Olympiad Maths Prep

Track / Stage 4 / 152 of 340 #412 of 2000

Problem 412

AMC 12 late, AIME early
Combinatorics Difficulty 4.8 Find the answer

98. A, B, and C answered the same seven true/false questions. According to the rules, if they believed the statement was correct, they marked a “ \sqrt{ } ”; if they believed the statement was incorrect, they marked a “ ×\times ”. The results of A, B, and C's answers are shown in the table below. It is known that A, B, and C each got 5 questions right and 2 questions wrong.
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline A & ×\times & ×\times & \checkmark & ×\times & ×\times & ×\times & \checkmark \\
\hline B & \checkmark & ×\times & ×\times & ×\times & ×\times & \checkmark & ×\times \\
\hline C & \checkmark & \checkmark & \checkmark & \checkmark & ×\times & \checkmark & \checkmark \\
\hline
\end{tabular}

Question: What are the correct answers to these seven true/false questions?

Official solution

Reference answer: Correct, Incorrect, Correct, Incorrect, Incorrect, Correct, Correct

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.