Edutest Numerical Reasoning tests how your child thinks with numbers, more than what they've been taught, in 30 minutes without a calculator. These eight worked questions cover its main kinds, from number series to a logic puzzle.
Thinking with numbers: spotting a pattern, finding a rule and planning the steps of a problem. It's one of Edutest's two Ability tests, beside Verbal Reasoning, and these measure thinking, reasoning and problem solving, without necessarily relying on prior knowledge.
Edutest names the question types as series, matrices, arithmetical reasoning and deduction. Children shade bubbles on a paper answer sheet, so practise with a separate answer sheet as well as the questions.
Series, matrices, arithmetical reasoning and deduction are Edutest's own words. Data and estimation questions are arithmetical reasoning with a table or rounding added, so our practice gives them their own skill pages.
Children are tested at their current year level. Our questions are written for children in Years 6–7 applying for Year 7 or 8.
Find the missing number in a grid or a set of pairs
Testing one rule on every row
Arithmetical reasoning
Solve a word problem that takes several steps
Planning before calculating
Data
Answer from a table or a graph
Reading the condition exactly
Estimation
Choose the closest amount
Rounding and checking the size
Deduction
Use clues to work out who has which number
Ruling cases out
Eight sample questions with answers
Each one shows the answer and the working. Read them with your child and talk through why the right option is right. They run from series and grids to word problems, a logic puzzle and a table.
We wrote these in the style of the real test, for a strong student in Years 6–7. They are not from an Edutest paper.
Worked explanation 1
What number comes next in this series?
3, 4, 7, 12, 19, 28, …
AA.
37
BB.
39
CC.
38
DD.
40
Answer: B
Answer: B (39)
Look at the gaps between the numbers: +1, +3, +5, +7, +9. The gaps are the odd numbers in order, so the next gap is +11. 28 + 11 = 39, so the answer is 39.
The trap: 37 tempts children who spot that the gaps are growing but simply add the last gap of 9 again.
Why the other options are wrong
A (37): Adds 9 again instead of the next odd number.
C (38): Adds 10, as if the gaps grew by one each time.
D (40): Adds 12, guessing that the gaps grow by three.
Worked explanation 2
What number comes next in this series?
243, 162, 108, 72, 48, …
AA.
24
BB.
36
CC.
30
DD.
32
Answer: D
Answer: D (32)
The gaps (81, 54, 36, 24) are not equal, so try multiplying. 243 ÷ 3 × 2 = 162, 162 ÷ 3 × 2 = 108, and so on: each number is two-thirds of the one before. Two-thirds of 48 is 48 ÷ 3 × 2 = 32, so the answer is 32.
The trap: 24 tempts children who see the numbers shrinking fast and assume each one is halved.
Why the other options are wrong
A (24): Halves 48, but 162 is not half of 243.
B (36): Takes away 12, a guess at the next gap.
C (30): Takes away 18, a guess that does not follow the shrinking gaps.
Worked explanation 3
In each row, the three numbers follow the same rule. What number replaces the question mark?
First
Second
Third
4
3
11
6
5
17
7
2
16
9
4
?
AA.
22
BB.
13
CC.
17
DD.
36
Answer: A
Answer: A (22)
Test a rule on the first row and check it on the others. Double the first number and add the second: 4 × 2 + 3 = 11, 6 × 2 + 5 = 17, 7 × 2 + 2 = 16. For the last row, 9 × 2 + 4 = 22, so the answer is 22.
The trap: 17 tempts children who double the wrong number: 9 + 4 × 2 = 17, which fails the first row (4 + 6 = 10, not 11).
Why the other options are wrong
B (13): Just adds the two numbers, which gives 7 for the first row, not 11.
C (17): Doubles the second number instead of the first.
D (36): Multiplies the two numbers, which gives 12 for the first row, not 11.
Worked explanation 4
In each row, the three numbers follow the same rule. What number replaces the question mark?
First
Second
Third
5
7
8
6
4
14
8
10
14
9
?
20
AA.
47
BB.
15
CC.
7
DD.
