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 Post subject: GMAT Overlapping Sets (Data Sufficiency)
PostPosted: Thu Apr 22, 2010 9:02 am 
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210 players are participating in 2010’s lacrosse program. If 80 of the players have played for at least two seasons, and 70 of the players are left-handed, how many of the players have played for at least two seasons and are left- handed?
(1) 90 of the players who have played for less than two seasons are right handed.
(2) 130 of the players have played for less than two seasons.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C.Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D.Either statement BY ITSELF is sufficient to answer the question.

E.Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.


(A) The easiest way to answer this question is by building a table. The table should have three columns and 3 rows.
The columns should be labeled (from left to right): Left-handed, Right-handed, and Total. The rows should be labeled (from top to bottom): At least 2 seasons, Less than 2 seasons, and Total. The sum of the rows should add up to the total row and the sum of the columns should add up to the total columns.

We are told that there are 210 players participating. This means the “Total” cell at the bottom right of the table should enclose a 210. The total amount of players who have been participating for at least two seasons is 80. Total number of left-handed players is 70.

Image

Since each column should add up at the bottom-most entry and each row should add up the right-most entry, we see that we can calculate the total number of players playing for less than two seasons, 130, as also total number of right-handed players, 140.

Image

Let’s use Statement (1) - insert a 90 in the “Right-handed” column that crosses “Less than 2 seasons” row. The number of Left-handed players playing less than two seasons, 40, and then subtract in the Left-handed column from 70, to arrive at 30 players who have played for at least two seasons and who are Left-handed.

Image

Statement (1), therefore is sufficient. We can thus eliminate answer choices (C) and (E). To determine whether our answer is going to be (A) or (D) we have to evaluate statement (2).

Statement (2) tells us that 130 players have played for less than two seasons. This is not sufficient because we can calculate that information without the statement. If 210 players play in total and 80 players have played for at least two seasons, we can simply subtract 80 from 210 in the “Total” column to get 130 without having been given that information.

Image

So, Statement (2) alone is not sufficient and the answer is (A).
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