ASMO Math 2022 — Grade 7 — School Round

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.

Diagram below shows a parallelogram ABCD. N is the midpoint of AB and F is the midpoint of AD. Determine the ratio of the area of triangle AFN to the area of quadrilateral CDFN.

Let a, b and c be three real numbers such that $ab+bc+ac=4$. Determine the least possible value of $a^2+b^2+c^2$.

A lorry charges a rate of x cents per kg per mile. How much dollars (in cents) it cost 3 kg of goods to travel y miles, if the lorry driver decides to give his customer a 50% discount?

Determine the number of 7-digit positive integers such that the digits from left to right are non-increasing. (Examples of 7-digit non-increasing numbers are 5555555 and 9998766; An example of a number that is NOT non-increasing is 7776556)

Determine the number of ways of arranging 5 identical red balls and 13 identical blue balls on a straight line such that between any 2 red balls there is at least 1 blue ball.

Let $a_1,a_2,\ldots,a_n$ be positive integers, not necessarily distinct but with at least five distinct values. Suppose that for any $1\leq i<j\leq n$, there exist k, l, both different from i and j such that $a_i+a_j=a_k+a_l$. Find the smallest possible value of n.

Charly has 3 more 20 cents coins than 10 cents coins. The total value of her 20 cents coins is \$4.50 more than that of her 10 cents coins. How many 20 cents coins does Charley have?

The area of a rectangle remains unchanged when either its length is increased by 6 cm and width decreased by 2 cm, or its length decreased by 12 cm and its width increased by 6 cm. If the perimeter of the original rectangle is k cm, determine the value of k.

Lydia was born on 1 January 1995. Her father was born on 1 January 1963. In what year her father will be exactly 2 times as old as Lydia?

Two congruent isosceles triangles, ABC and EFG, overlap so that their bases are parallel and the vertex of each is the midpoint of the base of the other as shown. If the area of the overlap is 24cm2, what is the area of the triangle ABC?