Lesson 19.1: Logical Thinking, Number Puzzles, and Deductive Reasoning
Solve mystery number riddles using deductive logic, elimination, and balance scale equivalence.
⏱️ Reading Time: 15 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Mathematical Reasoning and Puzzles
Detectives at a math mystery escape room examine a clue: 'I am a 3-digit number. My tens digit is double my hundreds digit. My ones digit is odd, and the sum of my digits is 10.' By testing possibilities, they discover the mystery code is 127 (1 + 2 + 7 = 10, tens is double hundreds).
💡 Core Mathematical Concepts: Logical Thinking & Deductive Puzzles
Focus areas: Deductive logic, elimination, mystery numbers, balance scales, equality.
| Concept / Term | Mathematical Definition | Everyday Example |
|---|---|---|
| Deductive Reasoning | Using step-by-step facts and logic to eliminate impossibilities and arrive at a true conclusion | If a number is even, eliminate all odd numbers |
| Number Clues & Riddles | Constraints about digits, sums, multiples, and place values that narrow down possibilities | 'Between 40 and 50, divisible by 7' → 42 or 49 |
| Balance Scale Principle | Both sides of a balanced scale are equal in value; whatever you add or remove on one side must be done to the other | 2 Apples = 1 Pineapple |
| Substitution Logic | Replacing an unknown object or symbol with an equivalent known value | If 1 circle = 5, then 3 circles = 15 |
🔍 Practical Classroom & Everyday Examples
Example 1: Clue-by-Clue Elimination
Read the most restrictive clue first to discard the largest number of possibilities immediately.
Example 2: Balance Scale Equations
If 2 cubes + 50g = 150g, subtract 50g from both sides: 2 cubes = 100g, so 1 cube = 50g.
⚠️ Watch Out! Common Mistakes to Avoid
Common Error: Rushing to pick the first number that matches only one clue
Correction: A mystery number must satisfy ALL clues simultaneously!
Common Error: Ignoring the balance equality sign
Correction: If a scale is tipped down on one side, it is NOT equal; the lower side is heavier.
🎯 Quick Self-Check Challenge
Mystery Riddle: 'I am an even number between 30 and 40. I am a multiple of 6. What number am I?'
Answer & Explanation:
Multiples of 6 are 6, 12, 18, 24, 30, 36, 42. The only multiple between 30 and 40 is 36.
🎯 Key Learning Takeaways
Master Mathematical Reasoning and Puzzles fundamentals.
📄 Printable Worksheets (5 Available)
Download ready-to-print PDFs for offline student practice with separate parent/teacher answer keys.
G3-M-CH19-WS05
A4 • 15 Qs
Mathematical Reasoning and Puzzles — Worksheet 5
Logic Clues, Balance Scales, Magic Squares & Rules (Treasure Island Vault)
G3-M-CH19-WS04
A4 • 15 Qs
Mathematical Reasoning and Puzzles — Worksheet 4
Logic Clues, Balance Scales, Magic Squares & Rules (Robotics Lab Logic)
G3-M-CH19-WS03
A4 • 15 Qs
Mathematical Reasoning and Puzzles — Worksheet 3
Logic Clues, Balance Scales, Magic Squares & Rules (Math Olympiad Arena)
G3-M-CH19-WS02
A4 • 15 Qs
Mathematical Reasoning and Puzzles — Worksheet 2
Logic Clues, Balance Scales, Magic Squares & Rules (Escape Room Quest)
G3-M-CH19-WS01
A4 • 15 Qs
Mathematical Reasoning and Puzzles — Worksheet 1
Logic Clues, Balance Scales, Magic Squares & Rules (Secret Code Academy)
✍️ Lesson Practice Questions (50 Questions)
Solve these real-world challenges online, test your understanding, and reveal instant step-by-step explanations.
1
Short Answer
Hard
2 Marks
In a farmyard puzzle, there are 10 heads and 28 legs among chickens (2 legs) and cows (4 legs). How many cows are there in the farmyard?
A
4 cows
B
6 cows
C
5 cows
D
3 cows
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 cows
Step-by-Step Explanation:
If all 10 were chickens, there would be 20 legs. 28 - 20 = 8 extra legs. Each cow adds 2 extra legs: 8 ÷ 2 = 4 cows (and 6 chickens).
