Read the following statements and conclusions carefully. Assume that all the statements are absolutely true, even if they contradict commonly known facts. Based only on the given statements, determine which of the conclusions logically follows.
Statements:
Some Books are Old.
All Old things are Valuable.
No Valuable thing is Cheap.
Some Cheap things are Useful.
Conclusions:
(1) Some Books are not Cheap.
(2) Some Valuable things are Useful.
(3) No Book is Useful.
(4) Some Useful things are not Valuable.
Show answer & explanation
Correct answer: D
Explanation
Given Statements:
• Some Books are Old.
• All Old things are Valuable.
• No Valuable thing is Cheap.
• Some Cheap things are Useful.
Evaluation of Conclusions:
• Conclusion (1): Some Books are not Cheap.
Since some Books are Old and all Old things are Valuable, that portion of Books is Valuable. Since no Valuable thing is Cheap, those Books cannot be Cheap. Thus, conclusion (1) follows.
• Conclusion (2): Some Valuable things are Useful.
There is no definite positive relationship between Valuable things and Useful things. Thus, conclusion (2) does not follow.
• Conclusion (3): No Book is Useful.
There is no direct negative connection between Books and Useful things. Thus, conclusion (3) does not follow.
• Conclusion (4): Some Useful things are not Valuable.
Some Useful things are Cheap, and no Cheap thing is Valuable. Therefore, those Useful things which are Cheap can never be Valuable. Thus, conclusion (4) follows.
Hence, only conclusions (1) and (4) follow.