Quiz: some comments
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A: Fold.
If you push and he calls, the T45 from the blinds makes it virtually 0 EV. No reason to risk your whole stack for that.
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You're overlooking something here. It costs you 900 more to move in, and your opponent will call so you'd be getting pot odds of 1145:900, or 56:44.
That's pretty good considering that your hand is almost even money running hot and cold. At worst your opponent is a 53.5:46.5 favourite, but if his pair is 88/77/66/55, he's only a 51:49 favourite. The odds the pot is laying you are too good to pass up (despite the risk of losing your 900 stack). Folding would be an error.
Look at it another way: consider your overall Chip-EV for the hand, taking account of the 100 you've already put in the pot. If you fold, your CEV for the hand is -100. If you move in, you'll have a 48% chance of winning 1045 and a 52% chance of losing 1000, for a CEV of -18.4. Even though moving in gives you overall negative CEV for the hand, it's still better than folding by a wide margin (81.6 chips to be exact). It is a winner-take-all tourney, so "survival" per se is not an important consideration.
So folding is wrong; the question then is whether to move in or call. (Incidentally, you can show that folding is wrong in Scenario B too by the same reasoning.)
When I originally crafted this quiz, I intended that the correct answer would be to reraise in scenario A and smoothcall in scenario B. I still think that's correct but it's closer than I thought and I have to think some more about the solutions to scenario A posed by The Grifter and Al Capone Junior. One thing to keep in mind is that with KdQd if we flop a flush draw or openended straight draw we are a favourite over a pocket pair less than queens (unless it flopped a set of course). We have either 14 or 15 outs, with two chances to hit. Using that information we can improve somewhat on their suggested strategy of smoothcalling preflop, then betting any flop with an ace, king, or queen. We'd be looking for a strategy that gives us an overall CEV for the hand greater than -18.4, the CEV of moving in preflop.
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