[ZeroGravitas]

There's two answers already that seem correct, but perhaps overcomplex, so here's my go.

He always chooses 4 from the top row, so he always gets 25, 50, 75, 100 and the rest are chosen randomly.

Using them in combination he can always trade 25/50 for a "2", 75/25 for a "3" and 100/25 for a "4" if he needs them to get the answer. Rather than work that out on the fly he just remembers it.

Taking it once step further he can do (75x ± 100)/25 and get 3x ± 4, or (75x ± 50) / 25 and get 3x ± 2 if that would be helpful.

One of the other answers points out that he can go further and multiply that 50 or 100 by any of the random numbers he's given, which would be equivalent to multiplying the ± constant by the same amount though he doesn't use that level of complexity in his answer.

So he's basically building a toolbox of potential moves based on knowing that he'll always get those 4 numbers. He doesn't need to do the full calculation each time.