SEAMO X 2020 — Paper B — Grade 3–4

Find $A$ in $1,3,6,15,33,A,\ldots$.

The four-digit number $\overline{37N5}$ is divisible by $35$. Find $N$.

Paul initially has three times Mary’s savings. Paul withdraws $180$ dollars while Mary saves another $40$ dollars, and their savings become equal. What were Mary’s initial savings?

Ten chickens lay ten eggs in ten days. How many eggs do thirty chickens lay in thirty days?

Powers mean repeated multiplication: $3^1=3$, $3^2=9$, $3^3=27$, $3^4=81$. Find the units digit of $3^{33}$.

Find $C$ in the cryptarithm $\overline{AT}\times\overline{AT}=\overline{CAT}$.

A box has $6$ red, $7$ yellow, $2$ white and $5$ black marbles. What is the least number drawn without looking to guarantee all four colours?

Evaluate $1-2+3-4+5-6+\cdots+101$.

Find the missing entry in $\begin{array}{rrrrr}1&3&5&7&9\\8&12&?&2&20\\5&9&12&8&19\end{array}$.

At $8{:}00$ am, Abel cycles from town $A$ to $B$ at $13\text{ km/h}$ while Ben cycles from $B$ to $A$ at $12\text{ km/h}$. Ben takes a one-hour break. The towns are $138\text{ km}$ apart. At what time do they meet?

Define $a\diamond b=(a+b)/2$ and $a\odot b=3a-b$. Find $(2\odot4)\diamond6$.

Following the arrows, how many paths lead from $A$ to $B$?

Distinct letters in EGGPLANT represent the digits $1$ to $7$ without repetition. The sum of the eight digits is odd and divisible by $3$. Find $G$.

The picture consists of three identical rectangles. Find the perimeter of one rectangle.

$A,B,C,D$ each represent one of the digits $2,3,5,7$. The sum inside each circle is $15$. Find $A$.