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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]  27 Feb 2009, 09:58
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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]  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]  27 Feb 2009, 11:40

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]  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]  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]  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

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Re: What percentage of the current fourth graders at Liberation [#permalink]  24 Nov 2014, 05:06
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Re: What percentage of the current fourth graders at Liberation [#permalink]  26 Nov 2014, 21:00
1
KUDOS
Lets say there are 100 student
statement 1 = 60 wore costume this year and 40 did not (insufficient)
statement 2 = (alone says nothing about current year students) so insufficient
Combining both,
60 wore costume this year and 40 did not
last year 32 did not wore costuming and 68 did (assuming last year also there were 100 students)
[here only we can conclude E is ans]
so 68 wore costumes last year and 60 this year, but we don't know that these overlapping 60 are same students or not
So IMO E is correct ans.
Re: What percentage of the current fourth graders at Liberation   [#permalink] 26 Nov 2014, 21:00
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