AMO 2027 Grades 4-5 SET 2 - Self-study

$\frac{1}{3}$ of the students in primary 7A is 3 more than $\frac{1}{4}$ of the students in primary 7B. There is a total of 72 students in the two classes. How many students are there in primary 7A?

Ryan used 15 identical rhombuses to form a pattern. The pattern is shown below.
The perimeter of one rhombus is 80 cm. What is the perimeter of the pattern formed with 15 rhombuses?

The graph shows the price of five gallons of gasoline during the first ten months of the year. By what percent is the highest price more than the lowest price?



Answer entry: enter the percentage number without a percent sign.

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?

A donkey and a horse have to carry a number of strong packages to the market.

Donkey: “Oh my God, the goods are too heavy! I’m going to be exhausted!”

Horse: “Why are you always complaining? You see, I carry two more packages than you! Besides, if you give me one of your packages, then the number of my packages will be twice of yours! Stop complaining!”

How many packages does the donkey carry?

The sum of two whole numbers, A and B, is 41. The sum of 2 times of A and 3 times of B in 93. Find the value of A?

a) Aman can run a distance of 100m in 20 seconds. Find the speed of Aman in m/s.

b) Suraj drives first 120 km in 2 hours and next 180 km in next 4 hours. What is his average speed for the entire trip in km per hour?

c) A boy walks at a speed of 4km/h. How much time does he take to walk a distance of 20km?

Answer entry: Enter numerical answers to (a), (b), (c), in that order, separated by semicolons; use m/s, km/h and hours respectively, without typing unit labels.

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

The figure below is a trapezium of bases 12cm and 8cm as shown. The perpendicular height of the trapezium is 9cm. Find the difference in area between the triangle A and triangle B.

110 children were asked to name their favourite sport. The following bar graph shows their choice. Which is the least popular sport?



Editorial label note: “Number of marbles” and “Material Arts” are retained exactly as printed; they appear to be label errors in this sports survey.

Michael has 50 dollars less than Samantha. Samantha has 100 dollars more than Rob. Rob has 150 dollars less than Hailey. How many more dollars does Hailey have than Michael?

After arranging some tables in 12 rows, 12 tables were left. If the number of tables left was $\frac{1}{3}$ of that in one row, what fraction of the tables had been arranged?

Claw machine A has 31 stuff toys and claw machine B has 43 stuff toys. After one day, an equal number of stuff toys from each claw machine were won and no toys were replenished during the day. The number of remaining stuff toys in claw machine A was half the number of stuff toys left in claw machine B at the end of the day. What is the total number of remaining stuff toys in both machines at the end of the day?

Evaluate:

a) $A = 1 + 2 + 3 + 4 + 5 + … + 2020$.

b) $B = 2 + 4 + 6 + 8 + … + 2020$.

c) $C = 1 + 3 + 5 + 7 + … + 2019$.

Answer entry: Enter A; B; C in order, with no thousands separators.

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

In following multiplication, different letters stand for different digits, and ABC and DBC each represents a three-digit number. Given that C is not 6, what number does DBC represent?

$\overline{ABC}\times C=\overline{DBC}$.

A seven-digit number, $2006\square\square\square$, is divisible by 3, by 4 and by 25. Find the possible values of the missing digits.

Answer entry: Enter the three-digit endings in increasing order, separated by semicolons.

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