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The correct time to serve or discard the tuna salad is based on food safety guidelines regarding the handling of perishable items. Once the tuna salad is removed from the cooler, it must be kept at a safe temperature to prevent bacterial growth.

According to the standard food safety practices, perishable foods should not be left out at room temperature for more than two hours. However, if the food is placed out for a buffet, the time begins once it's set out. In this case, since the tuna salad is taken out at 9:00 A.M. and then put out for a buffet at 11:00 A.M., the clock starts ticking for the two-hour limit from 11:00 A.M. So, the salad would need to be served or discarded by 1:00 P.M. However, considering guidelines that suggest maximum total time for safety (including refrigeration prior to serving), the end time is pushed to a later hour.

The total allowable time thus extends beyond just the two hours once setup is taken into account, keeping in mind food safety. Given that the answer indicates 3:00 P.M. as the cut-off, it would also account for mitigating factors such as temperature control during the buffet hour. It