Difference between revisions of "2024 AMC 8 Problems"

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==Problem 1==
 
What is the ones digit of <cmath>222,222-22,222-2,222-222-22-2?</cmath>(Kipsta Ravindran)
 
<math>\textbf{(A) } 0\qquad\textbf{(B) } 2\qquad\textbf{(C) } 4\qquad\textbf{(D) } 6\qquad\textbf{(E) } 8</math>
 
 
 
[[2024 AMC 8 Problems/Problem 1|Solution]]
 
 
 
==Problem 2==
 
What is the value of this expression in decimal form?
 
<cmath>\frac{44}{11} + \frac{110}{44} + \frac{44}{1100}</cmath>
 
 
 
<math>\textbf{(A) } 6.4\qquad\textbf{(B) } 6.504\qquad\textbf{(C) } 6.54\qquad\textbf{(D) } 6.9\qquad\textbf{(E) } 6.94</math>
 
 
 
[[2024 AMC 8 Problems/Problem 2|Solution]]
 
 
 
==Problem 3==
 
 
 
==Problem 4==
 
When Yunji added all the integers from <math>1</math> to <math>9</math>, she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out?
 
 
 
<math>\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9</math>
 
 
 
[[2024 AMC 8 Problems/Problem 4|Solution]]
 
 
 
==Problem 5==
 
Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of <math>6</math>. Which of the following integers cannot be the sum of the two numbers?
 
 
 
<math>\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9</math>
 
 
 
[[2024 AMC 8 Problems/Problem 5|Solution]]
 
 
 
==Problem 6==
 
 
 
==Problem 7==
 
 
 
==Problem 8==
 
On Monday Taye has $2. Every day, he either gains $3 or doubles the amount of money he had on the previous day. How many different dollar amounts could Taye have on Thursday, 3 days later?
 
 
 
<math>\textbf{(A) } 3\qquad\textbf{(B) } 4\qquad\textbf{(C) } 5\qquad\textbf{(D) } 6\qquad\textbf{(E) } 7</math>
 
 
 
[[2024 AMC 8 Problems/Problem 8|Solution]]
 
 
 
==Problem 9==
 
 
 
==Problem 10==
 
 
 
==Problem 11==
 
 
 
==Problem 12==
 
 
 
==Problem 13==
 
 
 
==Problem 14==
 
 
 
==Problem 15==
 
 
 
Let the letters <math>F</math>,<math>L</math>,<math>Y</math>,<math>B</math>,<math>U</math>,<math>G</math> represent distinct digits. Suppose <math>\underline{F}~\underline{L}~\underline{Y}~\underline{F}~\underline{L}~\underline{Y}</math> is the greatest number that satisfies the equation
 
 
 
<cmath>8\cdot\underline{F}~\underline{L}~\underline{Y}~\underline{F}~\underline{L}~\underline{Y}=\underline{B}~\underline{U}~\underline{G}~\underline{B}~\underline{U}~\underline{G}.</cmath>
 
 
 
What is the value of <math>\underline{F}~\underline{L}~\underline{Y}+\underline{B}~\underline{U}~\underline{G}</math>?
 
 
 
<math>\textbf{(A)}\ 1089 \qquad \textbf{(B)}\ 1098 \qquad \textbf{(C)}\ 1107 \qquad \textbf{(D)}\ 1116 \qquad \textbf{(E)}\ 1125</math>
 
 
 
[[2024 AMC 8 Problems/Problem 15|Solution]]
 
 
 
==Problem 16==
 
 
 
==Problem 17==
 
 
 
==Problem 18==
 
 
 
==Problem 19==
 
 
 
==Problem 20==
 
 
 
==Problem 21==
 
A group of frogs (called an army) is living in a tree. A frog turns green when in the shade and turns yellow
 
when in the sun. Initially, the ratio of green to yellow frogs was <math>3 : 1</math>. Then <math>3</math> green frogs moved to the
 
sunny side and <math>5</math> yellow frogs moved to the shady side. Now the ratio is <math>4 : 1</math>. What is the difference
 
between the number of green frogs and the number of yellow frogs now?
 
 
 
<math>\textbf{(A) } 10\qquad\textbf{(B) } 12\qquad\textbf{(C) } 16\qquad\textbf{(D) } 20\qquad\textbf{(E) } 24</math>
 
 
 
[[2024 AMC 8 Problems/Problem 21|Solution]]
 
 
 
==Problem 22==
 
 
 
==Problem 23==
 
 
 
==Problem 24==
 
 
 
==Problem 25==
 
 
 
==See Also==
 
{{AMC8 box|year=2024|before=[[2023 AMC 8 Problems|2023 AMC 8]]|after=[[2025 AMC 8 Problems|2025 AMC 8]]}}
 
* [[AMC 8]]
 
* [[AMC 8 Problems and Solutions]]
 
* [[Mathematics competition resources|Mathematics Competition Resources]]
 

Revision as of 13:48, 25 January 2024

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