Quick rule: only the three aromatic amino acids absorb UV light, and you can remember them as the W, Y, F trio (tryptophan, tyrosine, phenylalanine). Strip away the non-aromatic options first: leucine, proline and arginine have no ring, so they contribute almost nothing to absorbance and can be eliminated at once.
That leaves tryptophan as the only aromatic choice here. Its indole ring is the most efficient absorber of the three, absorbing about ten times more strongly than tyrosine or phenylalanine, with peak absorbance near 280 nm. Because of this, the more tryptophan a protein contains, the higher its absorbance at 280 nm. Laboratories use exactly this property to read protein concentration off A280 values. So adding tryptophan gives the biggest jump in UV absorption.
Ref: Rebecca James, Self Assessment and Review of Biochemistry, 3rd edn.