AMO 2017 Grade 4

Find the value of 98 − 87 + 76 − 65 + 54 − 43 + 32 − 21 + 10.

The sum of the digits of the number 315 is 9. What is the least number greater than 315 whose sum of the digits is 9?

Sandy multiplies 2 × 5 × 7 × 2 × 5 × 7 × 2 × 5 and writes the product as a whole number. What is the sum of the digits of this number?

Find the value of 30 × 7 + 10 × 4 − 15 × 5 − 5.

Summer vacation lasts for 76 days. During summer vacation, what is the greatest number of Fridays that could occur?

What is $\frac12$ of $\frac45$ of $\frac9{10}$ of 75?

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 8 rows combined?

The cost of 3 pencils and 2 markers is \$26. The cost of 2 pencils and 3 markers is \$24. What is the total cost of 7 pencils and 7 markers?

At Springfield Elementary School, a shelf contains either 4 math books or 9 spelling books. On 20 shelves at Springfield Elementary, there are 117 spelling books and some number of math books. All 20 shelves are full. How many math books are there on the shelves?

Dillon works at the park every third day. William works at the park every fourth day. Francis works at the park every fifth 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)

Given:

△ + □ + ○ = 16

△ + □ + □ = 15

△ + △ + □ = 12

What is the value of ○ + ○ + □?

What is the greatest multiple of 29 that has exactly 3 digits?

Nine 1cm by 1cm tiles are arranged in 3 rows and 3 columns to form a single square as shown. The perimeter of the square is 12cm. 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?

What is the smallest 3-digit number that is divisible by both 32 and 36?

A certain book has its pages numbered from 1 to 100. Then any page number that contains the digit 5 is entirely erased. What is the sum of all of the numbers that were erased?

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. What are the first three digits of the number they chose?

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. How many unit cubes are completely surrounded by six other unit cubes? (This means that each face is shared with a face of another cube.)

In the cryptarithm shown, each letter represents a different digit. What is the greatest 3-digit value that can equal SUM? A cannot equal 0.

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

Karen can paint a wall in 2 hours. Stephanie takes 3 hours to paint the same size wall. How many minutes will it take for Karen and Stephanie working together to paint the same wall?