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Because Mosul province shared borders with the newly formed Turkey so it was easier to claim, while other rich areas were quite far plus oil was not discovered yet in those places such Saudi Arabia, Kuwait and other rich places.
Also Mosul province was not occupied by the British in military operation, but the Ottoman army withdrew so they probably thought that might give them further cause to claim it, the oil was the icing on the cake.
No, I wasn't around in 1918 to count the population of Mosul, but I am sure the Ottomans and later maybe the British most likely did where you can refer to their census records for yourself.
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