Data Sufficiency

sanjib wrote:How many of the 60 cars sold last month by a certain dealer had neither power windows nor a stereo?
(1) Of the 60 cars sold, 20 had a stereo but not power windows.
(2) Of the 60 cars sold, 30 had both power windows and a stereo

An easy way to solve this problem is to set up a double set matrix. In our matrix we have two main categories: power windows and stereo. More specifically, our table will be labeled with:

1) Power windows (PW)

2) No power windows (No PW)

3) Stereo

4) No stereo

(To save room on our table headings, we will use the abbreviations for some of these categories.)

We are given that a total of 60 cars were sold last month. We are trying to determine how many cars sold had neither power windows nor a stereo.

Let's fill all this information into a table. Note that each row sums to a row total, and each column sums to a column total. These totals also sum to the grand total, designated by 60 at the bottom right of the table.



We need to determine the value for the question mark in the table.

Statement One Alone:

Of the 60 cars sold, 20 had a stereo but not power windows.

Let's fill the information from statement one into our matrix.



Statement one does not provide enough information to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Of the 60 cars sold, 30 had power windows and stereo.

Let's fill the information from statement two into our matrix.



Statement two is insufficient to answer the question. Eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know that of the 60 cars sold, 20 had a stereo but not power windows and that 30 had power windows and stereo. We can fill all this into our matrix.



We see that we still do not have enough information to determine how many cars sold had neither power windows nor a stereo.

The answer is E