  We show that the luminosity dependence of the red clump stars on age and
metallicity can cause a difference of up to < ~0.6 mag in the mean absolute I
magnitude of the red clump between different stellar populations. We show that
this effect may resolve the apparent ~0.4 mag discrepancy between red
clump-derived distance moduli to the Magellanic Clouds and those from, e.g.,
Cepheid variables. Taking into account the population effects on red clump
luminosity, we determine a distance modulus to the LMC of 18.36 +/- 0.17 mag,
and to the SMC of 18.82 +/- 0.20 mag. Our alternate red clump LMC distance is
consistent with the value (m-M){LMC} = 18.50 +/- 0.10 adopted by the HST
Cepheid Key Project. We briefly examine model predictions of red clump
luminosity, and find that variations in helium abundance and core mass could
bring the Clouds closer by some 0.10--0.15 mag, but not by the ~0.4 mag that
would result from setting the mean absolute I-magnitude of the Cloud red clumps
equal to the that of the Solar neighborhood red clump.
