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After 1:50, serving American in pub is unjustifiable (9)

Ross

I believe the answer is:

illogical

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'unjustifiable' is the definition.
Both the definition and answer are adjectives. Perhaps there's a link between them I don't understand?

'after 150 serving american in pub' is the wordplay.
'after' says to put letters next to each other.
'150' becomes 'IL' (Roman numerals for 1 and 50).
'serving american' becomes 'GI' (informal term for someone serving in the US milita).
'in' means one lot of letters goes inside another.
'pub' becomes 'local' (one's local pub).
'gi' inserted inside 'local' is 'logical'.
'il' next to 'logical' is 'ILLOGICAL'.

'is' acts as a link.

Can you help me to learn more?

(Other definitions for illogical that I've seen before include "Having no base" , "Lacking sound reasoning" , "Unsound" , "Without reason" , "lacking sense" .)

I've seen this clue in The Times.
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