Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
35 questions · official format, shuffled order
1 Which of these numbers is closest to 100?
Show worked solution
99.8 is 0.2 away; 100.3 is 0.3 away. 99.8 is closest.
2 Jo reads 20 pages every day. Kim reads 30 pages every 2 days. After 6 days, who has read more, and by how much?
Show worked solution
Jo 120 pages, Kim 90 pages: Jo, by 30 pages.
3 How many odd numbers between 20 and 80 are multiples of 3?
Show worked solution
21, 27, 33, 39, 45, 51, 57, 63, 69, 75: 10.
4 A wire 36 cm long is bent into a rectangle whose length is twice its width. What is the area of the rectangle?
Show worked solution
Width 6 cm, length 12 cm. Area 6 × 12 = 72 cm².
5 A box is packed with cubes: 3 rows of 4 cubes, in 2 layers. How many of the cubes touch the bottom of the box?
Show worked solution
One layer of 3 × 4 = 12 cubes.
6 If the day after tomorrow is Friday, what day was the day before yesterday?
Show worked solution
Tomorrow is Thursday, today Wednesday, yesterday Tuesday, and the day before yesterday Monday.
7 A square is divided into 4 equal squares and one of them is shaded. That shaded square is then divided into 4 equal squares and one of those is shaded darker. What fraction of the original square is shaded darker?
Show worked solution
¼ of ¼ = 1/16.
8 When all the whole numbers from 1 to 100 are written down, how many times is the digit 7 written?
Show worked solution
Ones place: 10 times. Tens place: 10 times (70–79). 20 altogether.
9 What number is exactly halfway between 1/4 and 3/8?
Show worked solution
Halfway between 4/16 and 6/16 is 5/16.
10 Three closed boxes are labelled APPLES, ORANGES and MIXED — but every label is on the wrong box. One fruit is taken from the box labelled MIXED, and it is an apple. Which box contains only oranges?
Show worked solution
MIXED holds apples. The box labelled ORANGES cannot hold oranges, so it holds the mixed fruit, leaving the box labelled APPLES for the oranges.
11 A clock loses 4 minutes every hour. It is set correctly at 12 noon. What does it show when the real time is 6:00 pm?
Show worked solution
6 × 4 = 24 minutes slow: 5:36 pm.
12 How many rectangles of any size (squares count too) can be found in this 3 by 3 grid?
Show worked solution
6 × 6 = 36.
13 Ali has 3 more marbles than Ben, and Cal has twice as many as Ali. Together they have 45 marbles. How many does Ben have?
Show worked solution
Ben 9: 9 + 12 + 24 = 45 ✓.
14 A two-digit number has digits that add to 11, and its tens digit is 3 more than its units digit. What is the number?
Show worked solution
7 + 4 = 11 and 7 − 4 = 3, with 7 in the tens: 74.
15 Three quarters of two thirds of 60 is
Show worked solution
⅔ of 60 = 40, and ¾ of 40 = 30.
16 A rectangle 8 cm by 6 cm has a diagonal of 10 cm. It is cut along the diagonal into two triangles, which are then placed together along their 8 cm sides to make a single triangle. What is the perimeter of that triangle?
Show worked solution
10 + 10 + 6 + 6 = 32 cm.
17 Which of these is not a factor of 360?
Show worked solution
360 ÷ 16 = 22.5, so 16 is not a factor. 18, 24 and 45 all divide 360 exactly.
18 A sheet of paper is folded in half, then in half again. The corner where all the folds meet is snipped off. When the paper is unfolded, what is the shape of the hole?
Show worked solution
The snipped triangle is reflected across both folds into four triangles meeting at the centre, which make a square.
19 A bus has 40 seats. At the first stop two fifths of the seats are filled. At the second stop half of the empty seats are filled. At the third stop 6 people get off. How many people are seated now?
Show worked solution
16 + 12 = 28, then 28 − 6 = 22.
20 The sum of three consecutive odd numbers is 63. What is the largest of them?
Show worked solution
Middle number 21, so 19, 21 and 23.
21 A tap can fill a bath in 12 minutes. The drain can empty a full bath in 18 minutes. With the tap on and the drain open, how long does it take to fill a quarter of the bath?
Show worked solution
The bath fills in 36 minutes, so a quarter takes 9 min.
22 How many different three-digit numbers can be made using each of the digits 2, 5 and 8 exactly once?
Show worked solution
3 × 2 × 1 = 6: 258, 285, 528, 582, 825, 852.
23 A shop sells pens at 3 for $2, or in boxes of 10 for $6. Pens cannot be bought singly. What is the cheapest way to get at least 23 pens?
Show worked solution
Two boxes ($12) plus one pack of 3 ($2) = 23 pens for $14. Eight packs of 3 cost $16; one box and five packs cost $16.
24 Which fraction lies between 1/3 and 1/2?
Show worked solution
5/12 sits between 4/12 and 6/12. 1/4 and 2/7 are below 1/3; 3/5 is above 1/2.
25 An equilateral triangle with sides of 8 cm has the same perimeter as a regular hexagon. How long is each side of the hexagon?
Show worked solution
3 × 8 = 24, and 24 ÷ 6 = 4 cm.
26 Lily saves $5 in the first week, and each week she saves $2 more than the week before. How much has she saved after 8 weeks?
Show worked solution
Four pairs of $24: $96.
27 At a party each child is given 3 balloons and 4 balloons are left over. If each child were given 4 balloons instead, there would be 5 balloons too few. How many children are there?
Show worked solution
One extra per child needs 4 + 5 = 9 balloons, so 9 children. (There are 31 balloons.)
28 A cube with 3 cm edges is cut into 1 cm cubes. Compared with the original cube, the total surface area of all the small cubes is
Show worked solution
Original 54 cm². Small cubes 27 × 6 = 162 cm², which is three times as much.
29 What is 1 − 1/2 − 1/4 − 1/8 − 1/16?
Show worked solution
After taking 1/2 there is 1/2; after 1/4, 1/4; after 1/8, 1/8; after 1/16, 1/16.
30 Four friends sit in a row of four seats. Zoe is not at either end. Yas is somewhere to the left of Zoe. Xan is at the right-hand end, and Wil is next to Xan. Who is at the left-hand end?
Show worked solution
Seats 4 and 3 are Xan and Wil; Zoe takes seat 2; Yas is at the left end, which is also to the left of Zoe ✓.
31 A rectangular lawn is 60 m by 40 m. A path 2 m wide runs around the outside of it. What is the area of the path?
Show worked solution
64 × 44 − 60 × 40 = 2 816 − 2 400 = 416 m².
32 Buses leave a station every 12 minutes, the first at 6:05 am. How many buses leave between 7:00 am and 8:00 am, including any at exactly 7:00 or 8:00?
Show worked solution
7:05, 7:17, 7:29, 7:41, 7:53 — 5 buses. (The next is 8:05.)
33 At 6 pm the temperature is 14 °C, and it falls by 3 °C every hour. At what time is it −4 °C?
Show worked solution
18 ÷ 3 = 6 hours after 6 pm: midnight.
34 Two lines are drawn from the top corner of a large triangle to its base, as shown. How many triangles of any size are in the figure?
Show worked solution
3 small + 2 made of two + 1 whole = 6.
35 A number leaves a remainder of 2 when divided by 5, and a remainder of 3 when divided by 4. What is the smallest such number greater than 20?
Show worked solution
22 leaves 2 when divided by 4; 27 leaves 3 ✓.