ASMO Math 2022 — Grade 6 — School Round

Find the value of the following: $(20\times 24\times 28\times 32)\div (10\times 12\times 14\times 16)$.

A rectangular box is 6 cm deep, 4 cm wide, and 2 cm high. Vahn packs the box with cubes, each 2 cm by 2 cm by 2 cm, with no space left over. Find the number of cubes does he fit into the box.

The tower shown below is made by placing congruent cubes on top of each other with no gaps. Not all cubes are visible. Determine the number of cubes does the tower contain.

If 16 is added to one-third of a number, the result is three times the number. Find the number.

ABCD is a rectangle whose area is 12 square units. Determine the square units that are contained in the area of trapezoid ABFE.

The number 6 has exactly four different factors: 1, 2, 3, and 6. Determine the number of different factors does the number 36 have.

Sherry has five times as many books as Jay. Nairan has three times as many books as Jay. Sherry has 16 books more than Nairan has. Find the number of books does Jay have.

At a special sale, all hats sell at one price and all skirts sell at another price. Liz pays \$30 for 2 hats and 3 skirts. Mia pays \$23 for 5 hats and 1 skirt. Find the price of each skirt sold in dollars.

In a class of 26 students, 16 like chocolate ice cream and 15 like vanilla ice cream. However, 3 do not like either flavor. Find the number of students who like both chocolate and vanilla ice cream.

Winson is 1 month older than Rita. Vincy is 3 months older than Rita. Henry is 4 months older than Vincy. How much older than Winson is Henry, in months?

Lisa starts with the number 5 and counts by 8s. This results in the sequence 5, 13, 21, 29, 37, and so on. Find the twenty-fifth number in the sequence.

In the number 123000, the last three zeroes are called terminal zeroes. If the multiplication $70\times 60\times 50\times 40\times 30$ is done, determine the number of terminal zeroes will the product have.

The average weight of a group of children is 100 pounds. Desmond, who weighs 112 pounds, then joins the group. This raises the average weight of the group to 102 pounds. Determine the number of children were in the original group.

Each square contains one of the numbers 1, 2, 3, 4, 5, or 6 and each number is used once. Except for the top row, the number in each square is the difference of the numbers in the two squares above it. Determine the number in the square marked A.

P represents a counting number. Determine the value of P if $(P+P)/(P\times P)=1/3$.

Square ABCD is composed of nine congruent squares as shown. The area of the shaded region is 14 square meters. Find the area of square ABCD, in sq m.

R is a number such that $1\times 2\times 3\times 4\times 5\times 6\times 7=8\times 9\times 10\times R$. Find the value of R.

The number 6 has exactly four different factors: 1, 2, 3, and 6. How many counting numbers less than 15 have exactly two different factors?

The scale drawing of a rectangular room measures 6 cm wide by 10 cm long. The actual width of the room is 15 feet. Find the actual perimeter of the room, in feet.

A walkway (the shaded region) is built around a rectangular pool, as shown. The pool is 30 feet by 20 feet. The walkway is completely tiled with whole square tiles 2 feet by 2 feet. Find the fewest number of tiles that can be used.