We know that,
There are 2 people -> Mateo and Zahra who arrive at the gate at different times
Flight departs at 4 PM and there are certain rules to be followed here
If a passenger checks luggage, it must be checked by 3 PM
If a passenger arrived at the gate after 3:30 PM, they must have checked in online before 3:30 PM
If a passenger arrives after 3:50 PM, they cannot board
We need to know if Mateo reached gate later than Zahra
We are given the following statements,
Statement(1) -> Zahra was allowed to board but Mateo wasnt
Mateo failed to board if:
1. He arrived after 3:50PM
2. He arrived between 3:31PM and 3:50 PM without having checked in online
Zahra has biarded so she satsifies all requirements
Case 1:
Zahra: 3:21 PM
Mateo: 3:58PM
Mateo arrives later
Case 2:
Zahra: 3:45PM
Mateo: 3:44PM
Mateo arrived earlier
Both cases are possible
Statement (1) is insufficient
Statement (2) -> Only one traveler needed to check luggage and did so at 2:45pm, and only one checked in online before 3:30 pm
Luggage is checked in time
One checked one and the other didnt
We dont know who arrives after 3:30 here
But still we see 2 possibilities here
The checked in online person comes after 3:40
The not checked in online person arrives at 3:20
This is possible for both person and both of their cases vice versa
=> We cant check who arrived earlier or later
Statement(2) is insufficient
Combining (1) and (2),
Zahra boarded
Mateo didnt board
Exactly one checked in online
One checked in baggae at 2:45 (But this is not required at all in our case as we see ahead)
Again there are 2 cases possible here
Case 1: Mateo checked in online
Reason he couldnt board since he came after 3:50PM
Zahra didnt check online and must have arrived by 3:30 pm to board
Zahra- 3:20PM
Mateo- 3:57PM
Mateo arrived later
Case 2:
Mateo didnt check in online
Zahra checked in online
Mateo arrived at 3:40PM and is denied inside
Zahra arrives at 3:46PM and boards
Zahra - 3:46PM
Mateo - 3:40PM
Mateo arrived earlier
We see both possibilities and cant say who arrived earlier or later
Neither statement alone nor together is sufficient
E. Neither statement is sufficient