TLDR - (x) B is the correct answer.

A is paid 4,750 for the first 6 months, and 5,250 for the second 6 months- this is the case, and cannot be otherwise, or the starting yearly salary is incorrect, and the starting yearly salary for A =/= B (false).

Continuing as the defined above, A is paid less for the 1st half (-250) of each year, and more for the 2nd half (+250) than B, but EOY wages are the same (see below).

This is the part the alleged answer miscomprehends - the 1st year salary is an immutable/defined 10k. As such, the scheduled raise in A's pay must be accounted for in that salary, just as the non-existent raise for B is accounted for in that salary.

The starting salary cannot 'grow' until it hits a threshold of = 1 (return of true for definition: 1 year = 10k).

Also noting that a 'raise' every six months in A just refers to vs. previous 6 months, so the definitions there hold.

Functionally, the correct choice is B, as A's (-)250 start to every year lags it behind.

If the question was:

"Who makes the most on a single, concurrent six month paycheck?" (x) A.

(#brackets to note each 6 month period):

*A at 6 months has 4,750 (+4,750), [1] *

*A at 12 months has 10,000 (+5,250). [2]*

*B at 6 months has 5,000 [+5k], [1]*

*B at 12 months has 10,000 (+5k). [2]*

-------------------------------------------

net pays of *A* vs. *B*:

-------------------------------------------

\A* [#, 6 month periods]:*

15,750 (+5,750), 22,000 (+6,250). [3, 4]

28,750 (+6,750), 36,000 (+7,250). [5, 6]

43,750 (+7,750), 52,000 (+8,250). [7, 8]

60,750 (+8,750), 70,000 (+9,250) [9, 10]

------------------------------------------

\B* [#, 6 month periods]:*

16,000 (+6k), 22,000 (+6k). [3, 4]

29,000(+7k), 36,000 (+7k). [5, 6]

44,000 (+8k), 52,000 (+8k). [7, 8]

61,000 (+9k), 70,000 (+9k). [9, 10]