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.
15 questions · official format, shuffled order
1 How many multiples of 7 from 1 to 150 are not multiples of 4?
Show worked solution
150 ÷ 7 = 21 r 3, so 21 multiples of 7. Multiples of 28 up to 150: 28, 56, 84, 112, 140 — five. 21 − 5 = 16.
2 A tram leaves the wharf every 15 minutes and a ferry every 25 minutes. Both leave together at 9:00. When do they next leave together?
Show worked solution
Multiples of 25: 25, 50, 75 — and 15 divides 75. So 75 minutes after 9:00, which is 10:15.
3 A school orders 1 000 pencils, packed in boxes of 42. Every pencil must be boxed. How many empty spaces are there in the last box?
Show worked solution
1 000 ÷ 42 = 23 r 34, so 23 full boxes and 34 pencils in a 24th box. That box has 42 − 34 = 8 empty spaces.
4 Use the area model to find 463 × 27.
Show worked solution
8 000 + 1 200 + 60 = 9 260 and 2 800 + 420 + 21 = 3 241. 9 260 + 3 241 = 12 501.
5 Which of these numbers is divisible by both 4 and 9?
Show worked solution
2 376: 76 = 4 × 19 and 2 + 3 + 7 + 6 = 18. The others each fail one test: 1 236 (digit sum 12), 2 358 (58 is not a multiple of 4), 3 942 (42 is not), 4 532 (digit sum 14).
6 Which of these numbers is prime?
Show worked solution
111 = 3 × 37 and 117 = 9 × 13 (digit sums 3 and 9). 119 = 7 × 17. 121 = 11 × 11. 127 is not divisible by 2, 3, 5, 7 or 11, so it is prime.
7 Which number is both a square number and a triangular number?
Show worked solution
36 = 6 × 6, and 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36. 28 and 45 are triangular only; 16 and 25 are square only.
8 Two ribbons, 84 cm and 126 cm long, are cut into pieces that are all the same length, as long as possible, with nothing left over. How many pieces are there altogether?
Show worked solution
HCF of 84 and 126 is 42. 84 ÷ 42 = 2 pieces and 126 ÷ 42 = 3 pieces: 5 altogether.
9 3 000 chairs are set out in rows of 48. How many chairs are in the last, incomplete row?
Show worked solution
48 × 62 = 2 976, and 3 000 − 2 976 = 24. So 62 full rows and 24 chairs in the last one.
10 How many factors does 60 have?
Show worked solution
1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10 — six pairs, so 12 factors.
11 Tom's number is a multiple of 8 and less than 70. Uma's number is an odd multiple of 11 and greater than 20. What is the smallest possible difference between their numbers?
Show worked solution
Tom: 8, 16, 24, 32, 40, 48, 56, 64. Uma: 33, 55, 77 … 32 and 33 differ by 1 (so do 56 and 55).
12 Which is the best estimate of 689 × 42?
Show worked solution
700 × 40 = 28 000. (The exact product is 28 938.)
13 Use each digit card once to make a three-digit number multiplied by a one-digit number. What is the largest product you can make?
Show worked solution
752 × 9 = 6 768, which beats 952 × 7 = 6 664, 972 × 5 = 4 860 and 975 × 2 = 1 950.
14 A number leaves a remainder of 5 when divided by 6, and a remainder of 1 when divided by 4. Which of these could it be?
Show worked solution
29 = 6 × 4 + 5 and 29 = 4 × 7 + 1. The others fail one test: 11, 35 and 47 leave 3 when divided by 4; 31 leaves 1 when divided by 6.
15 Look at the number 7 236.1 It is divisible by 3.
2 It is divisible by 8.
3 It is divisible by 9.
Which statements are correct?
2 It is divisible by 8.
3 It is divisible by 9.
Which statements are correct?
Show worked solution
7 + 2 + 3 + 6 = 18, a multiple of both 3 and 9 (1 ✓, 3 ✓). 236 ÷ 8 = 29.5, so not divisible by 8 (2 ✗). 1 and 3.