AMO 2018 — Primary 5 (Grade 5)

What is the value of (888 + 666 + 444 + 111) − (555 + 333 + 222 + 777)?

Ashley has a rectangle made out of paper that is 8 cm by 12 cm. She folds it in half twice, first vertically and then horizontally. The new rectangle looks just like the original rectangle but smaller. What is the area of the new smaller rectangle in square cm?

Last holiday, Jonathan received $134 more than three times the money that Sally received. They received $710 altogether. How much money did Jonathan receive?

The figure shown is created by overlapping three 2 cm by 6 cm rectangles. What is the area, in cm², of the figure?

What is the remainder when 123456789 is divided by 9?

Find the sum of the following 117 + 104 + 91 + 78 + 65 + 52 + 39 + 26 + 13.

Gina has $1350 and receives $11 every week. James has $1650 and spends $19 per week. After how many weeks will they have the same amount of money?

Given □ + △ + ◇ = 30, △ + ◇ + ✶ = 22, ◇ + ✶ + □ = 26, and △ + ◇ + ✶ + □ = 37, find the value of ✶ + □ + △.

Jean has a collection of chips. If the chips are arranged in piles of 12, there will be 11 chips leftover. If the chips are arranged in piles of 21, there will be 20 chips leftover. What is the least number of chips that Jean owns?

In the following cryptarithm, each different letter represents a different digit. Find the last three digits of the largest possible sum. (Example, if your answer is 1234, then write 234.)

In the figure, the whole numbers from 1 through 7 are to be placed, one per square. The sum of the numbers in the left column, the sum of the numbers in the right column, and the sum of the numbers in each diagonal are the same. What is the largest possible product of the numbers across the gray row?

Four shaded right-angled triangles with leg lengths 1 cm × 4 cm, 2 cm × 4 cm, 3 cm × 4 cm, and 4 cm × 4 cm are fitted together to make a quadrilateral. This quadrilateral is then fit into a 5 cm × 8 cm rectangle. Find the area, in cm², of the quadrilateral that was formed (the shaded region). (Legs of a right-angled triangle are the sides beside the right angle)

Adam can paint a classroom in 6 hours. Ben can paint the same classroom in 12 hours. If they work together, each at their own rate, to paint this classroom, how many hours would they take?

The first 40 odd counting numbers are written. How many times does ‘3’ appear as a digit?

Tiffany looked at a clock and realized that the number of hours that had passed since midnight was five times the number of hours remaining until noon. What time did the clock show 1 hour ago? (Disregard the colon in your answer. Example, if your answer is 3:00, write 300)

A rectangular billboard has a length greater than its height and has an area of 120 square meters. There are lights around the perimeter of the billboard, one every meter. There are 46 lights around the perimeter of the billboard. How long is the billboard, in meters?

In a family, there are four children. Adam’s age is the sum of Beth’s and Carol’s ages. Four years ago, David’s age was the sum of Beth’s age then and Carol’s age then. Eight years ago, Adam’s age was twice David’s age then. Who is the oldest child in this family? (Write 001 if Adam, 002 if Beth, 003 if Carol and 004 if David)

In the following cryptarithm, each different letter represents a different digit in the 6-digit numbers. If B is not 0, find the last three digits of the smallest possible sum. (Example, if your answer is 12345, then write 345.)

Each of the whole numbers 1 through 9 is written on 9 cards, one number per card. Three cards are dealt to each of three players. The sum of Player One’s cards is 15. The sum of Player Two’s cards is 23. What is the highest single card Player Three could possibly have?

Jethro is now 3 times as old as his son Hezekiah. Six years ago, Jethro was 4 times as old as his son Hezekiah was then. Find the sum of Jethro’s and Hezekiah’s present ages.