11
Answer: C
Answer: C (7)
The rule must work for all three complete rows. Three times the first number, take away the second, gives the third: 15 − 7 = 8, 18 − 4 = 14, 24 − 10 = 14. In the last row 3 × 9 = 27, and 27 − ? = 20, so the missing number is 7.
The trap: 15 tempts children who fit a rule to the first row only (add the two numbers, take away 4) and never check it on the second row.
Why the other options are wrong
A (47): Adds 20 to 27 instead of working backwards to find what was taken away.
B (15): Uses 'add, then take away 4', which only fits the first row.
D (11): Takes the first number from the third (20 − 9), which is not the rule in any row.
Worked explanation 5
Ayesha has a 10 kg block of clay. She makes 8 bowls, each using 450 g of clay. With the clay that is left she makes as many plates as she can, each using 350 g. How many plates does she make?
AA.
19
BB.
18
CC.
28
DD.
17
Answer: B
Answer: B (18)
The bowls use 8 × 450 g = 3600 g. Then 10 kg = 10 000 g, so 10 000 − 3600 = 6400 g is left. 6400 ÷ 350 is 18 with 100 g over (18 × 350 = 6300). She can make 18 plates.
The trap: 28 tempts children who divide the whole 10 kg by 350 g and forget the clay already used for the bowls.
Why the other options are wrong
A (19): Rounds 18.3 up, but there is not enough clay for a 19th plate.
C (28): Ignores the bowls and divides all 10 000 g by 350 g.
D (17): Rounds the bowls up to 4000 g before dividing.
Worked explanation 6
A recipe for 12 pikelets uses 150 mL of milk and 2 eggs. Leilani has 1 litre of milk and 9 eggs. She can make more or fewer pikelets than the recipe, as long as every pikelet has the same share of milk and egg as a pikelet made from the recipe. What is the greatest number of pikelets she can make?
AA.
54
BB.
80
CC.
48
DD.
60
Answer: A
Answer: A (54)
Work out what each ingredient allows on its own. Milk: 1000 mL ÷ 150 mL = 6⅔ recipes, or 80 pikelets. Eggs: 9 eggs ÷ 2 = 4½ recipes, or 4½ × 12 = 54 pikelets. The eggs run out first, so the greatest number is 54. That is 4 full recipes plus a half recipe (6 pikelets with 1 egg), so it uses exactly 9 whole eggs and 675 mL of milk.
The trap: 80 tempts children who only check the milk and forget that the eggs also limit the batch.
Why the other options are wrong
B (80): Uses only the milk; there are not enough eggs for 80.
C (48): Makes only whole recipes (4 × 12), but the question allows part recipes.
D (60): Rounds 4½ recipes up to 5, which needs 10 eggs.
Worked explanation 7
Rua, Kai, Nadia and Sam each chose a different number from 9, 14, 16 and 21.
Rua's number and Sam's number add up to 30.
Nadia's number is a multiple of 7.
Kai's number is larger than Rua's but smaller than Sam's.
Who chose 21?
AA.
Rua
BB.
Kai
CC.
Nadia
DD.
Sam
Answer: D
Answer: D (Sam)
Two pairs add up to 30: 9 + 21 and 14 + 16. If Rua and Sam had 14 and 16, Nadia and Kai would have 9 and 21, so Nadia (a multiple of 7) would have 21 and Kai 9, but then Kai's number could not be larger than Rua's. So Rua and Sam have 9 and 21, Nadia has 14 and Kai has 16. Kai's 16 sits between Rua and Sam, so Rua has 9 and Sam has 21.
The trap: Nadia tempts children who see that 21 is a multiple of 7 and give it to Nadia straight away, forgetting that 14 is a multiple of 7 too.
Why the other options are wrong
A (Rua): Rua has 9, because Kai's 16 must be larger than Rua's number.
B (Kai): Kai has 16, which sits between Rua's 9 and Sam's 21.
C (Nadia): Nadia has 14; 21 is needed with 9 to make Rua and Sam's 30.
