AMO 2023 – Primary 5 (Grade 5)

Question 1

What is the ones digit of $1+1\times2+1\times2\times3+1\times2\times3\times4+\cdots+1\times2\times3\times4\times5\times6\times7\times8\times9$?

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Question 2

A box contains blue and orange markers in the ratio 5:3. After 10 orange markers are added, the ratio becomes 1:1. How many blue markers are in the box?

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Question 3

Twenty fifth graders recorded their usual daily hours of sleep in the dot plot. Each dot represents one student. What is the average number of hours?

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6.2 hours
7.5 hours
7.8 hours
8.0 hours

Question 4

Triangle $AMO$ is drawn on a grid of unit squares. Its vertices are grid intersections. What is its area in square units?

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10 square units
15 square units
16.5 square units
$\frac{65}{3}$ square units

A hand sanitizer kills 50% of the germs in each application, including repeated applications. Let $P$ be the percentage of germs killed after two applications. What is $100P$? Clarification: here $P$ is written as a proportion of the original number of germs, so $100P$ is the numerical percentage.

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Question 6

A number machine $nm$ takes two nonzero whole numbers $X,Y$, divides the larger by the smaller, and outputs the remainder $R$. What is the output for inputs 7 and 175?

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$-1$
0
4
5

Question 7

What is the sum of all natural numbers less than 28 that divide 28 exactly?

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Question 8

A path in the coordinate plane goes from $A=(2,1)$ through $B=(2,4)$, $C=(5,4)$ and $D=(5,2)$ to $E=(9,2)$. Each section is the straight segment joining its endpoints. What is the total length of the path?

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