AMO 2027 Grades 4-5 SET 35 - Self-study

The sum of 5 different non-zero whole numbers is 45. What is the largest possible value of the largest of these 5 numbers?

Enter one whole number, without units.

Find $(115+114+113+112+111)-(101+102+103+104+105)$.

Choose one option.

The two figures below are made from cubes with side length 3 cm. What is their total volume?



The standalone source redraws the same shapes as follows:



Assume each figure is packed with equal cubes, including hidden supporting cubes, and fits flush into the corner between perpendicular walls. Choose one option.

Find $25\times48+32\times25+25\times20$.

Choose one option.

Place the numbers 1 through 12 in the diagram, one in each circle, so that the sums along the three sides of the triangle are equal. What is the largest possible sum along one side?



Use every number exactly once. Each side includes its two corner circles. Enter one whole number.

In a leap year there were 53 Saturdays. What is the greatest possible number of Tuesdays in that year?

Choose one option.

Tiffany looked at a clock and realized that the number of hours passed since midnight was five times the number of hours remaining until noon. What time did the clock show 1 hour ago?

Choose one option.

A small cube of side 6 units is placed inside a large cubical container of side 8 units. Liquid is then poured into the large container. What is the volume of the liquid, in cubic units?



Assume 8 units is the inside edge length, the smaller cube is solid and fully submerged, and liquid fills all remaining space to the brim. Ignore wall thickness. Enter one whole number without units.

A garland of 200 flowers follows this repeating pattern: 4 red, 3 orange, 5 yellow, then 4 red, 3 orange, 5 yellow, and so on. What is the difference between the numbers of red and yellow flowers?

Enter one whole number, without units.

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

Two trains travel in the same direction on parallel tracks close to each other. Both trains start moving at the same time, but train X is 40 km ahead of train Y. If train X travels at a speed of 70 km/h and train Y travels at a speed of 75 km/h throughout the journey, in how many hours will train Y catch up with train X?

Shauna takes five tests, each worth a maximum of 100 points. Her scores on the first three tests are 76, 94, and 87. In order to average 81 for all five tests, what is the lowest score she could earn on one of the other two tests?

Isabella had a week to read a book for a school assignment. She read an average of 36 pages per day for the first three days and an average of 44 pages per day for the next three days. She then finished the book by reading 10 pages on the last day. How many pages were in the book?

There are 25 trees planted at equal distances along a straight road. The distance between the first and the eighth trees is 56 meters. What is the distance, in meters, between the first and the last trees?

The original price of a watch at a shop was 80 dollars. After selling the watch at a discount of 25%, the shop owner still made a profit of 25%. What was the cost price of a watch?