Measurements of the THz absorption and the time-resolved photoluminescence have been performed on the same GaAs quantum well sample. The strength of the absorption at the internal 1s-2p exciton transition frequency is used as a measure of the density of excitons in the sample. When the interband pump laser is resonant with the Is exciton frequency, induced absorption at the 1s-2p frequency is clearly seen. If the same density of carriers is created pumping in the continuum, no significant 1s-2p absorption is seen in a time window of 450 ps. Complementary time-resolved photoluminescence experiments, detecting the emission at the exciton energy under the same pump conditions, show the PL intensity in resonant and nonresonant cases to be similar. The counter-intuitive existence of luminescence at the exciton energy simultaneously with the absence of the 1s-2p absorption is consistent with the recent theoretical predictions of Kira et al., Phys. Rev. Lett. 81, 3263 (1998).