Section A
Multiple Choice — Questions 1 to 15
(+2 / -1)
1
number-sense
easy
Which number can go in the box to make the statement true?
☐ > 8176
Answer: D
The box must be greater than 8176.
7681 and 7816 are below 8000.
8167 < 8176 (the tens digit 6 is less than 7).
Only 8716 > 8176, so the box is 8716.
2
multiples
easy
How many numbers between 30 and 60 can be divided exactly by 8?
Answer: D
Multiples of 8 between 30 and 60:
32, 40, 48, 56.
That is 4 numbers.
3
multiplication
easy
9 + 9 + 9 + 9 = 6 × ☐
What is the missing number in the box?
Answer: C
9 + 9 + 9 + 9 = 36.
36 = 6 × 6.
So the box is 6.
4
fractions
medium
Which of the following shows 3/4 of the figure shaded?
Options A–D are the four shaded figures shown in the image.
Answer: B
To show 3/4, the whole must be split into 4 equal parts (by area) with 3 shaded.
B is a square split into four equal small squares with a corner-to-corner diagonal.
Two small squares are fully shaded (2/4) and two are half-shaded triangles (another 1/4), giving 3/4.
(A shades 8 of 12 squares = 2/3; C shades 2 of 5 sectors; D shades 3 of 4 vertical strips, but those strips are unequal in area.)
5
measurement-mass
easy
Mr Loh bought a loaf of bread (14 slices) as shown. Which of the following could be the mass of the loaf of bread?
Answer: D
A 14-slice loaf weighs a few hundred grams.
5 g and 50 g are far too light (one slice alone weighs more).
1 kg is too heavy for an ordinary loaf.
About 500 g is the sensible estimate.
6
time
medium
What is 25 minutes before the time shown on the clock? Give your answer using the 24-hour clock.
Answer: A
The minute hand points to 11 (55 minutes) and the hour hand is just before 4, so the clock shows 3:55 (15:55).
25 minutes before 3:55 is 3:30.
In the 24-hour clock this is 15 30.
7
perimeter
medium
Which of the following figures have the same perimeter?
Answer: A
Count the unit edges around each shape:
Figure A (a 3×3 block) = 12
Figure B (an H-shape) = 16
Figure C = 14
Figure D (a 6-square staircase) = 12
Figures A and D both have a perimeter of 12 units.
8
money
easy
Andy has 3 fifty-dollar notes, 7 five-dollar notes and 6 twenty-cent coins. How much money does Andy have?
Answer: D
3 × $50 = $150
7 × $5 = $35
6 × 20¢ = $1.20
Total = $150 + $35 + $1.20 = $186.20
9
bar-graph
medium
The bar graph shows the number of students from four Primary 3 classes who borrowed books from the school library. How many more boys than girls from the four classes borrowed books?
Answer: A
Boys: 20 + 10 + 25 + 15 = 70
Girls: 10 + 15 + 5 + 25 = 55
Difference = 70 − 55 = 15
10
measurement-mass
medium
What is the mass of the bunch of bananas shown on the scale?
Answer: C
On the 5 kg dial the needle is a little past the 3 kg mark.
It is about four small 100 g divisions beyond it.
So the mass is 3 kg 400 g.
11
fractions
easy
Which pair of fractions are equivalent fractions?
Answer: C
2/6 = 1/3 and 3/9 = 1/3, so they are equal.
(4/8 = 1/2; 6/10 = 3/5; 4/9 ≠ 3/9.)
12
patterns
medium
James uses triangles and lines to form figures that follow a pattern. Figure 1 has 2 triangles and 7 lines, Figure 2 has 4 triangles and 12 lines, Figure 3 has 6 triangles and 17 lines. How many triangles are there in the figure which has 47 lines?
Answer: C
The number of lines goes 7, 12, 17, … increasing by 5 each time.
So lines = 5 × (figure number) + 2.
For 47 lines: 5n + 2 = 47 → n = 9.
Triangles = 2 × (figure number) = 2 × 9 = 18.
13
algebra-symbols
medium
☾ × ☾ = 49 and ♥ × ♥ = 81.
What is the product of ♥ and ☾ ?
Answer: D
☾ × ☾ = 49 → ☾ = 7
♥ × ♥ = 81 → ♥ = 9
Product ♥ × ☾ = 9 × 7 = 63
14
measurement-volume
medium
Daniel wanted to fill a pail completely with water. He used 2 identical bottles to fill half the pail, and each bottle has a capacity of 300 ml. He used 5 identical cups to fill the remaining half of the pail. What was the capacity of a cup?
Answer: A
Half the pail = 2 × 300 ml = 600 ml.
