SEAMO 2021 — Paper B — Grade 3–4

Question 1

If $1+2+\cdots+m=253$, find $m$.

$20$
$21$
$22$
$23$
$24$

Question 2

Shawn and Matthew have $76$ books altogether. Shawn has three times as many books as Matthew. How many does Shawn have?

$19$
$27$
$47$
$57$
None of the above

Question 3

A rectangular frame has outer dimensions $9\text{ m}$ by $6\text{ m}$ and a uniform width of $1\text{ m}$. Find its area.

Question illustration

$17$
$19$
$35$
$54$
None of the above

Question 4

Evaluate $100-99+98-97+96-95+\cdots+4-3+2-1$.

$48$
$49$
$50$
$99$
$100$

Question 5

Define $m\star n=(m+n)/2$. Find $3\star(6\star8)$.

Question 6

A whole number is multiplied by $6$, increased by $6$, divided by $6$, and decreased by $6$, giving $6$. Find the original number.

$10$
$11$
$12$
$13$
$14$

A traffic policeman questions three teenagers. Adrian says, “I have a driving licence.” Ben says, “I do not know how to drive.” Chris says, “Ben does not know how to drive.” Exactly one statement is true. Which conclusion follows?

Adrian and Ben can both drive.
Ben and Chris can both drive.
Only Adrian can drive.
Ben cannot drive.
Chris cannot drive.

Question 8

There are $19$ chickens, ducks and goats altogether, with $56$ legs. How many goats are there?

$10$
$9$
$8$
$7$
$6$

Question 9

Distribute $100$ apples as evenly as possible among nursery children. At least one child receives $3$ apples. What is the maximum number of children?

$36$
$47$
$49$
$51$
$53$

Question 10

How many routes can the insect take from $A$ to $C$ through $B$ in the diagram?

Question illustration

$8$
$9$
$10$
$11$
$12$

Question 11

Five whole numbers have mean $20$. One number is changed to $18$, and the new mean is $18$. What was the original number?

$26$
$28$
$30$
$32$
$34$

Question 12

Oranges are put into bags. If each bag contains $5$ oranges, $14$ remain. If each bag contains $7$ oranges, another $2$ bags are needed. How many oranges are there?

$76$
$78$
$80$
$82$
$84$

Question 13

Evaluate $\left(\frac1{1\times2}+\frac1{2\times3}+\cdots+\frac1{2021\times2022}\right)\times2022$.

$2020$
$2021$
$2022$
$2023$
None of the above

Question 14

In the subtraction shown, find the two-digit number $AB$.

Question illustration

$32$
$38$
$44$
$54$
$65$

Question 15

Find the sum of the marked exterior angles $a+b+c+d$.

Question illustration

$180^\circ$
$270^\circ$
$360^\circ$
$450^\circ$
None of the above

Question 16

Find the missing number in the array $\begin{array}{rrr}40&24&8\\45&19&13\\29&5&12\\?&15&17\end{array}$.

$49$
$50$
$51$
$52$
$53$

Question 17

A number consists of $2021$ digits, all $5$. Find its remainder when divided by $13$.

Question 18

The four triangles consist of $9$ equal line segments. Put $4$ beads at equal intervals on each segment as shown, sharing beads at common vertices. How many beads are needed?

Question illustration

$20$
$21$
$22$
$24$
$25$

Question 19

Javier follows the staircase route home shown. The overall horizontal and vertical distances are $120\text{ m}$ and $70\text{ m}$. How far does he walk?

Question illustration

$70\text{ m}$
$95\text{ m}$
$120\text{ m}$
$190\text{ m}$
None of the above

Question 20

How many rectangles are in the L-shaped grid?

Question illustration

$22$
$24$
$25$
$26$
$27$