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AMO 2023 – Primary 6 (Grade 6)

Question 1

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?

Question illustration
  1. 12
  2. 20
  3. 24
  4. 25

Question 2

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?

Question illustration
  1. 6.2 hours
  2. 7.5 hours
  3. 7.8 hours
  4. 8.0 hours

Question 3

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

Question illustration
  1. 10 square units
  2. 15 square units
  3. 16.5 square units
  4. $\frac{65}{3}$ square units

Question 4

A survey of 30 middle school students records their weekly hours on digital devices. In its boxplot, the right part of the box is much narrower than the left part. Which observation is reasonable?

Question illustration
  1. Something must have gone wrong with the settings of the data analysis software.
  2. The data were not put in order properly.
  3. The numbers in the third quarter of the data set are closer to each other.
  4. The left side of the box represents more than 50% of the data.

Question 5

A hand sanitizer kills 60% 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.

Question illustration
  1. 68
  2. 84
  3. 98
  4. 120

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 6 and 135?

Question illustration
  1. 1
  2. 3
  3. 4
  4. 5

Question 7

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

Question illustration
  1. 11
  2. 20
  3. 28
  4. 84

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?

Question illustration
  1. 6 units
  2. 8 units
  3. 10 units
  4. 12 units

Question 9

Ten numbers have mean 12. Removing one number reduces the mean to 8. What number was removed?

Question illustration
  1. 20
  2. 36
  3. 48
  4. 52