Absorbance maxima of polyenes [closed]

Can anyone tell me how to approach this question from USNCO 2013?

The question boils down to: which molecule has the longest conjugated $$\pi$$-system? The answer is (A). For such a system, the particle-in-a-box model is a decent approximation and one can show that larger systems absorb at lower energies, i.e. longer wave-lengths.