Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.

Statements:       Some reds are blues.

                          All blues are greens.

                          Some greens are not yellows.

Conclusions:      I. Some yellows are reds.

                           II. Some yellows are blues.

                           III. Some greens are reds.

Solution

Some reds are blues (I) + All blues are greens (A) ⇒ Some reds are greens (I) + Some greens are not yellows (O) ⇒ No conclusion. Hence, conclusion I does not follow.  All blues are greens (A) + Some greens are not yellows (O) ⇒ No conclusion. Hence, conclusion II does not follow. Some reds are blues (I) + All blues are greens.(A) = Some reds are greens.(I) ⇒ conversion ⇒  Some greens are reds (I) Hence, conclusion III follows. Alternate Method: Conclusion I: Not necessarily true based on given venn diagram. Conclusion II:  Not necessarily true based on given venn diagram. Conclusion III:  It is true based on given venn diagram. Hence, option (d) is the correct answer.