SEAMO 2016 — Paper B — Grade 3–4

Question 1

Find the missing number in the diamonds.

Question illustration

$4$
$5$
$6$
$7$
None of the above

Question 2

The digits $358421$ repeat without end. Find the sum of the first $68$ digits.

$246$
$252$
$261$
$273$
$284$

Question 3

A new operation $\star$ satisfies $3\star4=13$, $5\star9=24$, and $7\star7=28$. Find $13\star8$.

$45$
$46$
$47$
$48$
None of the above

Question 4

How many squares in the grid contain the dot?

Question illustration

$8$
$10$
$12$
$14$
$16$

Question 5

Find the value of the group of four diamonds in the picture equations.

Question illustration

$23$
$29$
$37$
$39$
$41$

Question 6

Find the number in $[(\square+4)\times8]\div12=48$.

$68$
$70$
$74$
$76$
None of the above

Question 7

In this magic square, every row, column and diagonal has the same sum. Find $S$.

Question illustration

$5$
$6$
$8$
$9$
$10$

Question 8

Calculate $1-2+3-4+\cdots+73-74+75$.

$37$
$38$
$39$
$40$
None of the above

Question 9

A bag contains $12$ red, $10$ white, $8$ yellow, $3$ blue and $2$ black balls. Without looking, how many balls must be drawn to guarantee four of the same colour?

Question illustration

$15$
$19$
$20$
$25$
None of the above

Question 10

Circles $A,B,C$ have areas $380$, $400$, $420$ square centimetres. Their overlap regions have the areas shown. Find the area covered by the three circles.

Question illustration

$780$
$820$
$960$
$1200$
None of the above

Question 11

Eight numbers are arranged in increasing order. Their mean is $55$. The mean of the first five is $46$ and the mean of the last four is $68$. Find the fifth number.

$32$
$44$
$58$
$62$
$74$

Question 12

Emma adds $1+2+3+4+\cdots$ on a calculator. She accidentally omits one number and obtains $305$. Which number did she miss?

Question illustration

$16$
$17$
$18$
$19$
$20$

Question 13

Find each interior angle of a regular pentagon.

Question illustration

$106^\circ$
$108^\circ$
$114^\circ$
$240^\circ$
$300^\circ$

Question 14

For example, $3^4$ means multiplying four copies of $3$ and $2^5$ means multiplying five copies of $2$. What is the units digit of $222^{222}$?

$2$
$4$
$6$
$8$
None of the above

Question 15

The symbol $\gt $ means greater than, for example $5\gt 3$. Whole numbers $x,y$ satisfy $\frac{x}{19}\gt \frac35\gt \frac{y}{19}$. Which listed value can be $x+y$?

$4$
$13$
$15$
$23$
None of the above

Question 16

Put the numbers $2,3,4,5,6,7,8$, each once, in the seven circles. Each straight line of three circles sums to $15$. Find the centre number $m$.

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$5$
$6$
$7$
$8$
None of the above

Question 17

A test has $20$ questions. A correct answer earns $7$ points, a wrong answer loses $4$, and a blank earns $0$. Joan scores $100$. How many questions does she leave blank?

$3$
$2$
$1$
$0$
None of the above

Question 18

A right triangle has perimeter $12\text{ cm}$ and area $6\text{ cm}^2$. Find its longest side.

Question illustration

$3$
$5$
$7$
$9$
None of the above

Medan is $90\text{ km}$ from Lake Toba. Henry leaves Medan at $8$ a.m. at $90\text{ km/h}$. Annisa leaves $20$ minutes later at $120\text{ km/h}$. How far is Annisa from Lake Toba when Henry arrives?

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$8$
$10$
$12$
$14$
None of the above

Question 20

Wang has some apples. Giving each family member $4$ apples leaves $10$ apples; giving each $6$ apples leaves him $6$ apples short. How many apples does Wang have?

Question illustration

$40$
$42$
$44$
$46$
None of the above