Homesweet Learning helps students learn!
AMC8 2022 Test Paper
Complete the quiz in 40 minutes. Do the quiz as if you are taking the real test. You score will be compared with other students taking the same test to give you a ranking among your peers.
To get a human or AI tutor to help you, click Register
Sample Question 2:

Consider these two operations: What is the value of \((5 \, \blacklozenge \, 3) \, \bigstar \, 6?\)

\(\textbf{(A) } {-}20 \qquad \textbf{(B) } 4 \qquad \textbf{(C) } 16 \qquad \textbf{(D) } 100 \qquad \textbf{(E) } 220\)




Answer Keys

Question 2: D


Solutions

Question 2
Step 1: Substitute the given values, \(5\), \(3\), and \(6\), into the defined operations.
The operation \(5 \, \blacklozenge \, 3\) translates to \(5^2 - 3^2\).

Step 2: Solve for \(5^2 - 3^2\). This results in \(25 - 9\), which simplifies to \(16\).

Step 3: Plug the result of \(5 \, \blacklozenge \, 3\) into the second operation \(\bigstar \). Therefore, our equation is now \(16 \, \bigstar \, 6\), which translates to \((16 - 6)^2\).

Step 4: Solve for \((16 - 6)^2\). This results in \(10^2\), which simplifies to \(100\).

So, \((5 \, \blacklozenge \, 3) \, \bigstar \, 6 = 100\), which corresponds to answer choice \(\boxed{\textbf{(D) } 100}\).