Question 1

Calculate: 36 ÷ 9 × 5 + 10 − 8

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 36 ÷ 9 = 4, then 4 × 5 = 20. Step 2: Now we have 20 + 10 − 8. Step 3: Addition and Subtraction (left to right): 20 + 10 = 30, then 30 − 8 = 22.

Question 2

Solve: 2 × 15 − 18 ÷ 3 + 4

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 2 × 15 = 30 and 18 ÷ 3 = 6. Step 2: Now we have 30 − 6 + 4. Step 3: Subtraction and Addition (left to right): 30 − 6 = 24, then 24 + 4 = 28.

Question 3

What is the smallest 4-digit number that is divisible by both 8 and 12?

Accepted Answer

Step 1: Find LCM(8, 12). Prime factorization: 8 = 2³, 12 = 2² × 3. Step 2: LCM = 2³ × 3 = 24. Step 3: The smallest 4-digit number is 1000. Step 4: Divide 1000 by 24: 1000 ÷ 24 = 41.666... Step 5: Round up to 42. Step 6: Multiply: 42 × 24 = 1008. Step 7: Verify: 1008 ÷ 8 = 126 ✓, 1008 ÷ 12 = 84 ✓.

Question 4

A number is divisible by 9. Which of the following statements must be true?

Accepted Answer

Step 1: Divisibility rule for 9: sum of all digits must be divisible by 9. Step 2: If a number is divisible by 9, then the sum of its digits is divisible by 9. Step 3: Since 9 = 3 × 3, any number divisible by 9 is also divisible by 3 (because if digit sum is divisible by 9, it's also divisible by 3). Step 4: Therefore, the number must be divisible by 3.

Question 5

Which of the following numbers is NOT divisible by 3?

Accepted Answer

Step 1: Apply divisibility rule for 3: sum of all digits must be divisible by 3. Step 2: Check 4827: 4 + 8 + 2 + 7 = 21, divisible by 3. Check 5634: 5 + 6 + 3 + 4 = 18, divisible by 3. Check 7249: 7 + 2 + 4 + 9 = 22, NOT divisible by 3. Check 6351: 6 + 3 + 5 + 1 = 15, divisible by 3. Step 3: Therefore, 7249 is NOT divisible by 3.

Question 6

A number leaves remainder 2 when divided by 5. Which of the following could be the last digit of this number?

Accepted Answer

Step 1: If a number leaves remainder 2 when divided by 5, the last digit determines divisibility by 5. Step 2: Numbers ending in 0 or 5 are divisible by 5 (remainder 0). Numbers ending in 1 or 6 leave remainder 1. Numbers ending in 2 or 7 leave remainder 2. Numbers ending in 3 or 8 leave remainder 3. Numbers ending in 4 or 9 leave remainder 4. Step 3: Therefore, the last digit must be 2 or 7.

Question 7

A number is divisible by both 4 and 6. Which of the following must also divide this number?

Accepted Answer

Step 1: A number divisible by both 4 and 6 must be divisible by their LCM. Step 2: LCM(4, 6) = 12 (since 4 = 2², 6 = 2 × 3, LCM = 2² × 3 = 12). Step 3: Therefore, any number divisible by both 4 and 6 must be divisible by 12.

Question 8

Evaluate: 60 ÷ 5 + 3 × 4 − 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 60 ÷ 5 = 12 and 3 × 4 = 12. Step 2: Now we have 12 + 12 − 2. Step 3: Addition and Subtraction (left to right): 12 + 12 = 24, then 24 − 2 = 22.

Question 9

Which of the following numbers is divisible by 11?

Accepted Answer

Step 1: Apply divisibility rule for 11: alternating sum of digits (starting from right) must be divisible by 11. Step 2: For 5742: (2 - 4 + 7 - 5) = 0, which is divisible by 11. Step 3: Therefore, 5742 is divisible by 11.

Question 10

Simplify: 48 ÷ 6 + 12 × 2 − 5

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 48 ÷ 6 = 8 and 12 × 2 = 24. Step 2: Now we have 8 + 24 − 5. Step 3: Addition and Subtraction (left to right): 8 + 24 = 32, then 32 − 5 = 27.

Question 11

Evaluate: 100 − 20 × 3 + 15 ÷ 3

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 20 × 3 = 60 and 15 ÷ 3 = 5. Step 2: Now we have 100 − 60 + 5. Step 3: Subtraction and Addition (left to right): 100 − 60 = 40, then 40 + 5 = 45.