Worked explanation 8
At a school trivia night, each team chose one joker round. The team's score for that round was doubled. The table shows each team's scores before any doubling and its joker round. Which team had the highest final score?
Team
Round 1
Round 2
Round 3
Joker round
Owls
8
6
9
Round 2
Foxes
7
8
8
Round 1
Hawks
9
9
7
Round 3
Seals
6
10
7
Round 2
AA.
Hawks
BB.
Owls
CC.
Seals
DD.
Foxes
Answer: C
Answer: C (Seals)
Add each team's three scores, then add the joker round score once more. Owls 23 + 6 = 29, Foxes 23 + 7 = 30, Hawks 25 + 7 = 32, Seals 23 + 10 = 33. Seals had the highest final score.
The trap: Hawks tempts children who add the scores but forget to double the joker rounds (Hawks have the best total, 25, before doubling).
Why the other options are wrong
A (Hawks): Hawks lead before doubling but finish on 32.
B (Owls): Owls doubled their lowest round and finish on 29.
D (Foxes): Foxes finish on 30.
How should your child tackle each kind?
Each kind of question has one habit that saves the most marks. Ask your child to say the habit out loud while working: a rule they can say is a rule they can check.
Series: find the gaps
Work out the difference between each pair of neighbours. If the gaps aren't steady, look at how they change, or try multiplying.
Matrices: test the rule on every row
A rule that works on the first row is a guess until it works on all of them.
Word problems: plan the steps first
Say what has to be found and the order of the sums before doing any of them.
Data: find the condition
Words such as more than, least or every decide which numbers count.
Deduction: start with the tightest clue
Begin with the clue that leaves the fewest possibilities, then test each case against every other clue.
How is it different from the Mathematics test?
Mathematics checks what your child has been taught; Numerical Reasoning checks how they use it. Mathematics is a separate Edutest test, one of the Achievement tests, and it measures year-level maths: numbers, measurement, algebra, space and data.
The two overlap: a child who is slow with times tables or fractions loses time in both. But a reasoning question rarely says which operation to use, and working that out is the question.
How is it marked, and how fast must your child work?
Fast, and with an answer for every question. Edutest says there are no marks lost for wrong or blank answers, so a blank never scores and a guess sometimes does.
Edutest's practice page gives the size of each test: 20 practice questions per test; real tests have 40 to 60. A real test fits all its questions into 30 minutes, and many students will not finish every question.
Plan one pass that answers everything your child can see a way into, then a guess for the rest, then the skipped ones if time is left. Edutest doesn't allow calculators, rulers, dictionaries, working-out paper, mobile phones, smart watches and fitness trackers, so practise without a calculator at home too.
Results are compared with thousands of students in the same year level across Australia, and Edutest says most students get only half the questions right. So a first practice score near the middle is normal for a strong student.
Each question above has a wrong option built from a common slip. Find it with your child and match it to this list: that's the habit to fix.
Repeating the last gap. In a series whose gaps grow, adding the last gap again gives the option beside the answer.
Fitting a rule to one row. In the second grid, a rule that works on the first row fails on the second.
Forgetting what has been used. In the clay question, dividing the whole block ignores the bowls already made.
Checking one limit, not both. The pikelet recipe has two ingredients; the one that runs out first decides.
Giving the obvious number to the obvious person. In the logic puzzle, two of the numbers are multiples of 7.
Skipping one instruction. In the trivia table, forgetting to double the joker round picks the wrong team.
How can your child practise Numerical Reasoning?
Little and often works well here. A few mixed questions most days, done without a calculator and then talked through, build speed and the habits above.
When your child is ready for the clock, Practice test 1 has a full Numerical Reasoning section on Edutest's time. Afterwards you'll see results by skill, so you know which kinds of question cost the most marks. The other tests have sample pages too: Verbal Reasoning, Reading Comprehension and Mathematics.
See where your child stands
Practice test 1 marks every answer and shows results by skill: what your child already does well and the three skills to work on next.
Sample
Practise for the real test
Practice test 1 is free. Then packs from A$109 for 12 months, or A$9 a week, per exam.
