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.

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

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

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