Question 12

Simplify: 5 + 8 ÷ 4 × 2 − 3

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 8 ÷ 4 = 2, then 2 × 2 = 4. Step 2: Now we have 5 + 4 − 3. Step 3: Addition and Subtraction (left to right): 5 + 4 = 9, then 9 − 3 = 6.

Question 13

A number is divisible by 15. Which of the following statements must be true?

Accepted Answer

Step 1: 15 = 3 × 5, where gcd(3,5) = 1. Step 2: If a number is divisible by 15, it must be divisible by both 3 and 5 (since they are coprime factors). Step 3: Divisibility by 3: sum of digits is divisible by 3. Divisibility by 5: last digit is 0 or 5. Step 4: Therefore, the number must be divisible by both 3 and 5, and its last digit must be 0 or 5.

Question 14

Simplify: 144 ÷ 12 + 8 × 3 − 5 + 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 144 ÷ 12 = 12 and 8 × 3 = 24. Step 2: Rewrite as 12 + 24 − 5 + 2. Step 3: Addition and Subtraction (left to right): 12 + 24 = 36, 36 − 5 = 31, 31 + 2 = 33. Therefore, answer is 33.

Question 15

Evaluate: 5 + 3 × 2² − 8 ÷ 4 + 1

Accepted Answer

Step 1: Apply BODMAS — Exponents first. 2² = 4. Step 2: Rewrite as 5 + 3 × 4 − 8 ÷ 4 + 1. Step 3: Multiplication and Division (left to right): 3 × 4 = 12 and 8 ÷ 4 = 2. Step 4: Rewrite as 5 + 12 − 2 + 1. Step 5: Addition and Subtraction (left to right): 5 + 12 = 17, 17 − 2 = 15, 15 + 1 = 16. Therefore, answer is 16.

Question 16

What is the value of 72 − 36 ÷ 6 + 4 × 5 − 10?

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 36 ÷ 6 = 6 and 4 × 5 = 20. Step 2: Rewrite as 72 − 6 + 20 − 10. Step 3: Addition and Subtraction (left to right): 72 − 6 = 66, 66 + 20 = 86, 86 − 10 = 76. Therefore, answer is 76.

Question 17

Simplify: 100 − 50 ÷ 5 × 2 + 8 − 3

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication (left to right). 50 ÷ 5 = 10, then 10 × 2 = 20. Step 2: Rewrite as 100 − 20 + 8 − 3. Step 3: Addition and Subtraction (left to right): 100 − 20 = 80, 80 + 8 = 88, 88 − 3 = 85. Therefore, answer is 85.

Question 18

Calculate: 8 × 9 − 24 ÷ 3 + 6 − 2 × 5

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 8 × 9 = 72, 24 ÷ 3 = 8, and 2 × 5 = 10. Step 2: Rewrite as 72 − 8 + 6 − 10. Step 3: Addition and Subtraction (left to right): 72 − 8 = 64, 64 + 6 = 70, 70 − 10 = 60. Therefore, answer is 60.

Question 19

Evaluate: 120 ÷ 4 + 15 × 2 − 18 ÷ 3 + 5

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 120 ÷ 4 = 30, 15 × 2 = 30, and 18 ÷ 3 = 6. Step 2: Rewrite as 30 + 30 − 6 + 5. Step 3: Addition and Subtraction (left to right): 30 + 30 = 60, 60 − 6 = 54, 54 + 5 = 59. Therefore, answer is 59.

Question 20

A five-digit number 3a7b2 is divisible by 4 and 11. What is the value of a + b?

Accepted Answer

Step 1: For divisibility by 4, the last two digits (b2) must form a number divisible by 4. So b2 ∈ {12, 32, 52, 72, 92}, meaning b ∈ {1, 3, 5, 7, 9}. Step 2: For divisibility by 11, (3 + 7 + 2) − (a + b) = 12 − a − b must be divisible by 11. Step 3: 12 − a − b ≡ 0 (mod 11), so a + b ≡ 1 (mod 11). Step 4: Since a, b are single digits and b is odd, testing: if a + b = 1, then a = 0, b = 1 (b2 = 12, divisible by 4 ✓). Step 5: Verify: 30712 ÷ 4 = 7678 ✓, and (3+7+2) − (0+1) = 11 ✓.

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