New signs with their own rules, digits in the wrong places, patterns of calculations, triangle puzzles and coins that are not tens.
OftenIn many papers, especially GL AssessmentAbout 60 seconds a question in the test
The big idea
Entrance papers like puzzles that test whether you can follow a rule you have never met. A new sign, such as a star between two numbers, comes with its own rule: write the rule out again with the numbers in their places, then work it out.
Other puzzles hide the answer in a pattern. A pattern of calculations grows the same way from line to line; say how each number comes from the first one, and use the same links for any line you want.
Some puzzles have two clues, such as two numbers that add up to one total and multiply to make another. List what fits one clue, then test each against the other.
Tips that save marks
Write the rule out with the numbers in place before working anything out.
With digits in the wrong places, look at the last digits first.
On a planet where 4 pips make a tok, carry in fours, not tens.
A worked example
A new sign means double the first number, then add the second. What is 5 star 3?
Double the first number: 5 doubled is 10.
Add the second number: 10 and 3 make 13.
Answer: 13.
Now try five
Try each one before you look at the answer: answering from memory is what makes it stick. Tap an option to check it. Most children get three or four right at first; five out of five means move on to the next topic.
Question 1Aim for about 60 seconds
The sign ★ means a ★ b = 4 × a + 5 × b. For example, 4 ★ 1 = 4 × 4 + 5 × 1 = 21. What is 2 ★ 4?
Show the worked answer
Answer: A, 28
How to work it out
The first number is 2 and the second is 4: 4 × 2 + 5 × 4 = 8 + 20 = 28.
Why the other options are wrong
B (54): This adds before multiplying; work out 4 × 2 and 5 × 4 separately, then add.
C (12): This forgets to multiply the second number by 5.
D (22): This forgets to multiply the first number by 4.
E (26): This puts 4 where a goes; in 2 ★ 4 the first number is 2, so 2 is the one multiplied by 4.
Question 2Aim for about 60 seconds
Look at the pattern in the table. Which line of the pattern starts with 30²?
Line
Calculation
1
3² = 1² + 4 × 2
2
4² = 2² + 4 × 3
3
5² = 3² + 4 × 4
Show the worked answer
Answer: C, 30² = 28² + 4 × 29
How to work it out
In every line the number squared on the right is 2 less than the one on the left, and the number multiplied by 4 is the one in between.
So 30² = 28² + 4 × 29.
Check: 900 = 784 + 116.
Why the other options are wrong
A (30² = 28² + 4 × 28): The number multiplied by 4 is 1 less than 30, so 29, not 28.
B (30² = 28² + 4 × 30): The number multiplied by 4 is the one between the two squared numbers, 29, not 30.
D (30² = 29² + 4 × 29): The number squared on the right is always 2 less than the one on the left, so 28, not 29.
E (30² = 28² + 2 × 29): Every line of the pattern multiplies by 4, not 2.
Question 3Aim for about 60 seconds
On the island of Tumbo the coins are pips, toks and muns: 6 pips make 1 tok, and 7 toks make 1 mun. What is 4 toks 1 pip take away 1 tok 5 pips? Give the answer with the fewest coins.
Show the worked answer
Answer: B, 2 toks 2 pips
How to work it out
There are not enough pips (1 is less than 5), so change 1 tok into 6 pips: 3 toks and 7 pips.
Then 7 − 5 = 2 pips and 3 − 1 = 2 toks.
So the answer is 2 toks 2 pips.
Why the other options are wrong
A (2 toks 6 pips): This changes a tok into 10 pips; here a tok is 6 pips.
C (3 toks 4 pips): This takes the smaller number of pips from the larger; you cannot take 5 from 1, so change a tok into 6 pips.
D (3 toks 2 pips): This changes a tok into pips but still counts that tok; there is one tok fewer.
E (2 toks 4 pips): This takes away a tok but then takes the smaller number of pips from the larger.
Question 4Aim for about 60 seconds
This calculation has the right digits, but some are in the wrong places: 22 × 6 = 73. Which calculation uses exactly the same digits, in the same pattern, and is correct?
Show the worked answer
Answer: D, 36 × 2 = 72
How to work it out
The digits are 2, 2, 3, 6 and 7.
The pattern is a 2-digit number times a one-digit number makes a 2-digit number.
Trying the digits in each place, only 36 × 2 = 72 is correct.
Why the other options are wrong
A (62 × 3 = 72): 62 × 3 makes 186, not 72, so this is not correct.
B (23 × 2 = 46): This calculation is correct, but it has a 4 where the given digits have a 7; it must use exactly the same digits.
C (22 × 6 = 73): This is the calculation as given: 22 × 6 is 132, not 73.
E (73 × 2 = 26): 73 × 2 makes 146, not 26, so this is not correct.
Question 5Aim for about 60 seconds
In this puzzle the number in each square is the sum (the two added) of the numbers in the two circles next to it. What number goes in the circle marked ?
Show the worked answer
Answer: B, 24
How to work it out
Adding the three squares counts every circle twice: 31 + 21 + 38 = 90, so the three circles add up to 45.
The square opposite the ? is 21, made of the other two circles, so the ? is 45 − 21 = 24.
Why the other options are wrong
A (14): This would be right for the bottom left circle; the ? is the top circle.
C (45): This is all three circles added together; take away the square opposite the ?.
D (48): This forgets to halve: the three squares added count every circle twice.
E (7): This would be right for the bottom right circle; the ? is the top circle.
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