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What percentage of the current fourth graders at Liberation [#permalink]
27 Feb 2009, 09:58

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

62% (02:10) correct
37% (01:12) wrong based on 67 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.

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.

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.

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

The correct answer is E.

gmatclubot

Re: What percentage of the current fourth graders at Liberation
[#permalink]
25 Feb 2013, 15:06