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What percentage of the current fourth graders at Liberation

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What percentage of the current fourth graders at Liberation [#permalink] New post 27 Feb 2009, 09:58
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

66% (02:01) correct 34% (01:13) wrong based on 86 sessions
What percentage of the current fourth graders at Liberation Elementary School dressed in costume for Halloween for the past two years in a row (both this year and last year)?

(1) 60% of the current fourth graders at Liberation Elementary School dressed in costume for Halloween this year.
(2) Of the current fourth graders at Liberation Elementary School who did not dress in costume for Halloween this year, 80% did not dress in costume last year.
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Feb 2013, 03:14, edited 1 time in total.
Edited the question and added the OA.
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Re: DS.. [#permalink] New post 27 Feb 2009, 11:36
I think the answer is E.

Statement 1: 60% of the current fourth graders at Liberation Elementary School dressed in costume for Halloween this year.

This alone does not give any details about the previous year so A and D are out.

Statement 2: Of the current fourth graders at Liberation Elementary School who did not dress in costume for Halloween this year, 80% did not dress in costume last year.

This statement alone does not give the % for this year so B is out.

Looking at them together we are still missing the info on the percentage of students who wore costume this year but did not wear it last year. so C is out.
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Re: DS.. [#permalink] New post 27 Feb 2009, 11:40
Answer C

Say there are total of 100 4th graders last year and this year

With A you cannot do anything

Let the number of people/100 who got dressed this year equal to x
number of people/100 who got dressed last year = y

given who did not get dressed this year = 80/100 of who did not get dressed last year
100-x = 80/100(100-y) equation 1

Combining A and B
60 people go dressed this year
so eq 1 becomes 40 = 80/100(100-y), now u can find the value of y. add x&y u get the answer

The total number of people got dressed will the the same irrespective of the number of students u choose...so C
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Re: DS.. [#permalink] New post 28 Feb 2009, 01:50
A,B and D are ruled out

Total Stud = 100
Current = 60%

Last year did not dress for Halloween = 40 * 80/100 = 32
So it is 68 who got dressed

with the two values you can ge the combined % so it is C
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Re: DS.. [#permalink] New post 28 Feb 2009, 16:16
It should be E. Even after combining both the statements, it does not clarify how many of 60% students that did not dress costume this year did dress last year.
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Re: What percentage of the current fourth graders at Liberation [#permalink] New post 15 Jan 2013, 02:54
bunuel,
could u please provide a double set approach soln for this Qs?

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Re: What percentage of the current fourth graders at Liberation [#permalink] New post 25 Feb 2013, 15:06
OA is E.
This is the explanation from MGMAT.

We can divide the current fourth graders into 4 categories:

(1) The percentage that dressed in costume this year ONLY.
(2) The percentage that dressed in costume last year ONLY.
(3) The percentage that did NOT dress in costume either this year or last year.
(4) The percentage that dressed in costume BOTH years.

We need to determine the last category (category 4) in order to answer the question.

(1) INSUFFICIENT: Let's assume there are 100 current fourth graders (this simply helps to make this percentage question more concrete). 60 of them dressed in costume this year, while 40 did not. However, we don't know how many of these 60 dressed in costume last year, so we can't divide this 60 up into categories 1 and 2.

(2) INSUFFICIENT: This provides little relevant information on its own because we don't know how many of the students didn't dress up in costumes this year and the statement references that value.

(1) AND (2) INSUFFICIENT: From statement 1 we know that 60 dressed up in costumes this year, but 40 did not. Statement 2 tells us that 80% of these 40, or 32, didn't dress up in costumes this year either. This provides us with a value for category 3, from which we can derive a value for category 2 (8). However, we still don't know how many of the 60 costume bearers from this year wore costumes last year.

Since this is an overlapping set problem, we could also have used a double-set matrix to organize our information and solve. Even with both statements together, we can not find the value for the Costume Last Year / Costume This Year cell.

Costume This Year
No Costume This Year
TOTALS

Costume Last Year

8

No Costume Last Year
32

TOTALS
60
40
100


The correct answer is E.
Re: What percentage of the current fourth graders at Liberation   [#permalink] 25 Feb 2013, 15:06
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