SEAMO X 2023 — Paper B — Grade 3–4

Find the $10$th term of $1,2,4,5,10,11,22,23,46,\ldots$.

How many rectangles are in the figure?

Find the remainder when the number consisting of $2023$ digits all $1$ is divided by $7$.

One straight line divides the circle into two regions. How many regions can six lines divide it into?

The $2023$rd term in $\frac11,\frac12,\frac22,\frac13,\frac23,\frac33,\frac14,\frac24,\frac34,\frac44,\ldots$ is $m/n$ as written. Find $m+n$.

There are $126$ cartons of apples. Each contains between $120$ and $144$ apples inclusive. At least $k$ cartons are guaranteed to contain the same number. Find the largest such $k$.

How many consecutive trailing zeros are in $625\times128\times25\times4$?

A teacher takes $51$ pupils on a boat excursion. A big boat holds $6$ passengers and a small boat $4$. Eleven boats are hired. How many are small?

A small equilateral triangle is inscribed in a circle, which is inscribed in a larger equilateral triangle. Their areas are in the reduced ratio $m:n$. Find $m+n$.

Mark and Nick run in the same direction on a circular track of length $400$ m at $200$ and $160\text{ m/min}$ respectively. Starting together, after how many minutes do they meet again?

In the figure, $AB=BD$, $FA=AC$, $BC=CE$. Triangle $ABC$ has area $10\text{ cm}^2$. Find the area of triangle $DEF$.

Evaluate $(1+\frac1{47})+(2+\frac2{47})+(3+\frac3{47})+\cdots+(47+\frac{47}{47})$.

The five-digit number $\overline{m679n}$ is divisible by $72$. Find $m+n$.

In the diagram, $AD\parallel BC$, $BC=1.5AD$, $[ADE]=16\text{ cm}^2$ and $[BEC]=18\text{ cm}^2$. Find the total shaded area.

Grass grows at a constant daily rate. $27$ oxen finish it in $6$ days and $23$ in $9$ days. How many days can it sustain $24$ oxen?