no, it's an exercise in "inclusion/exclusion".

our "universe" (of recording titles that exist to be distributed) has 9,300 things in it (you can think of this as the "master list" of all recordings currently sold).

L handles 7,100 of these recordings, meaning there is 2,200 L doesn't carry.

M handles 5,200 of these recordings, so even if 2,200 of those are the ones L doesn't handle, that makes for a 3,000 overlap (titles they both distribute). so obviously, (c) isn't true.

(you could approach this "the other way": there are 4,100 titles M doesn't distribute. since L distributes 7,100, even if 4,100 of them were the ones L doesn't distribute, we still have a 3,000 overlap<---same figure for "shared distributed titles").

now we just have to decide between (a) and (b). is 3,000 more than 1/2 of what L carries? if so, pick (a).

is 3,000 more than 1/2 of what M carries? if so, pick (b).

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our universe breaks down like so:

total number of titles = 9,300

titles only L carries = A

titles only M carries = B

tiles both L and M carry = C.

the problem tells us:

A + C = 7,100

B + C = 5,200

A+B+C = 9,300

the "object" is to find C, which the above shows is 3,000. you can do it algebraically like this:

B = (A+B+C) - (A+C)

C = (B+C) - B

or:

A = (A+B+C) - (B+C)

C = (A+C) - A

we know A+B+C and A+C from the beginning: A+B+C = 9,300, and A+C = 7,100, so B = 2,200, thus C = 5,200 - 2,200 = 3,000 (first method)

or A = 9,300 - 5,200 = 4,100, so C = 7,100 - 4,100 = 3,000 (second method).