The other half (600 ml) is filled by 5 cups.
Each cup = 600 ÷ 5 = 120 ml.
15
money
hard
A supermarket promotion sells cookies at $12 per packet with the offer 'Buy 2 packets and get 1 packet free'. Mrs Mandy left the supermarket with 10 packets of cookies. What was the least amount of money she could have paid?
Answer: C
For every 2 packets bought she gets 1 free (3 packets for $24).
To get the most free packets, buy 7 packets: that earns 3 free (7 ÷ 2 = 3), giving 10 packets in all.
Cost = 7 × $12 = $84.
(Buying only 6 earns 3 free = 9 packets, which is not enough.)
Section B
Open Answer — Questions 16 to 25 (4 marks each, no penalty)
(+4)
16
number-puzzle
hard
Andy is thinking of a 4-digit number between 2000 and 4000. The digit in the hundreds place is twice the digit in the thousands place. The digit in the ones place is 5 less than the digit in the tens place. All the digits add up to 20. What number is Andy thinking of?
Answer: 3683
The thousands digit is 2 or 3, and hundreds = 2 × thousands.
Let tens = t and ones = t − 5.
If thousands = 3, hundreds = 6: 3 + 6 + t + (t − 5) = 20 → 2t + 4 = 20 → t = 8, ones = 3.
(Thousands = 2 gives a non-whole tens digit.)
The number is 3683.
17
division
medium
Mrs Tan baked 390 cookies. Mrs Lee baked 255 cookies. They packed all their cookies into packets, with each packet holding 6 cookies. What is the least number of packets needed to contain all the cookies?
Answer: 108
Total cookies = 390 + 255 = 645.
645 ÷ 6 = 107 remainder 3.
107 packets hold 642 cookies, and 1 more packet is needed for the last 3.
Least number of packets = 108.
18
time
medium
Benjamin took 4 hours and 50 minutes on a flight from Singapore to Taipei. He took another 45 minutes moving from the airport to his hotel. He reached his hotel at 14 15. What time did Benjamin leave Singapore? Give your answer in the 24-hour clock (e.g. 0840).
Answer: 0840
Work backwards from 14 15.
Subtract 45 minutes → 13 30.
Subtract 4 hours 50 minutes → 08 40.
Benjamin left Singapore at 08 40.
19
money
medium
Shop A sells 6 apples for $8.50 and Shop B sells 8 apples for $11. Mdm Lee bought 24 apples from Shop A. Mrs Benson bought 24 apples from Shop B. How much did they pay in total? (Enter the amount in dollars, e.g. 67.)
Answer: 67
Shop A: 24 ÷ 6 = 4 sets × $8.50 = $34.
Shop B: 24 ÷ 8 = 3 sets × $11 = $33.
Total = $34 + $33 = $67.
20
area
hard
The figure is made up of one rectangle and two identical squares. The breadth of the rectangle is 21 cm. Each side of the square is 46 cm. Find the area of the figure in cm².
Answer: 6164
The two squares are stacked, so the rectangle's length = 2 × 46 = 92 cm.
Rectangle area = 21 × 92 = 1932 cm².
Two squares = 2 × (46 × 46) = 4232 cm².
Total = 1932 + 4232 = 6164 cm².
21
measurement-volume
medium
Mr Wong bought 8 litres of orange juice. His guests drank 6090 ml of it. He poured the remaining orange juice equally into 5 bottles. How much orange juice did he pour into each bottle? Give your answer in millilitres.
Answer: 382
8 L = 8000 ml.
Remaining = 8000 − 6090 = 1910 ml.
Each bottle = 1910 ÷ 5 = 382 ml.
22
before-after
medium
There were some passengers on a bus when it left bus stop A. At bus stop B, 9 passengers alighted from the bus. At bus stop C, 12 passengers boarded the bus and 5 passengers alighted, after which there were 47 passengers on the bus. How many passengers were there on the bus when it left bus stop A?
Answer: 49
Work backwards from 47.
Undo bus stop C (subtract the 12 who boarded, add back the 5 who alighted): 47 − 12 + 5 = 40 after bus stop B.
Undo bus stop B (add back the 9 who alighted): 40 + 9 = 49.
So 49 passengers left bus stop A.
23
word-problem
medium
Helen has 3 bottles. Bottle A contains 230 more buttons than Bottle B. Bottle C contains 4 times as many buttons as Bottle B. Bottle C contains 276 buttons. How many buttons does Helen have altogether?
Answer: 644
Bottle C = 276 = 4 × Bottle B → Bottle B = 69.
Bottle A = 69 + 230 = 299.
