AMO 2017 — Primary 5 (Grade 5)

What is the value of (115 + 114 + 113 + 112 + 111) − (101 + 102 + 103 + 104 + 105)?

How many digits does N have if N = 2 × 3 × 4 × 5 × 12 × 25?

Find the value of 10 × 1 − 9 × 2 + 8 × 3 − 7 × 4 + 6 × 5 − 5 × 6 + 4 × 7 − 3 × 8 + 2 × 9 − 1 × 10.

The product of the digits of the number 217 is 14. What is the least 3-digit odd number whose product of the digits is 6?

Summer vacation lasts for 85 days. During summer vacation, what is the greatest number of Fridays that could occur?

Amy spent $1/4$ of the cash in her wallet at the game store, $2/3$ of the remaining cash at a clothing store, $1/3$ of what was left for lunch, and $3/4$ of what remained at the shoe store. After spending all that money, she had 10 dollars left. How much cash did she have at first?

What is the greatest multiple of 37 that has exactly 3 digits?

Dillon works at the park every fourth day. William works at the park every fifth day. Francis works at the park every sixth day. They all worked together on Thursday. The park is open every day. On what day of the week will they all next work together? (If your answer is Monday, write 001; if it is Tuesday, write 002; and so on)

Sixteen 1cm by 1cm tiles are arranged in 4 rows and 4 columns to form a single square as shown. The perimeter of the square is 16cm. If the shape is cut into exactly two pieces along edges of the tiles, what is the greatest total perimeter of the two pieces, in centimeters, that can be made?

At Springfield Elementary School, a shelf contains either 4 math books or 9 spelling books. On 20 shelves at Springfield Elementary, there are a total of 135 of these books (some math and some spelling). All 20 shelves are full. How many math books are there on the shelves?

The first row has 2 dots. The second row has 4 dots. The third row has 6 dots. More rows are added. Each additional row has 2 more dots than the row before it. How many dots will there be in the first 31 rows?

Given that ▲ + ■ + ◆ = 14 and ■ + ◆ + ● = 19 and ◆ + ● + ▲ = 16 and ● + ▲ + ■ = 11, what is the value of ▲?

What is the difference between the sum of the multiples of 3 less than 100, and the sum of the multiples of 4 less than 100?

What’s the greatest 3-digit number that is divisible by both 32 and 36?

Jason has a 3cm × 3cm × 3cm wooden cube. He removes a 2cm × 2cm × 2cm wooden cube from one corner of the 3cm × 3cm × 3cm cube. What is the surface area, in cm², of the remaining solid that has a volume of 19 cm³?

Lucy is Sherry’s mother. Lucy’s age and Sherry’s age have the same digits but in reverse order. In 13 years, Lucy will be twice as old as Sherry. How old was Sherry 2 years ago?

Ari, Barry, and Carrie chose a number. Ari said the number was a multiple of 3, 5, and 11. Barry said the number was a multiple of 2 and 7. Carrie said the number had 4 digits, one of which was a 9, but none of which were 6. Find the last 3 digits of the number they chose?

The cube at the right is constructed of the same sized figures as shown. How many figures does the cube contain?

There are 165 unit cubes arranged in 5 square layers with no space between the cubes as shown. The layers are 1 by 1, 3 by 3, 5 by 5, 7 by 7, and 9 by 9. If a sixth layer with the same pattern is added to the bottom of the figure, how many unit cubes are completely surrounded by six other unit cubes?

A 2cm by 2cm by 2cm solid cube is cut in two identical rectangular solids, as shown. The top half is fully flipped over one edge so that they are now tightly side-by-side. What is the volume of the new rectangular solid (in cm³)?