You got these, but here is a longer winded explanation:
2. The near-universal intuition is that the balloon leans backward as you accelerate. Well, the intuition is wrong. Your job is to deduce how the balloon does move and to explain it to the interviewer.
Untie the helium balloon and let it hit the moonroof. It becomes a spirit level. The balloon is a “bubble” of lower-density helium in higher-density air, all sealed in a container (the car).
Gravity pulls the heavy air downward, forcing the light balloon against the moonroof.
When the car accelerates, the air is pushed backward, just as your body is. This sends a lighter-than-air balloon forward. When the car brakes suddenly, the air piles up in front of the windshield. This sends the balloon backward. Centrifugal force pushes the air away from the turn and sends the balloon toward the center of the turn. Of course, the same applies when the balloon is tied to something; it’s just less free to move. The short answer to this question is that the balloon nods in the direction of any acceleration.
4. Every page number has a digit in the units column. With N pages, that’s N digits right there. All but the first 9 pages have a digit in the tens column. That’s N – 9 more digits.
All but the first 99 pages have a digit in the hundreds column (accounting for N – 99 more digits).
I could go on, but not many books have more than 999 pages. A book with 1,095 digits in its page numbers won’t, anyway.
This means that 1,095 must equal:
N + (N – 9) + (N – 99).
This can be simplified to:
1,095 = 3N – 108.
That means that 3N = 1,203, or N = 401. That’s the answer, 401 pages.