If I use this card when I have 9 cards in my trash, does this card become the 10th card in my trash, allowing me to gain 1 memory?
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Official Ruling
No, Option cards go to the trash after their effects activate, so you still have 9 cards in your trash when the effect checks to see how many cards there are. You don't gain 1 memory.
Source: BT4-111 Jack Raid