According to a recent census, West Egg had more mansions per ca-pita

Question

According to a recent census, West Egg had more mansions per ca-pita last year than East Egg, while East Egg had slightly fewer residents than West Egg. Since the census, West Egg and East Egg have each seen the demolition of a dozen dilapidated mansions within their respective borders, and no new mansions have begun construction. It must be true, therefore, that _________.

Which of the following best completes the passage?

A) West Egg and East Egg both have more cared-for mansions than dilapidated mansions.
B) West Egg has more mansions than East Egg.
C) West Egg has more mansions per capita than East Egg.
D) West Egg and East Egg have the same number of mansions.
E) West Egg has more residents than East Egg

chetan2u · Accepted Answer

Hi,

OA is B, since it can be said with surety that the number of mansions are higher in west egg than east egg..

we are given last year per capita mansions was more in west egg and also the population was more in west egg..
so the number of mansions in west egg= number per capita * popualtion will be greater as both  number per capita and popualtion  is higher in west egg than east egg..
This year only 12 mansions have been demolished and new constructed, so this year too  number of mansions will be higher in west egg than east egg

But can we say the same about C..
C talks of mansions per capita, which is dependent on  number of mansions and population ...
we know the changes in number of mansions, but nothing about population..
the population too if unchanged will give you an answer YES for C,
But if the population has increased in west and decreased in east, the answer can be NO..

so E need not be true, as we are not told anything about change in population..

WaterFlowsUp · Answer

west Egg: Let's say 
Before demolition # of houses =20
# of resident = 10
Per capita =2

Eas egg 
# of houses=17
# of people=9
per-capita= 1.95

after demolotion of a dozenmansion

WEST egg
# of houses= 8
east egg
# of houses= 5

Therefore B can be inferred

kelvind13 · Answer

Shouldn't 'C' also be the right answer here,

Per Capita for west: 
8/10 = 0.8

Per Capita for East:
5/9 = 0.55

0.8 > 0.55

I picked C and I'm still not sure why this isn't the right answer.

Nick90 · Answer

My Approach to solve this one is .......

1) West egg more mentions per capita than East engg (number of mansions / total population )
2) East engg has slightly fewer residents (assume equal) to West engg .

Now from these points you can infer that West has more mansions than East has .

Also this point says , demolition has equal impact on both east and west mansions ....this tells number of mensions reduced in east is equal to that of west .
So   we can say that west still has more mansions than east has  .

2016MBAcandidate · Answer

Why is E wrong?

In must be true question rephrasing premise is also a correct answer

dina98 · Answer

picked E. I can see how B can possibly be correct but E is not incorrect.

PrakharGMAT · Answer

Hi  chetan2u  /  daagh ,

I am stuck between B and C.
OA is B.
 Can you please assist why is C incorrect.

chetan2u · Answer

Hi,
E is incorrect because we are not told anything about the change in population

if the population has increased in west and decreased in east, YES..
But if the population has decreased in west and increased in east, NO..

We cannot assume that the relative value of last year are true for this year unless specified

newconcept123 · Answer

Hey Guys
Look at these two sentences:
West Egg had more mansions per ca-pita last year than East Egg, while East Egg had slightly fewer residents than West Egg.
Pay attention to "slightly" which means:
West Egg mansion per capita * residents > East Egg mansion percapita* residents 
And both West Egg and East Egg will demolite same amount of mansions, so still, West Egg mansions are more than East Egg.

sonaxi · Answer

As per chetan2u 's logic,nothing can be assumed about the change in population, as it could have increased or decreased. This is the reason why E is incorrect and why C is uncertain.

C talks about mansion per capita = Total mansion/Total population. Since, this option is dependent on population and we are uncertain about fluctuation in population between the two points, C is uncertain.

However, going by the same logic, B is also uncertain. B talks about number of mansions, which product of mansions per capita & total population. Since the answer is dependent on total population and following the logic that you stated for C and E, their is a possibility that population of West Egg has declined extremely drastically and is now way less than East Egg. In that scenario, the number of mansions will be less in West Egg then East Egg. 
If we are using the logic that we cannot assume population increase or decrease and ruling out option E and C, we should apply the same logic to A.

chetan2u · Answer

Hi  sonaxi ..
You are correct that the mansions are dependent on population and per capita..
So let's see what was the case before demolition..
W had more mansions per capita and more population too last year..
So ofcourse more mansions per capita and more population MEANS more mansions last year..