2
Short Answer
Hard
2 Marks
I am thinking of a 2-digit number. It is an odd multiple of 7. The sum of its digits is 10. What is my number?
A
91
B
49
C
28
D
35
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 (9 + 1 = 10, odd). The number is 91.
3
Short Answer
Hard
2 Marks
If Scale 1 shows: 1 Triangle = 2 Squares, and Scale 2 shows: 1 Square = 3 Circles, how many Circles will balance 1 Triangle?
A
6 Circles
B
5 Circles
C
4 Circles
D
8 Circles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 Circles
Step-by-Step Explanation:
1 Triangle = 2 Squares = 2 × (3 Circles) = 6 Circles.
4
Short Answer
Hard
2 Marks
Why must the center number of a 3x3 magic square with digits 1 to 9 always be 5?
A
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
B
Because 5 is the largest digit
C
Because 5 is an even number
D
By random coincidence only
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
Step-by-Step Explanation:
The center cell participates in 4 equations, requiring the exact arithmetic mean of 1 to 9, which is 5.
5
Short Answer
Medium
1 Mark
Maya solves an input-output puzzle where Input 2 → 5 and Input 3 → 6. She announces the rule is '+ 3'. Then Input 4 gives 7, but for Input 5 the table shows 10. What did Maya overlook?
A
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
B
Maya's rule is completely impossible
C
Function tables can never have numbers above 9
D
Input 5 should give 15
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
Step-by-Step Explanation:
Always check that the rule works consistently for every single row in the table.
6
Short Answer
Medium
1 Mark
Oliver claims that 7, 7, 7 can never form a row in a magic square with sum 21 because magic squares must always have 3 different numbers. Is Oliver correct?
A
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
B
No, magic squares must always use the same number
C
No, 7+7+7 is not 21
D
Yes, because rows cannot add to 21
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
Step-by-Step Explanation:
In a standard mathematical magic square, all entries must be distinct unique numbers.
7
Fill in the Blanks
Medium
1 Mark
Find the missing input: The function rule is 'Subtract 7, then multiply by 2'. The output is 16. What was the input?
A
15
B
14
C
16
D
18
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
Work backwards: 16 ÷ 2 = 8. 8 + 7 = 15.
8
Fill in the Blanks
Medium
1 Mark
A magic square row contains the numbers [ 8 ], [ ? ], and [ 6 ]. If the magic sum is 24, what number is missing in the middle?
A
10
B
12
C
9
D
14
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
10
Step-by-Step Explanation:
8 + 6 = 14. 24 - 14 = 10.
9
Short Answer
Medium
1 Mark
An input-output conveyor machine converts: Input 2 → 8, Input 4 → 16, Input 6 → 24. What will the machine output when the input is 9?
A
36
B
32
C
40
D
28
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
36
Step-by-Step Explanation:
The rule is 'Multiply by 4'. 9 × 4 = 36.
10
Short Answer
Medium
1 Mark
A lock combination riddle: 'I am a 3-digit number. My hundreds digit is 3. My tens digit is twice my hundreds digit. My ones digit is 1 less than my tens digit.' What is the code?
A
365
B
364
C
354
D
342
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
365
Step-by-Step Explanation:
Hundreds = 3. Tens = 3 × 2 = 6. Ones = 6 - 1 = 5. The number is 365.
11
Short Answer
Medium
1 Mark
At the Treasure Island Vault, a balance scale shows that 2 identical brass weights balance a 50g weight and a 30g weight. What is the weight of one brass weight?
A
40g
B
35g
C
50g
D
80g
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
40g
Step-by-Step Explanation:
50g + 30g = 80g. 80g ÷ 2 = 40g each.
12
Multiple Choice
Easy
1 Mark
If 1 Circle + 1 Square = 20 and 1 Circle = 14, what is the value of 1 Square?
A
6
B
7
C
5
D
8
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6
Step-by-Step Explanation:
20 - 14 = 6.
13
Multiple Choice
Easy
1 Mark
If 1 Star + 1 Star + 1 Star = 27, what is the value of 1 Star?
A
9
B
8
C
7
D
6
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
9
Step-by-Step Explanation:
27 ÷ 3 = 9.
14
Multiple Choice
Easy
1 Mark
A function machine rule is: 'Multiply input by 4 and add 3'. What is the output for input 5?
A
23
B
20
C
25
D
27
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
23
Step-by-Step Explanation:
(5 × 4) + 3 = 20 + 3 = 23.
