Data Sufficiency

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)?

(A) 60% of the current fourth graders at Liberation Elementary School dressed in costume for Halloween this year.

(B) 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.


I think the answer is C .. can anyone explain why should it be E and not C

Answer not known

Source MGMAT

(B) 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.

Here, we do not have enough info to conclude how many dressed in Costume last year.
It only says of those who did not dress this year, 80% did noy
What about those from current year who did not dress who dressed in costume last year?

I think I was able to come up with percentages of who dressed and who didn't for the two years, but you still don't know how many fourth graders there were for each year. I don't think you can be assuming a constant number of fourth graders.

1.) 60 students dressed in haloween constume this year---insufficient

2.) 80% of the people who did not dress this year did not dress even last year.

Insufficient. This we dont done know what number of people did not dress this year.

Combine A+B

40% students did not dress this year. so 80%*40% of total did not dress last year. Now this gives only the data percentages. How many number of people are actully present is not specified in the question.

Thus E.

IMO E

A is not sufficient

From B
Let
Number of students did not dress last year =L
Number of students did not dress last year =P
L=0.8P;-------- 1
Total number of students =X;

(X-L)+(X-P)/2X ; Not possible with one equation 1.

from A
P=0.6X

Now we can get the percentage. But this is not asked in the question.Question is about calculating number students who dressed straight for 2 years.

Hence E

Summary:
Percentage of total number of students who are dressed can be calculated but not the intersection of students who dressed for both years.

Hope i made some sense !

The question does ask for percentages, so we don't need the actual number of kids.

I thought of the calculation as such:

Total (100%) = 3rd grade + 4th grade + neither - both

From A, we know 4th grade = 60%
From B, I think we can calculate the neither - (100%-60%)*80% = 32%

All we know from B is about the overlap of those that didn't dress this year and last year. There's nothing that allows us to pinpoint the % dressed in 3rd grade (and thus determine the both). It could be 8% (no double dressers) or it could be 68% (all kids dressed in 4th dressed in 3rd plus those that dressed in third but not forth).