SEAMO 2020 — Paper C — Grade 5–6

Define $m*n=m^n$. If $n*5=243$, find $n$.

Use eight different digits chosen from $1$ to $9$ to fill $[\square\div\square\times(\square+\square)]-[\square\times\square+\square-\square]$. Find the greatest possible value.

How many triangles can be formed by joining three vertices of the cube shown?

Lucas invested $1000$ dollars in $2018$. He lost $18\%$ in the first year and gained $25\%$ in the second. What was his overall percentage gain or loss?

In rectangle $ABCD$, triangles $AED$ and $BFC$ are identical isosceles triangles, as shown. If the area of $AED$ is $202\text{ cm}^2$, find the rectangle’s area.

The $101$-digit number consists of fifty $6$s, digit $m$, then fifty $5$s. Find the possible digits $m$ for divisibility by $7$.

In the $4\times4$ grid, every line segment is one unit long. What is the longest distance from $A$ to $B$ if each line segment can be traversed only once?

How many triangles are in the figure?

Choose two different numbers from $\{5,6,7,\ldots,15\}$ with an even sum. How many choices are there?

After Wattana spent $35$ dollars, his money and James’s were in ratio $3:4$. Wattana then received $220$ dollars and James spent $50$ dollars. Wattana now had twice James’s amount. How much did Wattana have initially?

Let $A=2^{248}$ and $B=3^{155}$. Which statement is correct?

Evaluate $\dfrac{(1+7/1)(1+7/2)\cdots(1+7/9)}{(1+9/1)(1+9/2)\cdots(1+9/7)}$.

In $\overline{ABC}+\overline{DEF}=\overline{HIJ}$ each letter represents a different nonzero digit. Find the smallest possible $H+I+J$.

Matchsticks form square grids: twelve make a $2\times2$ grid and twenty-four make a $3\times3$ grid. If $1300$ form an $m\times m$ grid, find $m$.

A quarter circle of radius $14$ cm contains two semicircles with diameters on its radii. Their intersection is shaded A and the region outside both is shaded B. Using $\pi=22/7$, which are true: (i) A has area $28\text{ cm}^2$; (ii) A has area $30\text{ cm}^2$; (iii) A and B have equal area; (iv) A is larger than B?

An interior point $O$ of an equilateral triangle has perpendicular distances $4,5,6$ cm to its sides. Find the triangle’s height.

Evaluate $11+22+33+\cdots+1089+1100$.

In triangle $ABC$, $\angle BAD=80^\circ$, $\angle DAC=20^\circ$, and $BD$ bisects $\angle ABC=40^\circ$, as shown. Find $m=\angle ACD$.

Among integers from $1000$ to $1999$, how many have a units digit greater than the hundreds digit?

A fair die is rolled twice. What is the probability that the sum is prime?