I've gone up short, less than 100m, 28% inclines with a 34 x 23
34/50 11-23 was plenty for 'ride for heart 50km' charity run which runs on a couple of highways. gps data shown here

well, his is the 75km run. but the 50km run is not much different.

• Total distance ridden: 76.91 km
  Climbing distance: 11.54 km
  Descent distance: 12.08 km
  Flat distance: 53.29 km
  Total elevation gain: +613 m / -606 m (*2)
  Climb grade: 1.7% ave, 8% max
  Descent grade: -1.5% ave, -8.9% max

I did the 50km version in 1h 40min riding solo.