I don't think the market sizing approach is correct- Here's my approach

It is not correct indeed. Let me point out some conceptual mistakes:

Total number of sets of wheels

1. You state that the life span of a wheel is 10 years, and of a vehicle is 20 years. That means that the segmentation between "new" and "old" doesn't work as you assume. The "new" cars will have their alloys last for 10 years. So EVERY car that is 1-10 years old (basically 50% of the total: 100m) will be running on their first wheel and when they get to year 10 they replace the wheel. That whell will last from year 11-20 (another 50% of the total: 100m).
2. A simpler way to do this is to consider that each vehicle uses 2 sets of wheels over their lifetime. So over 20 years, the 200m vehicles will need 200 x 2 sets of wheels = 400 sets of wheels OVER THEIR LIFETIME (20 years).
3. To convert to a single year, you will need to divide by 20 years: 400m / 20 years = 20m sets per year.
4. Let me note this: I would rather have you divide the population in two segments: cars year 1-10; and cars year 11-20. Why? Check the next part of the answer.

Total number of wheels in a set

You assume that you'll need 5 wheels per set. This is wrong. You need 5 wheels for the new vehicles (years 1-10). But when they get to year 10 they need to replace 4 wheels, but not the spare wheel. So you have to assume different values here. 

A few more issues:

• You are assuming that penetration of alloy wheels will increase for older cars. I believe one could argue the opposite. When the car is older you don't spend money to improve the car, you rather consider that it is approaching the end of it's useful life, you are probably making fewer miles with that car (more likely to be a second car) and would rather use worse parts. So instead of INCREASING penetration, I would decrease.
• You are ignoring that accidents may require changing a wheel before it reaches its useful life.
• You are ignoring that US population is increasing, which means that assuming that there's a stable vehicle park is quite a stretch... this would mean a decrease in vehicles per capita. One could argue that is the case, but this point would have to be verbalized and justified. There are also some other effects could be considered (e.g. exports of used vehicles).
• Please note that I would not expect a candidate to consider both of these (increasing population, exports) but at least having one of them (or at least justifying Why it doesn't have a meaningful impact) would be expected.

Hey there 😊

Thanks for sharing your reasoning — your logic is actually very structured and shows great thought! You’re breaking the market down into new car demand vs. replacement demand, and accounting for wheel type and volume per car, which is exactly the kind of structured thinking interviewers love to see 👏

A couple of small tweaks you might want to consider:

✨ Steady-state assumption — 20 years = 5% of cars replaced yearly, not 10% (so 200m ÷ 20 = 10m → you're correct here, but just watch that steady-state logic is clearly explained if asked).

✨ Replacement logic — You're right to distinguish the two wheel types and apply the correct replacement % — this step is often overlooked and you handled it well.

All in all: Your approach is MECE, well-structured and very close to perfect. The numbers are solid, and you’re layering assumptions clearly (which is key for market sizing cases). If this was in an interview — well done 💯

Let me know if you want to sanity check the math further or prep more like this!

Best,
Alessa 😊