Question

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.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

1. With this information, there are three other categories of cars that are unknown: those equipped with both a stereo and power windows, with power windows but with no stereo, and with neither power windows nor a stereo; NOT sufficient.
2. Again there are three other categories that are unknown: those with a stereo but no power windows, with power windows with no stereo, and with neither power windows nor a stereo; NOT sufficient.

• From (1) and (2) together, it can be deduced that there were 60 -50 = 10 cars sold that did not have a stereo. However, it is unknown and cannot be concluded from this information how many of these cars did not have a stereo but did have power windows or did not have either a stereo or power windows.
• The correct answer is E; both statements together are still not sufficient.