1959 AMC 12 Problem 47
Attempt Problem 47 of the 1959 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1959 AMC 12 solutions, or check the answer key.
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47.
Assume that the following three statements are true:
I. All freshmen are human.
II. All students are human.
III. Some students think.
Given the following four statements:
All freshmen are students.
Some humans think.
No freshmen think.
Some humans who think are not students.
Those which are logical consequences of I, II, and III are:
Answer: A
Small Hint:
Use the person whose existence is asserted in statement III
Big Hint:
Combine “some students think” with “all students are human”
Solution:
Statement III supplies at least one student who thinks. By statement II, that student is human, so some human thinks and statement follows. Nothing relates freshmen to students, says whether freshmen think, or guarantees a thinking human outside the students. Thus none of or follows.
Therefore, the correct answer is A.