Essentially, what the Germans were seeking to find in the people being brought to the camps were skilled laborers. Keep in mind these prisoners are doing everything from mining to making uniforms and pillows which will be used by the German forces. Young - middle aged male laborers were the most valuable, with children as young as ten being accepted into work forces. There was no set age or cut-off, so to speak: it was at the discretion of the evaluating Germans as to whether or not prisoners seemed fit for labor. Young men were fairly obviously acceptable, but the older you were, the more difficult it would be to determine work ability. Germans could study anything from perception, how one carries themselves, to walking ability, to speed, physical strength, size, muscle definition, etc. to evaluate someone. Frail old men would not be accepted. Neither would those who were very clearly sick, lame, or disabled. Eventually, prisoners began to learn this, so even if they were feeling sick or weak, it was important for them to try and fake their way through the inspection line - it was literal life vs. death for them. In some instances, a more sympathetic German might let someone join a labor group who they should have (by Nazi standards) discarded.

Simply passive the line and being put into a work group would not indefinitely secure your life, however: if a worker slacked off or was not able to keep up, they would get a beating at the least, and death sentence at most. Some valuable workers were able to secure infirmary or hospital time by a sympathetic German or someone with connections.

In the earlier days of the war it was far easier for the Germans to simply kill someone, but as the German advance on the Eastern Front stalled around Stalingrad and the Germans slowly became forced to retreat, combined with loss of ground to the British and Americans in Africa and Italy, and later on to the Allied Expeditionary Force in 1944, the necessity of labor became strong enough that the Germans could not simply kill off a prisoner - desperation made it so that younger and older prisoners were forced into labor.

This was the same policy that the German army ran under - in the early war days, the soldiers were young and fit, or experienced WWI veterans. If a soldier was injured, he was secured passage from the front lines and time to recuperate in a hospital until he was fit for duty. As the tide began to turn, wounded Germans were forced to return to the front lines and fight prematurely. Older men and veterans and increasingly younger children, even girls, could be given a gun as the tide of war was very clearly changed, and Germany sought simply to secure itself as much time to prepare for the end as possible. By the time the Russians reached Berlin, they were fighting mostly old men and children.

The Perfect Nazi - Martin Davidson

The Liberator - Alex Kershaw

The Man Who Broke into Auschwitz - Denis Avey

Simple things: elderly people, small children, middle aged women, and the sick would be killed immediately in most cases because it was likely that their work output would be poor or mediocre at best. Teenagers, young men and women, and some middle aged people were kept because they were the most efficient laborers. They could offset the costs of keeping them there.