15
Multiple Choice
Easy
1 Mark
In a 3x3 magic square using digits 1 to 9, what is the sum of any row, column, or diagonal?
A
15
B
12
C
18
D
20
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
The magic sum of a standard 1-9 3x3 square is 15.
16
Short Answer
Hard
2 Marks
In a farmyard puzzle, there are 10 heads and 28 legs among chickens (2 legs) and cows (4 legs). How many cows are there in the farmyard?
A
4 cows
B
6 cows
C
5 cows
D
3 cows
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 cows
Step-by-Step Explanation:
If all 10 were chickens, there would be 20 legs. 28 - 20 = 8 extra legs. Each cow adds 2 extra legs: 8 ÷ 2 = 4 cows (and 6 chickens).
17
Short Answer
Hard
2 Marks
I am thinking of a 2-digit number. It is an odd multiple of 7. The sum of its digits is 10. What is my number?
A
91
B
49
C
28
D
35
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 (9 + 1 = 10, odd). The number is 91.
18
Short Answer
Hard
2 Marks
If Scale 1 shows: 1 Triangle = 2 Squares, and Scale 2 shows: 1 Square = 3 Circles, how many Circles will balance 1 Triangle?
A
6 Circles
B
5 Circles
C
4 Circles
D
8 Circles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 Circles
Step-by-Step Explanation:
1 Triangle = 2 Squares = 2 × (3 Circles) = 6 Circles.
19
Short Answer
Hard
2 Marks
Why must the center number of a 3x3 magic square with digits 1 to 9 always be 5?
A
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
B
Because 5 is the largest digit
C
Because 5 is an even number
D
By random coincidence only
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
Step-by-Step Explanation:
The center cell participates in 4 equations, requiring the exact arithmetic mean of 1 to 9, which is 5.
20
Short Answer
Medium
1 Mark
Maya solves an input-output puzzle where Input 2 → 5 and Input 3 → 6. She announces the rule is '+ 3'. Then Input 4 gives 7, but for Input 5 the table shows 10. What did Maya overlook?
A
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
B
Maya's rule is completely impossible
C
Function tables can never have numbers above 9
D
Input 5 should give 15
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
Step-by-Step Explanation:
Always check that the rule works consistently for every single row in the table.
21
Short Answer
Medium
1 Mark
Oliver claims that 7, 7, 7 can never form a row in a magic square with sum 21 because magic squares must always have 3 different numbers. Is Oliver correct?
A
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
B
No, magic squares must always use the same number
C
No, 7+7+7 is not 21
D
Yes, because rows cannot add to 21
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
Step-by-Step Explanation:
In a standard mathematical magic square, all entries must be distinct unique numbers.
22
Fill in the Blanks
Medium
1 Mark
Find the missing input: The function rule is 'Subtract 7, then multiply by 2'. The output is 16. What was the input?
A
15
B
14
C
16
D
18
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
Work backwards: 16 ÷ 2 = 8. 8 + 7 = 15.
23
Fill in the Blanks
Medium
1 Mark
A magic square row contains the numbers [ 8 ], [ ? ], and [ 6 ]. If the magic sum is 18, what number is missing in the middle?
A
4
B
6
C
3
D
8
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4
Step-by-Step Explanation:
8 + 6 = 14. 18 - 14 = 4.
24
Short Answer
Medium
1 Mark
An input-output conveyor machine converts: Input 2 → 8, Input 4 → 16, Input 6 → 24. What will the machine output when the input is 9?
A
36
B
32
C
40
D
28
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
36
Step-by-Step Explanation:
The rule is 'Multiply by 4'. 9 × 4 = 36.
25
Short Answer
Medium
1 Mark
A lock combination riddle: 'I am a 3-digit number. My hundreds digit is 3. My tens digit is twice my hundreds digit. My ones digit is 1 less than my tens digit.' What is the code?
A
365
B
364
C
354
D
342
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
365
Step-by-Step Explanation:
Hundreds = 3. Tens = 3 × 2 = 6. Ones = 6 - 1 = 5. The number is 365.
26
Short Answer
Medium
1 Mark
At the Robotics Lab Logic, a balance scale shows that 2 identical brass weights balance a 50g weight and a 30g weight. What is the weight of one brass weight?
