Of the 25 cars sold at a car dealership, some had auto

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Of the 25 cars sold at a car dealership, some had auto transmission and some had antilock brakes. How many of the cars had auto transmission but not antilock brakes?

1) All of the cars that had antilock brakes also had auto transmission.
2) Two of the cars had neither auto transmission nor antilock brakes.

OA E
Source: — Data Sufficiency |

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by deloitte247 » Sat Aug 31, 2019 2:19 am

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Total number of cars = cars with antilock + cars with auto transmission + cars with both antilock and auto transmission + cars with neither antilock nor auto transmission

Question: How many cars had auto transmission but not antilock brakes?
i.e Find the difference of cars that had auto transmission and cars that have both antilock and auto transmission.

Statement 1: All of the cars that had antilock brakes also had auto transmission.
Antilock = both
25 = (both + auto transmission) - (both + neither)
25 = auto transmission + neither
The information provided is not enough to evaluate auto transmission - both to get the value of cars with auto transmission but no antilock brakes. Hence, statement 1 is NOT SUFFICIENT.

Statement 2: Two of the cars had neither auto transmission nor antilock brakes.
Therefore, statement 2 is NOT SUFFICIENT.

Combining the 2 statements together;
25 = auto transmission + neither
neither = 2
So, auto transmission = 25 - 2 = 23.
But the value or both and or antilock is still unknown. Therefore, we cannot evaluate auto transmission - both/
Hence, the two statements together are NOT SUFFICIENT.

Answer = option E