Question

3. You have three stars. Star A has an apparent magnitude of 7, Star B has an apparent magnitude of 2, and Star C has an apparent magnitude of -4.
Is it possible to determine which star appears brightest. If so, which one appears brightest?
Is it possible to determine if any of these stars are visible from Earth. If so, which ones are visible from Earth?
Is it possible to determine which star has the most luminosity? If so, then which star has the highest luminosity?

4. How would your answers to question #3 change (if at all) if the word "apparent" were changed to "absolute"?

Answer 1

"Apparent magnitude" means how bright a star looks to
a person on Earth.

-- The star that appears brightest is the one with the
lowest-number apparent magnitude . . . Star-C, at -4 .

-- All of them are visible from Earth, but may require some 'help'. 
The dimmest stars visible with good human eyes under dark,
non-polluted skies are those with apparent magnitude around 6.
Stars B and C would be visible to the unaided eye, but Star-A
would require binoculars.
Around here, a few miles outside of the Chicago city limits, we're
lucky to see Magnitude-4 without binoculars.

-- It's not possible to determine which star has the highest luminosity.
The apparent magnitude depends on the star's distance from Earth
as well as its luminosity.
A flashlight 3 feet from your face appears much brighter than any
star, although any star is more luminous than the flashlight. 
Distance from you has a lot to do with it.
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"Absolute magnitude" means how bright each star would appear
to a person on Earth if all stars were at the same distance from us.
(The distance happens to be 32.6 light years.)  It only depends on
the star's real luminosity, not on its distance.

-- It's not possible to determine which star appears brightest.
Star-C (absolute -7) would appear brightest if all stars were
equal distances from us.  But a flashlight ... which has a huge-
number absolute magnitude because we couldn't see at all from
32.6 light years away ... can appear very bright from 3 feet in
front of your face.

-- They're all visible from Earth, but a star with absolute magnitude
greater than 6 would need binoculars (or better) to be visible.

-- Yes, if you know a star's absolute magnitude, then you know its
luminosity.  The lowest-number absolute magnitudes are the ones
that would appear brightest if all stars were the same distance from
us, so they're the stars with the greatest luminosity.  From this group,
that's Star-C.