What power supply do I need for my LED light strips?
Stick with what the seller has told you.
The one thing you don't know is the rated voltage (forward) of each LED.
If you cut out LEDs and don't see a change one of two things is going on.


There is a current limiter inline to the diodes.
You have reached maximum intensity, and going with any fewer LEDs would cause a short life span. After you get to maximum intensity, more current does not show a greater intensity, it just damages the LEDs. 


As always, it would help if you had the data sheet for the LEDs, so could know the maximum POWER (V x I =P) that the diodes could handle. Then you could figure out no matter how many LEDs you were using what the voltage should be. 

By removing that section of strip, you may have shortened their life. See if the seller can fill in that info gap.