The game requires us to determine the order of 9 workers being hired - B C D E F G H I J. The question asks which of the following must be workers hired #8 and #9th.
The following rules apply:
(1) F & I were hired on the same day as each other and no one else was hired on that day. This rule tells us that we have one day when two workers were hired - F & I, but we do not yet know which day it is.
F I
(2) C & G were hired on the same day as each other, and no one else was hired. This rule also tells us that we have another day when exactly two workers were hired - C & G
C G
(3) On each of the other days, exactly one worker was hired. Since we have 9 workers total, and 4 of them were hired on two days, we have five workers left that must be hired over 5 days. Hence, we can conclude that overall it took 7 days to hire all 8 workers.
2-2-1-1-1-1-1
(4) E was hired before B
E > B This rule tells us that B cannot be hired on day 1 and E cannot be hired on day 7.
1 2 3 4 5 6 7 ~B ~E
(5) H was hired before D
H> D
This rule tells that H cannot be #7 and D cannot be hired on day 1
1 2 3 4 5 6 7 ~B ~E ~D ~H
(6) D was hired after I but before E
I > D > E
Taken together with rules (1) and (4) we have the following chain:
F I > D> E > B
We can see that the earliest B could be hired is day 4, the earliest E could be hired is day 3, D - day 2. We can also infer that the latest F & I could be hired is day 4, D - day 5, E day-6.
