The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.

Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.

Let's evaluate the conclusions using Venn diagrams or logical containment:
From the statements, we have a nested relationship:

Twenty⊂Thirty⊂Forty⊂Sixty⊂Seventy
Conclusion I: "Some forty are thirty." Since all thirty are forty, the region of thirty forms a part of forty. Therefore, some forty are definitely thirty. This conclusion follows.

Conclusion II: "Some seventy are sixty." Since all sixty are seventy, the region of sixty is entirely inside seventy. Therefore, some seventy are sixty. This conclusion follows.

Conclusion III: "No thirty is twenty." Since all twenty are thirty, there is a positive overlap where all twenty are thirty. Thus, saying "No thirty is twenty" is false. This conclusion does not follow.

Hence, only conclusions I and II follow.