AMO 2016 Grade 6

Find the value of $(4 × 6 × 8 × 10) ÷ (2 × 3 × 4 × 5)$.

What is the value of $(74 × 20) − (32 × 20) − (22 × 20)$?

How many square units (units²) bigger is a $6 × 6$ square than a $5 × 5$ square?

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 is 18. When B = 5 and D = 7, what is the value of F?

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

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 3 days?

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

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

In a parking lot, there are 70 cars, all of which are black or blue and all of which are Fords or Dodges. There are 17 black Dodges. There are 27 blue cars. There are 37 Fords. How many blue Fords are there?

Two $13 × 17$ rectangles overlap as shown to form a $13 × 31$ rectangle. What is the area of the overlap region?

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.

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?

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 “30”, but not any that are numbered “31”?

Two rectangles, each $6\text{ cm} × 10\text{ cm}$, overlap to form the 8-sided shape in the diagram. The overlap is a rectangle with counting 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?

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 dollars for just a lift ticket, 20 dollars for just a ski lesson, or 70 dollars 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)

The number in the center of each box is the result of operations that use the four numbers in the corners of the same box. Each of the four corner numbers in a box must be used exactly once. The same set of operations is used for each box. What number should replace the N?

Joseph put candles on a cake. He lit $1/4$ of those candles. Then he lit 5 more of the candles on the cake. As a result, exactly $1/3$ of the candles on the cake were lit. What was the total number of candles on the cake?