To determine which star has a higher apparent magnitude, we must consider how luminosity, distance, and temperature affect apparent brightness.
Since both stars have equal luminosities but Star A is closer to Earth, it will appear brighter to us. Apparent magnitude is lower (brighter) for objects that appear more luminous from our perspective.
Star B, being farther away, will appear dimmer despite having a lower surface temperature, which affects its intrinsic brightness but not the fact that luminosity is equal.
Thus, Star A will have a higher apparent magnitude (which means it will have a lower numerical value for magnitude) because it is at a lesser distance.
So, the correct response is: Star A will have a higher apparent magnitude because it is at a lesser distance. However, keep in mind that in the context of astronomical metrics, a higher apparent magnitude number means a dimmer star, so Star A will have a lower apparent magnitude number.