A
40g
B
35g
C
50g
D
80g
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
40g
Step-by-Step Explanation:
50g + 30g = 80g. 80g ÷ 2 = 40g each.
27
Multiple Choice
Easy
1 Mark
If 1 Circle + 1 Square = 20 and 1 Circle = 14, what is the value of 1 Square?
A
6
B
7
C
5
D
8
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6
Step-by-Step Explanation:
20 - 14 = 6.
28
Multiple Choice
Easy
1 Mark
If 1 Star + 1 Star + 1 Star = 27, what is the value of 1 Star?
A
9
B
8
C
7
D
6
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
9
Step-by-Step Explanation:
27 ÷ 3 = 9.
29
Multiple Choice
Easy
1 Mark
A function machine rule is: 'Multiply input by 4 and add 3'. What is the output for input 5?
A
23
B
20
C
25
D
27
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
23
Step-by-Step Explanation:
(5 × 4) + 3 = 20 + 3 = 23.
30
Multiple Choice
Easy
1 Mark
In a 3x3 magic square using digits 1 to 9, what is the sum of any row, column, or diagonal?
A
15
B
12
C
18
D
20
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
The magic sum of a standard 1-9 3x3 square is 15.
31
Short Answer
Hard
2 Marks
In a farmyard puzzle, there are 10 heads and 28 legs among chickens (2 legs) and cows (4 legs). How many cows are there in the farmyard?
A
4 cows
B
6 cows
C
5 cows
D
3 cows
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 cows
Step-by-Step Explanation:
If all 10 were chickens, there would be 20 legs. 28 - 20 = 8 extra legs. Each cow adds 2 extra legs: 8 ÷ 2 = 4 cows (and 6 chickens).
32
Short Answer
Hard
2 Marks
I am thinking of a 2-digit number. It is an odd multiple of 7. The sum of its digits is 10. What is my number?
A
91
B
49
C
28
D
35
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 (9 + 1 = 10, odd). The number is 91.
33
Short Answer
Hard
2 Marks
If Scale 1 shows: 1 Triangle = 2 Squares, and Scale 2 shows: 1 Square = 3 Circles, how many Circles will balance 1 Triangle?
A
6 Circles
B
5 Circles
C
4 Circles
D
8 Circles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 Circles
Step-by-Step Explanation:
1 Triangle = 2 Squares = 2 × (3 Circles) = 6 Circles.
34
Short Answer
Hard
2 Marks
Why must the center number of a 3x3 magic square with digits 1 to 9 always be 5?
A
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
B
Because 5 is the largest digit
C
Because 5 is an even number
D
By random coincidence only
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
Step-by-Step Explanation:
The center cell participates in 4 equations, requiring the exact arithmetic mean of 1 to 9, which is 5.
35
Short Answer
Medium
1 Mark
Maya solves an input-output puzzle where Input 2 → 5 and Input 3 → 6. She announces the rule is '+ 3'. Then Input 4 gives 7, but for Input 5 the table shows 10. What did Maya overlook?
A
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
B
Maya's rule is completely impossible
C
Function tables can never have numbers above 9
D
Input 5 should give 15
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
Step-by-Step Explanation:
Always check that the rule works consistently for every single row in the table.
36
Short Answer
Medium
1 Mark
Oliver claims that 7, 7, 7 can never form a row in a magic square with sum 21 because magic squares must always have 3 different numbers. Is Oliver correct?
A
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
B
No, magic squares must always use the same number
C
No, 7+7+7 is not 21
D
Yes, because rows cannot add to 21
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Yes, standard magic squares require all numbers in the grid to be distinct (unique)
Step-by-Step Explanation:
In a standard mathematical magic square, all entries must be distinct unique numbers.
37
Fill in the Blanks
Medium
1 Mark
Find the missing input: The function rule is 'Subtract 7, then multiply by 2'. The output is 16. What was the input?
A
15
B
14
C
16
D
18
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
Work backwards: 16 ÷ 2 = 8. 8 + 7 = 15.
38
Fill in the Blanks
Medium
1 Mark
A magic square row contains the numbers [ 8 ], [ ? ], and [ 6 ]. If the magic sum is 30, what number is missing in the middle?
A
16
B
18
C
15
D
20
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
16
Step-by-Step Explanation:
8 + 6 = 14. 30 - 14 = 16.
