Climbing above 6,000 meters (nearly 20,000 feet) is nothing that should be taken lightly. Even if the actual vertical of the climb is just over 1,000 meters (3,500 feet).
I arrived in Arequipa, Peru after three weeks of skiing up in the Colorado Rockies. I was camped at about 9,000 feet and would get up to 12,000 feet on some days while skiing. Granted, I took the chairlift, but I convinced myself this was sufficient time to be ready for a climb to 6,000 meters. I was nearly right.