Now what has happened since last year..
Same number of mansions are demolished. So same number being taken out, the larger number will remain larger..
So We has more mansions than E..
B should be true and certain

GMATYoda · Answer

Veritas Prep Official Explanation:

The question reveals that West Egg had more mansions per capita and East Egg had fewer people. But “since the census” all we know is that both West Egg and East Egg have 12 fewer dilapidated mansions. We can conclude only that the total number of mansions in both places has decreased equally, and therefore West Egg must still have more mansions than East Egg. We do not have any information about the residents after the census. It’s possible East Egg’s population has increased dramatically, or that West Egg’s has decreased. We therefore cannot make any conclusions “per capita.”

dcummins · Answer

OFFICIAL EXPLANATION
 
The correct answer is (B).

The question reveals that West Egg had more mansions per capita and East Egg had fewer people. But “since the census” all we know is that both West Egg and East Egg have 12 fewer dilapidated mansions. We can conclude only that the total number of mansions in both places has decreased equally, and therefore West Egg must still have more mansions than East Egg. We do not have any information about the residents after the census. It’s possible East Egg’s population has increased dramatically, or that West Egg’s has decreased. We therefore cannot make any conclusions “per capita.”

gmexamtaker1 · Answer

Hi experts, 
Even though I have read all the above comments I still can't understand why I should choose B over E. Could somebody shed some light on this problem?

aniket16c · Answer

West Egg had more mansions per capita last year than East Egg, while East Egg had slightly fewer residents than West Egg
 
Mansion at West Egg = A. Mansions at East egg = B.
Residents at West Egg = X. Residents at East egg = Y.

As per the statement: A/X > B/Y

and Y< X 
Now smaller denominator on B/Y side means for A = B, the condition cannot be true. Hence, A > B

Since the census, West Egg and East Egg have each seen the demolition of a dozen dilapidated mansions within their respective borders, and no new mansions have begun construction 
The trick is to understand the "a dozen" is literally 12 mansions, and it is not used figuratively to mean considerable number of mansions.
Another observation is a year has passed since the demolition. Hence, we do not know the change in population within the year.

Hence after demolition, the inequality remains A-12 > B-12
Option B: West Egg has more mansions than East Egg.
Exactly what the inequality A-12 > B-12 says

Option E: West Egg has more residents than East Egg
As mentioned before, we are not sure what the change has been in the population since the census

We have not been given any statement about the number of people after

pradeepgontla · Answer

I've seen a few confusing theories above and would like to give my view on why B and not C.

C. Let us assume that there is no change in population then as the number of houses demolished are same there will be a variance in percaptia number of houses for each city and we can't capture all the conditions correctly.

B. Since the demolition is same we can clearly conclude that western egg has more number of houses than eastern egg.

sagarsangani123 · Answer

Lets understand this problem with Tim, Jim, their friends and chocolates.

Tim <-> West Egg
Jim <-> East Egg
Friends <-> Residents
Chocolates <-> Mansion

Tim-> 10 friends -> 40 chocolates -> 4 chocolates per friend
Jim-> 5 friends -> 15 chocolates -> 3 chocolate per friend

West Egg has fewer residents than East Egg <-> Jim has fewer friends than Jim
Mansions per capita are higher in West Egg <-> Jim's group has higher chocolates per friend

Dozen (12) of mansions are demolished in both West Egg and East Egg<-> 12 chocolates are eaten both in Tim's group and Jim's group

Only certainty:
Mansions left in West Egg are still higher than East Egg (Answer Choice B) <-> 28 chocolates with Tim's group and 3 chocolates in Jim's group

Kapil1650 · Answer

B is correct but why E is wrong .??

Posted from my mobile device

Parthkulkarni · Answer

The key is reading 'slightly fewer' residents. It's to be taken as almost equal

According to a recent census, West Egg had more mansions per ca-pita

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According to a recent census, West Egg had more mansions per ca-pita

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