio for X and Y?
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nikita.nanda1810
Hi Bunuel, want to understand why statement 1 is insufficient.

If we take the total as 'T' and from statement 1 - then those who buy at least one newspaper = 0.73T

No. who buy Y = 0.73T/8

Y/T = 0.73T/8 / T

Can you please confirm the error in splitting the 'at least one' number of 0.73T in the given ratio for X and Y?
0.73T is “X or Y or both,” not X + Y.
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given x=7y, where x and y are no of people purchasing newspaper X and Y respectively
we need to find the value of y/t, where t be the total no. of people
1: from it we can just get that 0.73 of t is the no of people who buy either X or Y or both i.e. the union value of the set , since 0.27 of t buy neither. ----INSUFFICEINT
2: just states that 0.7 of y is the no of people who buy both the newspapers i.e. intersection of the set.---INSUFFICIENT
together 1 and 2 we can formulate 7y + y - 0.7y=0.73 of t
solving this we can certainly get the value of y/t or the percentage of people who buy Y newspaper.
hence C
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@Bunel - According to me answer is A only. I am already given X: Y ratio. Now I just want to understand if this is exhaustive or not. A) lets me know which fall in neither bucket. So I know what is % of either X or Y. Question is who buys Y not who only buys Y. We don't need intersection information for it.
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I had the same confusion and when I started writing my detailed answer here for query - I realised the mistake I was making. For all the others - who may waste time similar to me and get confused.

1 - neither = Either x or either Y = Only X + Only Y + X intersection Y
From question premise x/y = 7/1
Let the ratio factor be k => x/y = 7k/1k
This 7k will be only X and overlap of X with Y
Same implies for Y
So 8k will be only X + only Y + 2 intersection of X & Y

Now Statement 1 will give us 1- neither = Only X + Only Y + Intersection only once. Thus if we divde this by 8 we will not get share of Y since intersection is doubly counted. So we need Statement 2. The moment I can subtract the intersection I get Only X + Only Y + Intersection and then if I apply *1/8 I will get my answer. Took 2 hours to get here - but a good tricky one!



Bunuel

0.73T is “X or Y or both,” not X + Y.
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Let number of people who purchase newspaper Y be k then number of people who purchase newspaper X is 7k
The question is asking what percentage of population purchases newspaper Y. So value of k
8k - both + neither = 100
Statement 1 - neither = 27
8k - both + 27 = 100
We still have two unknowns. Insufficient

Statement 2 - 70% of people who purchase newspaper Y also purchase newspaper X
both = 0.7k
So we get 8k - 0.7k + neither = 100
We still cannot find unique value of k. Insufficient

Combining statements 1 and 2 - neither = 27 and both = 0.7k
We get 8k + 0.7k + 27 = 100
7.3k = 73
k = 10
Percentage of population that purchases newspaper Y = k = 10%
So both statements together are sufficient. (C)
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