39
Short Answer
Medium
1 Mark
An input-output conveyor machine converts: Input 2 → 8, Input 4 → 16, Input 6 → 24. What will the machine output when the input is 9?
A
36
B
32
C
40
D
28
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
36
Step-by-Step Explanation:
The rule is 'Multiply by 4'. 9 × 4 = 36.
40
Short Answer
Medium
1 Mark
A lock combination riddle: 'I am a 3-digit number. My hundreds digit is 3. My tens digit is twice my hundreds digit. My ones digit is 1 less than my tens digit.' What is the code?
A
365
B
364
C
354
D
342
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
365
Step-by-Step Explanation:
Hundreds = 3. Tens = 3 × 2 = 6. Ones = 6 - 1 = 5. The number is 365.
41
Short Answer
Medium
1 Mark
At the Math Olympiad Arena, a balance scale shows that 2 identical brass weights balance a 50g weight and a 30g weight. What is the weight of one brass weight?
A
40g
B
35g
C
50g
D
80g
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
40g
Step-by-Step Explanation:
50g + 30g = 80g. 80g ÷ 2 = 40g each.
42
Multiple Choice
Easy
1 Mark
If 1 Circle + 1 Square = 20 and 1 Circle = 14, what is the value of 1 Square?
A
6
B
7
C
5
D
8
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6
Step-by-Step Explanation:
20 - 14 = 6.
43
Multiple Choice
Easy
1 Mark
If 1 Star + 1 Star + 1 Star = 27, what is the value of 1 Star?
A
9
B
8
C
7
D
6
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
9
Step-by-Step Explanation:
27 ÷ 3 = 9.
44
Multiple Choice
Easy
1 Mark
A function machine rule is: 'Multiply input by 4 and add 3'. What is the output for input 5?
A
23
B
20
C
25
D
27
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
23
Step-by-Step Explanation:
(5 × 4) + 3 = 20 + 3 = 23.
45
Multiple Choice
Easy
1 Mark
In a 3x3 magic square using digits 1 to 9, what is the sum of any row, column, or diagonal?
A
15
B
12
C
18
D
20
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
The magic sum of a standard 1-9 3x3 square is 15.
46
Short Answer
Hard
2 Marks
In a farmyard puzzle, there are 10 heads and 28 legs among chickens (2 legs) and cows (4 legs). How many cows are there in the farmyard?
A
4 cows
B
6 cows
C
5 cows
D
3 cows
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 cows
Step-by-Step Explanation:
If all 10 were chickens, there would be 20 legs. 28 - 20 = 8 extra legs. Each cow adds 2 extra legs: 8 ÷ 2 = 4 cows (and 6 chickens).
47
Short Answer
Hard
2 Marks
I am thinking of a 2-digit number. It is an odd multiple of 7. The sum of its digits is 10. What is my number?
A
91
B
49
C
28
D
35
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 (9 + 1 = 10, odd). The number is 91.
48
Short Answer
Hard
2 Marks
If Scale 1 shows: 1 Triangle = 2 Squares, and Scale 2 shows: 1 Square = 3 Circles, how many Circles will balance 1 Triangle?
A
6 Circles
B
5 Circles
C
4 Circles
D
8 Circles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 Circles
Step-by-Step Explanation:
1 Triangle = 2 Squares = 2 × (3 Circles) = 6 Circles.
49
Short Answer
Hard
2 Marks
Why must the center number of a 3x3 magic square with digits 1 to 9 always be 5?
A
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
B
Because 5 is the largest digit
C
Because 5 is an even number
D
By random coincidence only
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The center cell belongs to 4 lines (1 row, 1 column, 2 diagonals) and 5 is the exact median/average of numbers 1 to 9
Step-by-Step Explanation:
The center cell participates in 4 equations, requiring the exact arithmetic mean of 1 to 9, which is 5.
50
Short Answer
Medium
1 Mark
Maya solves an input-output puzzle where Input 2 → 5 and Input 3 → 6. She announces the rule is '+ 3'. Then Input 4 gives 7, but for Input 5 the table shows 10. What did Maya overlook?
A
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
B
Maya's rule is completely impossible
C
Function tables can never have numbers above 9
D
Input 5 should give 15
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The inputs might not be consecutive, or the rule might not apply to non-consecutive jumps without checking the input step size
Step-by-Step Explanation:
Always check that the rule works consistently for every single row in the table.