In a certain city, the ratio of the number of people who purchase news

Question

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.

Ypsychotic · Answer

imo, the number of people who do not purchase any newspaper= Total population- (the no. of people who buy newspaper x + the no. of people who buy newspaper y - who buy both), because the no of people who buy both are being counted twice. So, Statement 2 is needed to answer the question.

So, 0.27P=P-8x+y should be the equation, where y= no. of people who buy both newspapers.

IMO, option C.

RS81 · Answer

Let 
only x = a
only y = c
x&y = b
Neither x nor y = d

Given  
(A) = a + b + c + d = 100
(B) = (a+b)/(b+c) = 7/1 => a = 6b+7c

They are asking  b+c = ?

Statement 1: 
d=27 Insufficient

Statement 2: 
(b+c)*7/10=b =>
3b=7c
This equation combined with (A) & (B) is not enough

Lets combine statement 1 & 2 
we get 4 equations
a + b + c + d = 100
a = 6b+7c
d=27 
3b=7c
none of them are parallel so this is sufficient

Answer c

bhanu29 · Answer

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

X 
 X' 
 T 
 
  Y

y 
 
  Y'

T 
 x 
  
 t

Given x/y = 7/1
or x = 7y
    
 X 
 X' 
 T 
 
  Y

y 
 
  Y'

t-y 
 
  T 
 7y 
 t-7y 
 t

To find: y/t

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

X 
 X' 
 T 
 
  Y

y 
 
  Y' 
  
 0.27t 
 t-y 
 
  T 
 7y 
 t-7y 
 t

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.
    
 X 
 X' 
 T 
 
  Y 
 0.7y 
 0.3y 
 y 
 
  Y' 
 6.3y 
  
 t-y 
 
  T 
 7y 
 t-7y 
 t

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

Combining Statement 1 and Statement 2: 
    
 X 
 X' 
 T 
 
  Y 
 0.7y 
 0.3y 
 y 
 
  Y' 
 6.3y 
 0.27t 
 t-y 
 
  T 
 7y 
 t-7y 
 t

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

Sufficient 
 Answer C

mattisweb · Answer

"How many of the population of the city", not the total population.

Confusion · Answer

@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.

nikita.nanda1810 · Answer

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?

Bunuel · Answer

0.73T is “X or Y or both,” not X + Y.

pappal · Answer

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

Confusion · Answer

@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.

Goldenfuture · Answer

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!

Utkarsha20 · Answer

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)

In a certain city, the ratio of the number of people who purchase news

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