AMO 2027 Grades 2-3 SET 10 - Self-study

There are 5 rows of seats in a garden. There are 15 seats in the last row. If there is an increase of 3 seats, starting from the first row, how many seats are there in the garden?

Circle the shape with more edges.



Self-study input instruction (editorial): enter the two letter choices separated by a semicolon, in the order 1;2.

**Editorial input note:** Use no spaces before or after semicolons.

Alice loves roses. In her rose garden she has half as many pink roses as red, and four times as many red ones as white. There are 36 roses that are either yellow or white. Twenty are yellow. How many roses are in Heather’s garden?

Self-study correction (editorial): treat Heather as a mistaken name for Alice, referring to the same garden. Find its intended total.

Mark is planning to purchase an irregularly shaped plot of land. Referring to the above diagram, find the total area of the land.

During indoor recess the students got to vote on which movie to watch. The voting results are listed below. Use the bar graph to answer the questions. (Each small rectangle is 1 vote.)



a) How many more votes did Spy Kids receive than Brave?

b) How many fewer votes did Spy Kids receive than Up?

Self-study input instruction (editorial): enter both numbers separated by a semicolon, in the order a;b.

**Editorial input note:** Use no spaces before or after semicolons.

The length of a rectangular wooden board is thrice its width. If the width of the board is 100 cm, find the cost of framing it at the rate of \(\text{\$5}\) for 20 cm.

A short street where Bernard lives has 6 houses. One day 35 letters are delivered in his street and he receives more letters than anyone else. What is the smallest number of letters he may have received?

Self-study interpretation (editorial): treat each house as one recipient of letters, with Bernard being one of the six recipients.

Observe the pattern and the relationships among the numbers below:

2 ▽ 4 = 87

5 ▽ 1 = 54

3 ▽ 7 = 2120

6 ▽ 6 = 3635

Calculate 9 ▽ 8.

Self-study rule (editorial): multiply the two inputs, then concatenate the product with one less than the product, in that order.

The birthdays of two sisters are on the same day. The elder sister is 4 years older than the younger sister. When the sum of their ages reaches 50 years, how old is the younger sister?

What is the largest 2-digit number that can be divided by both 3 and 5?

a) In the following cryptarithm, all different letters stand for different digits. Find the sum (A + B + C).



b) In the following subtraction, M and N represent different digits. What is the value of M + N?



Self-study input instruction (editorial): enter the two digit sums separated by a semicolon, in the order a;b.

**Editorial input note:** Use no spaces before or after semicolons.

Pine trees are planted at regular intervals of 25 m along the stretch of road with pine trees planted at opposite ends of the road. If the road is 1500m long, how many pine trees are needed to be planted along the road?

Self-study interpretation (editorial): plant one row of trees along the road, including both endpoints.

Alice was travelling cross-country. The first day, she travelled 80 kilometres; the second day, 100 kilometres; the third day, 70 kilometres; the fourth day, 90 kilometres; and on the fifth day she travelled 60 kilometres. How many kilometres did she travel on the 15th day?

Self-study rule (editorial): continue the alternating changes of plus 20 kilometers, then minus 30 kilometers.

A football game started at 20 : 30. The game lasted 90 minutes. At what time did the game finish?

Self-study input instruction (editorial): enter the finish time using the 24-hour clock, in HH:MM form.

Find the missing number in the sequence:

137, 145, 148, 143, ..., 141, 170.

Self-study rule (editorial): the odd-position terms increase by 11, while the even-position terms decrease by 2.