Meaning of 'flagging'

[Oana]

Test No. incompl/advan-88 "GMAT Verbal Quiz (11)", question 3

Although all the athletes were full of life at the start of the marathon, towards the end of the race a few were showing signs of tiredness and were clearly ..........

(a) flogging
(b) failing
(c) flagging
(d) foiling

Test No. incompl/advan-88 "GMAT Verbal Quiz (11)", answer 3

Although all the athletes were full of life at the start of the marathon, towards the end of the race a few were showing signs of tiredness and were clearly flagging.

Correct answer: (c) flagging

Your answer was: incorrect
Although all the athletes were full of life at the start of the marathon, towards the end of the race a few were showing signs of tiredness and were clearly flogging.
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i don't really understand this expression. could you please explain it to me

Oana

[Torsten]

Flagging can be an adjective meaning exhausted or very tired.
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Test Of English for International Communication
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[Snoopy_Blah_Blah]

Why not failing? In my dictionary it means exhausted as well.