Data Sufficiency

sanju09 wrote: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.

It may be useful to use the Double Matrix Method to help us arrange our information. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of fourth graders, and the two characteristics are:
- costume this year or no costume last year
- costume last year or no costume last year

Since our goal is to find a certain percent, let's say that we have a population of 100 students. So, we get the following:

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919
Notice that I've placed a star in the top-left corner (dressed last year AND this year) to denote which box we need to answer our target question.

Target question: What percentage of the fourth graders dressed in costume both this year and last year

Statement 1: 60% of the current fourth graders at Liberation Elementary School dressed in costume for Halloween this year
Since we're saying that the total population is 100, there were 60 students who dressed in costume this year. This means that there were 40 students who did NOT dress in costume this year
We get:

We still don't have enough information to determine the number of students in the top-left box, so we cannot answer the target question with certainty.
Statement 1 is NOT SUFFICIENT

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.
If we let x = # of students who did NOT dress in costume for Halloween this year, then 0.8x represents the # of students who ALSO did not dress in costume last year.

We still don't have enough information to determine the number of students in the top-left box, so we cannot answer the target question with certainty.
Statement 2 is NOT SUFFICIENT


Statements 1 and 2 combined
Statement 1 tells us that 40 students did NOT dress in costume this year
Statement 2 tells us that 80% of those 40 students also did NOT dress in costume LAST year.
So, 32 students did not dress in costume for both years (which means 8 students dressed last year but not this year). We get:

We still don't have enough information to determine the number of students in the top-left box, so we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Once you learn how the Double Matrix Method works, try these additional practice questions:
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping- ... 83320.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html

Cheers,
Brent