Total = 299 + 69 + 276 = 644 buttons.
24
word-problem
hard
4 umbrellas and 5 raincoats cost $173 altogether. Each raincoat costs $13 more than each umbrella. Find the cost of each raincoat. (Enter the amount in dollars.)
Answer: 25
Replace each raincoat by (umbrella + $13):
4 umbrellas + 5 umbrellas + 5 × $13 = $173
9 umbrellas + $65 = $173 → 9 umbrellas = $108 → 1 umbrella = $12.
Each raincoat = $12 + $13 = $25.
25
gaps-and-posts
hard
Ben wants to hang some stars at an equal distance from each other on a string. The distance between the 1st star and the 4th star is 24 cm. How many stars can Ben hang on the string if the string is 3 m long? (The width of each string that hangs a star is negligible.)
Answer: 38
From the 1st star to the 4th star there are 3 equal gaps totalling 24 cm, so each gap = 8 cm.
On a 300 cm string: 300 ÷ 8 = 37 whole gaps (37 × 8 = 296 cm).
37 gaps hold 38 stars (the first star plus one after each gap).
Section C
Open Answer — Questions 26 to 31 (5 marks each, no penalty)
(+5)
26
money
hard
At a fruit stall, for every 5 oranges bought at $8, 2 oranges are given free. Each orange costs $1.50. Miss Hong paid for some oranges and received a total of 60 oranges. How much did Miss Hong pay? (Enter the amount in dollars.)
Answer: 70
Each deal gives 5 + 2 = 7 oranges for $8.
60 = 8 × 7 + 4, so 8 deals give 56 oranges for 8 × $8 = $64.
The remaining 4 oranges are bought singly at $1.50 each = $6.
Total = $64 + $6 = $70.
27
word-problem
hard
Factory A made 1252 chairs more than Factory B. Factory C made twice as many chairs as Factory B. After 3216 chairs were sold from Factory A, there were 5 times as many chairs in Factory B as in Factory A. How many more chairs were there in Factory C than Factory B?
Answer: 2455
Let Factory B = b.
Factory A = b + 1252; after selling, A = b + 1252 − 3216 = b − 1964.
Given B = 5 × (new A): b = 5(b − 1964) → b = 5b − 9820 → 4b = 9820 → b = 2455.
Factory C = 2b, so C − B = 2b − b = b = 2455.
28
number-pattern
hard
A number pattern is shown below.
1 8 8 9 1 1 8 8 9 1 1 8 8 9 …
What is the sum of the first 54 numbers of the number pattern?
Answer: 296
The numbers repeat every 5: (1, 8, 8, 9, 1), (1, 8, 8, 9, 1), (1, 8, 8, 9, 1), …
(The two 1s that appear together are the join between one group's last 1 and the next group's first 1.)
Each group of 5 sums to 1 + 8 + 8 + 9 + 1 = 27.
The first 54 numbers make 10 complete groups (50 numbers) plus 4 more (1, 8, 8, 9).
Sum = 10 × 27 + (1 + 8 + 8 + 9) = 270 + 26 = 296.
29
perimeter
hard
A worker completely covered a square-shaped floor with identical tiles using the tiling pattern shown. Each tile measures 23 cm by 46 cm. What is the perimeter of the floor? Give your answer in cm.
Answer: 736
One side of the square is the repeating unit 23 + 23 + 46 + 23 + 23 + 46 = 184 cm (four 46 cm basketweave blocks).
So the floor is 184 cm × 184 cm (exactly 32 tiles).
Perimeter = 4 × 184 = 736 cm.
30
bar-graph
hard
The bar graph shows the number of cakes sold in a bakery from Monday to Friday. The number of cakes sold is not shown on the scale. A total of 45 cakes were sold on Friday. How many cakes were sold from Monday to Thursday?
Answer: 165
Friday's bar is 4½ grid-spaces long and represents 45 cakes, so each grid-space = 10 cakes (each half-space = 5).
Reading the bars: Monday = 30, Tuesday = 20, Wednesday = 50, Thursday = 65.
Monday to Thursday = 30 + 20 + 50 + 65 = 165 cakes.
31
before-after
hard
There was an equal number of red and green beans in a box. After taking out 170 red beans and adding 250 green beans, the number of green beans became 8 times as many as the number of red beans. How many beans were there altogether at first?
Answer: 460
Let each colour start with x beans.
Red now = x − 170, green now = x + 250, with green = 8 × red:
x + 250 = 8(x − 170) → x + 250 = 8x − 1360 → 7x = 1610 → x = 230.
At first there were 230 + 230 = 460 beans.