Okay if you look at the picture in the link you'll see the gun smith quest for the Last Word. I'm at part five and I don't think things are working correctly. First off I infused the gun from 200 to 257 and it didn't show any update on the quest for me infusing it. Next I'm not an English expert by any means. However the last to requirements I believe are switched.The reason I say this is when you read it, it makes no sense and I think that's why it wont let me gain any progress in this quest.
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Okay, now I know what you're referring to. Step 2 is for PvE: you have to get seven precision kills within one magazine (no reloading). Step 3 is for PvP: you have to get seven precision kills in one match.