SEAMO 2019 — Paper B — Grade 3–4

Find $x$ in $1,2,3,6,12,23,44,x,164,\ldots$.

Find the sum of all digits of $11111\times99999$.

A double-decker bus has $66$ seats. At stop $1$, one commuter boards; at stop $2$, two board; at stop $3$, three board; and so on. At which stop are all seats taken?

$ABCD$ is a square and $EFGH$ a rectangle. Given $FB=2AF$, $BG=2GC$, $DH=2HC$, $DE=2AE$, $FB=4\text{ cm}$ and $AF=2\text{ cm}$, find the area of $EFGH$.

Sam has $63$ notes of denominations $2$ and $5$ dollars, worth $171$ dollars in total. How many $5$-dollar notes does he have?

The rectangle is subdivided into smaller rectangles with some areas labelled. Find area $A$.

Alice and her uncle’s ages sum to $33$. In $3$ years her uncle will be twice her age. How old is Alice now?

The figure consists of two squares and four identical rectangles. The squares have areas $64\text{ cm}^2$ and $4\text{ cm}^2$. Find the perimeter of one rectangle.

Fill the seven boxes in the addition with the numbers $1$ to $7$ so the sum is $100$. Find the largest two-digit number in the addition.

A child tells the truth on Mondays, Wednesdays and Fridays, and lies on other days. On which day will he say, “Tomorrow I will speak the truth”?

Evaluate $1-2+3-4+5-6+\cdots+2017-2018+2019$.

In the $3\times3$ magic square, every row, column and diagonal has the same sum. Find $A+B+C+D$.

Powers mean repeated multiplication: $2^1=2$, $2^2=2\times2$, $2^3=2\times2\times2$, and so on. Find the units digit of $3^{10}$.

A palindromic pair consists of two numbers whose digits are reversed, such as $13$ and $31$, $56$ and $65$, $92$ and $29$. How many two-digit palindromic pairs sum to $99$?

The digit $0$ is used $31$ times to print the page numbers of a book. How many pages does the book have?

Figure $1$ has perimeter $10\text{ cm}$. Find the perimeter of the figure formed using $36$ squares in this pattern.

In a certain month there are $5$ Sundays, three falling on even-numbered dates. What weekday is the $24$th?

Find the sum of the first $170$ terms of $11,7,13,2,11,7,13,2,11,\ldots$.

Car $A$ travels from town $x$ to $y$ at $40\text{ km/h}$ and car $B$ from $y$ to $x$ at $50\text{ km/h}$. They pass each other $20\text{ km}$ from the midpoint. Find the distance between the towns.

Ms Woodley gives $5$ sweets to each student and has $32$ left. If she gives $8$ each, $5$ students get none. How many sweets does she have?