AMO 2027 Grades 4-5 SET 1 - Self-study

There are a total of 1290 children in 2 childcare centers, A and B. 20% of the children in Center A and 40% of the children in Center B are girls. If both centers have 336 girls, how many children does Center B have?

There are 650 pages in a storybook. How many times does the digit 5 appear in the page numbers?

A shop charges GST (Goods and Services Tax) of 7% on all items. Tyler paid 856 dollars for a stereo set at the shop. How much GST is charged for the stereo set?

There are 45 cars and motorbike in a car park. There are a total of 132 wheels. How many motorbikes are there?

Albert and Danny are running in a long-distance race. Albert runs at 6 miles per hour while Danny runs at 5 miles per hour. You may assume they run at a constant speed throughout the race. When Danny reaches the 25 mile mark, Albert is exactly 40 minutes away from finishing. What is the race's distance in miles?

It takes Harry 10 minutes to saw a piece of log into 3 equal lengths. How long does it take him to saw an identical piece of log into 6 equal lengths?

Find the next term of the following sequence:
2, 12, 1112, 3112, 132112, …

Tickets to a movie cost 7.25 dollars for adults and 5.50 dollars for students. A group of friends purchases 8 tickets for 52.75 dollars. How many adult tickets are purchased?

A group of businessmen were at a networking meeting. Each businessman exchanged his business card with every other businessman who was present. If there were 16 businessmen, how many business cards were exchanged?

From the top of a building, 600m above ground, a ball was dropped vertically downward. The ball rebounded vertically upward to 1/2 of the height from where it had fallen each time it hit the ground. Find the total vertical distance the ball had travelled in the air when it hit the ground for the fifth time.

The figure is made up of squares of equal size. How many more unshaded squares should be added so that 25% of the new figure is shaded?

In the addition shown, each of X, Y and Z represents a digit. What is the value of X + Y + Z?

$$\begin{array}{rrrr}&X&Y&Z\\&X&Y&Z\\+&&Y&Z\\\hline 1&6&7&5\end{array}$$

In the following cryptarithm, all different letters stand for different digits. Find the product of A and B.

$$\begin{array}{rrr}&A&A\\+&&A\\\hline B&0&8\end{array}$$

a) Today is Thursday. The day after 59 days will be which day of the week?

b) December 8th, 2007 was Saturday. What day of the week was it on December 8th, 2006?

c) On February 8th, 2005 it was Tuesday. What was the day of the week on February 8th, 2004?

d) If January 1st, 2006 was a Sunday, What was the day of the week January 1st, 2010?

Answer entry: write the four full English weekday names in order (a)–(d), separated by semicolons.

**Editorial input note:** Use no spaces before or after semicolons.

A road is 650m long. If trees are planted on both its sides at intervals of 5m. How many trees are planted on the both sides of the road if both ends of the road are also planted with trees?