AMO 2027 Grades 4-5 SET 3 - Self-study

The graph below shows the number of cars sold at a car sales centre from September to December.

a) What were the total number of cars sold in these 4 months?

b) If the centre manager gave 8000 dollars off for each car sold, how much in total saved by the customers in thousands?



Answer entry: enter (a); (b), separated by a semicolon, with (b) in thousands of dollars.

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

There are 10 people in a room. Every person shakes hand with every other person once and only once. How many handshakes are there?

In a candy shop, the shopkeeper allows the exchange of 3 sweet wrappers for 1 new sweet. Peter has 81 sweets at first. What is the largest possible number of sweets that Peter could have eaten?

Rowan and Emma each had an equal number of popsicles. After Rowan ate 25 popsicles and Emma ate 31 popsicles, Rowan had twice as many as Emma. How many popsicles did they each have at first?

Willy and Sam both had some savings. $\frac{2}{3}$ of Willy’s savings is $\frac{1}{5}$ of Sam’s savings. If Sam saved 84 dollars more than Willy, how much was their total savings?

200 flags are placed at adjacent of 7m along the road with flags placed at opposite ends of the road. How long is the road?

Find the area of the shaded compound shape. The length of each small block equals 2cm.

The tens digit of a two-digit number is three times the ones digit. The sum of the digits in the number is 8. What is the number?

Farmer Ben has only ducks and cows. He can not remember how many of each he has. Well, he does not need to remember because he knows he has 22 animals and that 22 is also his age. He also knows that the animals have a total of 56 legs, because 56 is also his father’s age. Assuming that each animal has all legs intact and no more, how many ducks does Farmer Ben have?

The length of a rectangle is 11 cm. The breadth is 4 cm shorter than the length. If the breadth is increased to twice the original breadth, and the length is increased by 7 cm, what is the new perimeter?

In the following alphabetic, all different letters stand for different digits. Find the sum of A + L + L.
$\overline{TEE}+\overline{LET}=\overline{ALL}$.

There are 8 lamp posts along a stretch of road. In between every 2 lamp posts, there are 2 trees. How many trees are there along that stretch of road?

Thomas has 9 dollars more than Tom. Alice has 20 dollars fewer than Tom. The total amount of money they have is 199 dollars. How much money does Thomas have?

Mrs Walker bought a box of paper clips. She shared the paper clips among her 4 children. Alice received 190 paper clips. Rita received 56 more paper clips than Jim. Jim received 25% of the paper clips while Tom received 20% of the paper clips. How many paper clips did Mrs Walker buy altogether?

January 1st, 2007 was Monday. What day of the week lies on January 1st, 2008?