How many people in Town X read neither the World newspaper nor the Glo

Hi

We should not assume that there were only two newspapers available in TownX.

Let a,b and c represent the number of people who read only World, Globe and Other respectively.
x represent the number of people who read both World and Globe.
y represent the number of people who read both Globe and Other.
z represent the number of people who read both World and Other.
m represents the number of people who read all the three newspapers.
n represent the number of people who do not read any newspaper.

[Note: You can represent the above information in the form of a Venn diagram for better understanding.]

We have to find c+n.

(1) Total number of people in the town and number of people who read no newspaper are given.
n=1000
a+b+c+x+y+z+m+n = 2500
a+b+c+x+y+z+m = 1500 ->(1)
We know the value of n but we do not know the value of c. The given information is insufficient to find the value of c.

(2)Number of people who read only Globe and who read only World is given.
b=700 and a=600
We do not know the total number of people in TownX. The given information is insufficient to find the value of c+n.

(1) + (2) - Combining statements (1) and (2)
Even by substituting b=700 and a=600 in equation (1), the value of c cannot be determined.

Answer: E

Why do we assume there are more than 2 newspapers?

In fact, we cannot assume that there are only two newspapers unless it is stated in the question. It is the same case for integers: we cannot assume that X can be only an integer unless it is stated in the question.

I still don't see why the answer is not A

ScottTargetTestPrep,
Since 1,000 people read no newspaper, we know at most 1,000 people read neither the World newspaper nor the Globe newspaper.
Please let me know ow do you find that at least 1000 people read neither the World newspaper nor the Globe newspaper.
If you add a 3rd newspaper vendor,say X, then if 500 people read only X. Then we can assume that out of 1000 people, there are atleast 500 people wh do not read either the World newspaper or the Global newspaper. Please help me to understand where am I wrong in my understanding

The 1,000 people who read no newspapers is the minimum figure for the number of people who read neither the World nor the Globe. If there are only two newspapers, then there are exactly 1,000 people who read neither the World nor the Globe. You can increase this number by adding a third newspaper, say newspaper X; if there are people who read only newspaper X, then the number of people who read neither the World nor the Globe is 1,000 + the number of people who read only X.
Following your example, let's say there are 500 people who read only X. Notice that these 500 people are not included in the 1,000 people who read no newspapers, because they read a newspaper, which is X. In this example, if there are no other newspapers, the number of people who read neither the World nor the Globe is 1,000 + 500 = 1,500.

Since the gmat officially says, "nothing is to be assumed unless written", why is this question classified as hard?

This Quant question turned into a CR question, real quick!

Hi Experts, Bunuel, KarishmaB,

Can you please share your approach to this question? Also, why are we assuming the existence of a "third newspaper"?

Thanks in advance.

The trick here is that we are not given that Town X has only 2 newspapers. If it were a question on subjects in a college (say, 'how many students took neither History not Chemistry?') would we assume that there are no other subjects? No, we wouldn't. Similarly, we cannot assume here that there are only 2 newspapers in this town.

Our standard sets formula is this:
Total = World + Globe - Both + Neither

Neither -> the number of people who read neither World nor Globe.


Statement 1: 1000 people read no newspaper. This is NOT our Neither. We know that our Neither is 1000 or more but what it is exactly, we don't know. It is possible that there are 100 people who read a newspaper (so not a part of this 1000) but do not read World or Globe. Then our neither would become 1100 and so, Neither could take many different values.
The only thing thing this statement tells us is that Total = 2500


Statement 2: Gives us 'only Globe' and 'only World.' We don't know the value of Both. We can use another formula here
Total = Only Globe + Only World + Both + Neither
But we have 2 unknowns, Both and Neither

Using both statements, we don't know 'Both' and we don't know 'Neither.'
Answer (E)

Thanks for such a clear explanation, KarishmaB. Understood now!