cassette mix & match question

i have 2 dura ace 7800 cassettes.
#1 corn cob 21-11 in excellent shape
#2 25-11 older cassette with lower gears pretty bad.

i have a race which has 6000' climbing and need a good cassette.....so can i

take the 25-23-21-19 single piece from the older cassette and put it behind the bottom 6 gears from the good 21-11 cassette= 25-23-21-19-16-15-14-13-12-11

thanks

Sure. If the larger cogs are in reasonably good condition, then "Why not?"

BUT, try it before the race to ensure that there aren't any conflicts with the chain.

The 16 - 19 is a bit of a jump isn't it?

16-19 is a real big jump, and it's in what is a sweet spot on a cassette for a lot of people. It's likely because of the 11 tooth cog on the one cassette. 11 teeth is hard to justify sometimes. On a descente in 50/11 at 100 rpm, that'll give you 35 mph. Of course with a 53 it's faster, at 37 mph. A lot of people would argue that an 11t doesn't even make much sense on a descent, that a 12t wouldn't cost you that much. Plus, with a 12t, you can another cog in that 16-19t range. FWIW, a 53/12 at 100 rpm gives you a speed of almost 35 mph. You're talking about gaining 2 mph with an 11t high gear instead of a 12t (This was assuming a tire circumference of 2100 mm......I thought I'd be generous.).

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Did Shimano ever officially produce a 11-25 Dura Ace 7800 cassette? I know they now make one for the 7900 group.

On the 12-25 the 17-19 and 21-23-25 were combined on the alloy carrier.
On the 11-21 the 17-18 and 19-21 were combined.
So unless you get creative with a dremel or a drill you're stuck with the 5 largest sprockets...

If you're mixing a 11-21 and a 12-25 then you could get:

11,12,13,14,15,17,19,21,23,25