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Difference between revisions of "2021 Mock AMC 8 Problems"

(→‎Problem 6)
(→‎Problem 7)
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==Problem 7==
 
==Problem 7==
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The number <math>N</math> is a positive <math>3</math> digit integer.
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•When <math>N</math> is divided by <math>80</math>, the remainder is <math>4</math>
 +
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•When <math>N</math> is divided by <math>3</math>, the remainder is <math>1</math>
 +
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•<math>N</math> is a perfect square.
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What is the sum of the digits of <math>N</math>?
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<math>\textbf{(A) }8\qquad\textbf{(B) }10\qquad\textbf{(C) }12\qquad\textbf{(D) }14\qquad \textbf{(E) }16</math>

Revision as of 13:30, 23 October 2021

Problem 1

What is the value of $1-2+3-4+5-6+7-8+9$?

$\mathrm{(A)}\ 4 \qquad\mathrm{(B)}\ 5 \qquad\mathrm{(C)}\ 6 \qquad\mathrm{(D)}\ 7 \qquad\mathrm{(E)}\ 25$

https://artofproblemsolving.com/wiki/index.php/2021_Mock_AMC_8_Problems/Problem_1

Problem 2

Aaron has a rectangular yard measuring $4$ feet by $10$ feet. How many $2$ inch by $5$ inch rectangular bricks can he fit in his yard?

$\mathrm{(A)}\ 4 \qquad\mathrm{(B)}\ 12 \qquad\mathrm{(C)}\ 24 \qquad\mathrm{(D)}\ 72 \qquad\mathrm{(E)}\ 144$

https://artofproblemsolving.com/wiki/index.php/2021_Mock_AMC_8_Problems/Problem_2

Problem 3

Amy, Bob, Cassie, and Darren are on a camping trip. Each of them has $4$ choices for what they wear on day $1$ of the camping trip. How many different arrangements of what they wear are possible on day $1$ of the camping trip?

$\textbf{(A) } 16 \qquad \textbf{(B) } 32 \qquad \textbf{(C) } 64 \qquad \textbf{(D) } 256 \qquad \textbf{(E) 500}$

Problem 4

A rectangle with positive integer side lengths has area $2021$. In how many ways is this possible?

$\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 3 \qquad \textbf{(D) } 4 \qquad \textbf{(E) } 5$

Problem 5

Fiona leaves her house to go to the airport. She drives for $30$ minutes at a constant rate of $40$ miles per hour, then walks for $20$ minutes at a constant rate of $3.6$ miles per hour. She then goes on a train going 50 miles per hour for 12 minutes. How far has she traveled?

$\textbf{(A) } 31.2 \qquad \textbf{(B) } 32.2 \qquad \textbf{(C) } 32.4 \qquad \textbf{(D) } 33.8 \qquad \textbf{(E) } 35.9$

Problem 6

Hexagon $ABCDEF$ has side length $4$. What is the area of this hexagon rounded to the nearest tenth??

$\textbf{(A) } 40.8 \qquad \textbf{(B) } 41.5 \qquad \textbf{(C) } 41.6 \qquad \textbf{(D) } 42.4 \qquad \textbf{(E) } 44.3$

Problem 7

The number $N$ is a positive $3$ digit integer.

•When $N$ is divided by $80$, the remainder is $4$

•When $N$ is divided by $3$, the remainder is $1$

•$N$ is a perfect square.

What is the sum of the digits of $N$?

$\textbf{(A) }8\qquad\textbf{(B) }10\qquad\textbf{(C) }12\qquad\textbf{(D) }14\qquad \textbf{(E) }16$

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