AMO 2021 – Primary 4 (Grade 4)

If it was Monday yesterday, what day of the week will it be in 100 days?

An open book shows two consecutive page numbers whose sum is 167. What is the page number of the next page?

There is no tax on school supplies. Matt pays 90 cents for three pencils and two erasers. Nancy pays 35 cents for one pencil and one eraser of the same types. How many cents does a pencil cost?

Alice uses a 10-dollar bill for a watermelon and receives 4 dollars change. She then uses a 20-dollar bill for apples and receives 7 dollars change. She has 17 dollars left. How many dollars did she have at first?

Each dot is one inch from its horizontal and vertical neighbors. What is the area of the quadrilateral, in square inches?

Two workers can paint one house in 2 days. How many houses can 12 workers paint in 12 days under the same conditions?

Oliver bought a 240-page book. He read $\frac15$ of the book yesterday and $\frac14$ of the remaining pages today. How many pages are left to read?

A garden has the shape shown. What is its perimeter in feet?

Emily has only 25-cent quarters and 10-cent dimes. She has six more quarters than dimes, worth 290 cents altogether. How many quarters does she have?

Four children have an average weight of 50 pounds. After a fifth child joins, the average is 53 pounds. How many pounds does the fifth child weigh?

There are 205 marbles. Andrew, Blake, Carter and David repeatedly take turns removing 1, 2, 3 and 4 marbles respectively, in that order, until none remain. Who takes the last marble? If fewer than a player’s usual number remain, that player takes the remaining marbles.

Eight children each ride a bicycle or a tricycle. There are 19 wheels altogether. How many bicycles are there?

How many triangles are formed by the drawn segments in the figure?

Clarification: the inner sloping segment is intended to reach the bottom base, despite the tiny gap in the original drawing.

Michael has nine stickers on a 3-by-3 grid. He cuts out three squares as one edge-connected piece. How many different sets of three stickers can he choose?

Find $11-13+15-17+19-21+23-25+27-29+31$.

Increasing a rectangle’s length by 2 cm increases its area by 14 square centimetres. Increasing its width by 3 cm instead increases its area by 24 square centimetres. What is the original perimeter in cm?

Three integers A, B and C sum to 115. A is three times B, and C is 15 greater than B. Find B.

A glass filled with water weighs 750 grams. After Jenny pours out half the water, the glass and remaining water weigh 400 grams. How many grams does the empty glass weigh?

A four-digit number is divisible by 5. Its hundreds digit is four times its tens digit, and the sum of its digits is 21. Find the number.

Maria makes marble patterns with 1 marble in step 1, 5 in step 2, 9 in step 3, and four more in each new pattern. She uses all her marbles to finish step 9. How many marbles does she have in total?

Clarification: all nine patterns are kept separately, as intended by the supplied answer key; the same marbles are not reused between steps.