Data Sufficiency

BTGmoderatorDC wrote: ↑

Tue Mar 14, 2023 8:00 pm

On her way home from work, Janet drives through several tollbooths. Is there a pair of these tollbooths that are less than 10 miles apart?

(1) The first tollbooth and the last tollbooth are 25 miles apart.
(2) Janet drives through 4 tollbooths on her way home from work.


OA C

Source: GMAT Prep

Given: On her way home from work, Janet drives through several tollbooths.

Target question: Is there a pair of these tollbooths that are less than 10 miles apart?

Statement 1: The first tollbooth and the last tollbooth are 25 miles apart.
There are several scenarios that satisfy statement 1. Here are two:

Case a: There are exactly 2 toll booths, and they are 25 miles apart. In this case, the answer to the target question is NO, there are NOT two toll booths that are less than 10 miles apart
Case b: There are exactly 3 toll booths (A, B and C). Their distances are: A......(5 miles)...B.......(20 miles).....C. In this case, the answer to the target question is YES, there ARE two toll booths that are less than 10 miles apart
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Janet drives through 4 tollbooths on her way home from work
There are several scenarios that satisfy statement 2. Here are two:
Let the toll booths be A, B, C and D.

Case a: A......(5 miles)....B.......(5 miles).....C.......(5 miles)....D In this case, the answer to the target question is NO, there are NOT two toll booths that are less than 10 miles apart
Case b: A......(15 miles)....B.......(15 miles).....C.......(15 miles)....D In this case, the answer to the target question is YES, there ARE two toll booths that are less than 10 miles apart
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Let's see if it is possible to satisfy both statements such that NO two toll booths are less than 10 miles apart.
So let's see what happens if we make every toll booth exactly 10 miles apart.
We get: A......(10 miles)....B.......(10 miles).....C.......(10 miles)....D
Since the total distance from the first and last toll booth is 30 miles (and not 25 miles as statement 1 suggests), we can be certain that at least one of the distance is above (between two adjacent tollbooths) MUST be less than 10 miles.
So, it must be the case that the answer to the target question is YES, there ARE two toll booths that are less than 10 miles apart

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C