Problem:
Alan, Beth, Carlos, and Diana were discussIng their possible grades in mathematics class this grading period. Alan said, "If I get an , then Beth will get an ." Beth said, "If I get an , then Carlos will get an ." Carlos said, "If I get an , then Diana will get an ." All of these statements were true, but only two of the students received an A. Which two receıved 's?
Answer Choices:
A. Alan, Beth
B. Beth,Carlos
C. Carlos,Diana
D. Alan,Diana
E. Beth, Diana
Solution:
If Alan received an "", then all the others would have received an "". If Beth received an "", then Carlos and Diana would also have received an "". Thus only Carlos and Diana received an "".
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions