AMO 2016 Grade 5

Find the value of (4 × 6 × 8) ÷ (2 × 3 × 4).

On Wednesday, the store sign said that the new video game would be available in 33 days. On what day of the week should the sign say that it will be available in only 2 days?

How many square units (units²) bigger is a 5 × 5 square than a 4 × 4 square?

What is the value of (74 × 50) − (32 × 50) − (23 × 50)?

A bicyclist takes 2 minutes, 30 seconds to travel a distance of 1 mile. At this rate, how many miles will the bicyclist travel in 1 hour?

Two 9 × 13 rectangles overlap as shown to form a 9 × 22 rectangle. What is the area of the overlap region?

Each letter in the ordered list A, B, C, D, E, F, G, H represents a number. The numbers are not necessarily different, which means that two letters can represent the same number. The sum of the values of any three adjacent letters (three letters in a row) is 20. When B = 6 and D = 9, what is the value of F?

Three students are in an election. Twenty votes are cast. Samantha has more votes than anyone else. What is the least number of votes she could have?

In the addition shown, different letters represent different digits. What is the value of A + B + C + D?

Find the least counting number which when divided by 5 gives a remainder of 1 and when divided by 12 gives a remainder of 3.

In a parking lot, there are 60 cars, all of which are black or blue and all of which are Fords or Dodges. There are 25 black Dodges. There are 18 blue cars. There are 25 Fords. How many blue Fords are there?

The Funny Book has its pages numbered in the following way: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, ... . That is, there is one 1, two 2s, three 3s, four 4s, five 5s, and so on. How many actual pages (including front and back) will the Funny Book have if it contains all possible pages that are numbered “1” through “20,” but not any that are numbered “21”?

The pyramid shown has 7 vertices, 12 edges, and 7 faces (one of which is a hexagon). At least one of the edges on each of the faces is to be colored red. What will be the least number of edges colored red?

Two rectangles, each 6 cm × 10 cm, overlap to form the 8-sided shape in the diagram. The overlap is a rectangle with counting (Natural or whole) numbers for its length and width. What is the least perimeter, in centimeters, that the 8-sided shape can have? [Diagram not drawn to scale.]

Given the cube is shown at the right. An ant travels from vertex A to vertex B, always walking along an edge of the cube. How many shortest paths are there from A to B?

How many three-digit counting numbers are exactly divisible by 6 but not exactly divisible by 9?

A Super-Brick is formed by arranging nine 1cm × 1cm × 1cm cubes into a 3cm × 3cm layer, 1cm thick. Two Super-Bricks are glued together into the L-shape shown. All faces of the L-shape are completely painted. What is the area of the painted surface in square centimeters?

Tom’s number has four digits in increasing order. The tens digit is the sum of the hundreds digit and the thousands digit. The ones digit is the sum of the other three. The sum of all four digits is 16. Find the last 3 digits of Tom’s number.

Consider the three-by-three grid shown (middle square removed). The counting numbers from 1 to 8 are placed in the squares (one number per square) so that the top row adds to 9, the bottom row adds to 21, the left column adds to 13, and the right column adds to 15. What is the sum: A + B + C + D?

A ski resort has three pricing options: \$60 for just a lift ticket, \$20 for just a ski lesson, or \$70 when both are bought together. On Sunday, 50 people bought exactly one of the three options. If 42 lift tickets and 23 lessons were sold, what was the mean or average purchase amount in dollars for these 50 people? (Round your answer to a nearest whole number)