Question 1

If 1/3 of a number is 24, what is 1/4 of that number?

Accepted Answer

Step 1: If 1/3 of the number is 24, then the number = 24 × 3 = 72. Step 2: Find 1/4 of 72: 72 ÷ 4 = 18. Therefore, the answer is 18.

Question 2

A number is divisible by 3 if the sum of its digits is divisible by 3. Which of the following numbers is divisible by 3?

Accepted Answer

Step 1: Apply the divisibility rule for 3: sum of digits must be divisible by 3. Step 2: For 4527: 4 + 5 + 2 + 7 = 18, and 18 ÷ 3 = 6 (divisible by 3). Step 3: Verify: 4527 ÷ 3 = 1509 (exact). Therefore, 4527 is divisible by 3.

Question 3

If 0.75 is expressed as a fraction in lowest terms, what is the denominator?

Accepted Answer

Step 1: Write 0.75 as 75/100. Step 2: Find GCD of 75 and 100, which is 25. Step 3: Divide both by 25: 75÷25 = 3 and 100÷25 = 4. Step 4: The fraction in lowest terms is 3/4. Therefore, the denominator is 4.

Question 4

Express 2/5 as a decimal.

Accepted Answer

Step 1: Divide 2 by 5. Step 2: 2 ÷ 5 = 0.4. Therefore, the answer is 0.4.

Question 5

Calculate: 72 ÷ 8 + 15 − 3 × 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first. 72 ÷ 8 = 9 and 3 × 2 = 6. Step 2: Expression becomes 9 + 15 − 6. Step 3: Addition and Subtraction (left to right): 9 + 15 = 24, then 24 − 6 = 18. Therefore, the answer is 18.

Question 6

Approximate: 4.8 × 5.2 (to the nearest whole number)

Accepted Answer

Step 1: Round 4.8 to 5 and 5.2 to 5. Step 2: Multiply: 5 × 5 = 25. Alternatively, calculate exactly: 4.8 × 5.2 = 24.96, which rounds to 25. Therefore, the answer is 25.

Question 7

Evaluate: 100 − 20 ÷ 4 + 3 × 5

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first. 20 ÷ 4 = 5 and 3 × 5 = 15. Step 2: Expression becomes 100 − 5 + 15. Step 3: Subtraction and Addition (left to right): 100 − 5 = 95, then 95 + 15 = 110. Therefore, the answer is 110.

Question 8

What is 64 ÷ 4 ÷ 2 + 12 × 1 − 5?

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication (left to right). 64 ÷ 4 = 16, then 16 ÷ 2 = 8. Also, 12 × 1 = 12. Step 2: Expression becomes 8 + 12 − 5. Step 3: Addition and Subtraction (left to right): 8 + 12 = 20, then 20 − 5 = 15. Therefore, the answer is 15.

Question 9

Simplify: 50 + 30 ÷ 5 − 2 × 8

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first. 30 ÷ 5 = 6 and 2 × 8 = 16. Step 2: Expression becomes 50 + 6 − 16. Step 3: Addition and Subtraction (left to right): 50 + 6 = 56, then 56 − 16 = 40. Therefore, the answer is 40.

Question 10

Which of the following numbers is divisible by both 6 and 8?

Accepted Answer

Step 1: A number is divisible by 6 if it is divisible by both 2 and 3. Step 2: A number is divisible by 8 if its last three digits form a number divisible by 8. Step 3: For divisibility by both 6 and 8, the number must be divisible by LCM(6,8) = 24. Step 4: Check 264: 264 ÷ 24 = 11 (exact). Therefore, 264 is divisible by both 6 and 8.

Question 11

A number is divisible by 11 if the difference between the sum of digits in odd positions and the sum of digits in even positions is divisible by 11. Which of the following is divisible by 11?

Accepted Answer

Step 1: Apply the divisibility rule for 11. Step 2: For 5742: Odd positions (right to left): 2 + 7 = 9. Even positions: 4 + 5 = 9. Difference: 9 - 9 = 0, which is divisible by 11. Step 3: Verify: 5742 ÷ 11 = 522 (exact). Therefore, 5742 is divisible by 11.

Question 12

Which of the following numbers is NOT divisible by 4?

Accepted Answer

Step 1: A number is divisible by 4 if its last two digits form a number divisible by 4. Step 2: Check 3216: last two digits = 16; 16 ÷ 4 = 4 (divisible). Step 3: Check 4528: last two digits = 28; 28 ÷ 4 = 7 (divisible). Step 4: Check 5634: last two digits = 34; 34 ÷ 4 = 8.5 (NOT divisible). Step 5: Check 7840: last two digits = 40; 40 ÷ 4 = 10 (divisible). Therefore, 5634 is NOT divisible by 4.

Question 13

Simplify: 144 ÷ 12 + 8 × 3 − 5

Accepted Answer

Step 1: Apply BODMAS/PEMDAS. First, division and multiplication from left to right: 144 ÷ 12 = 12 and 8 × 3 = 24. Step 2: Now we have 12 + 24 − 5. Step 3: Addition and subtraction from left to right: 12 + 24 = 36, then 36 − 5 = 31. Therefore, the answer is 31.

Question 14

What is 0.6 × 0.5 equal to?

Accepted Answer

Step 1: Multiply 0.6 × 0.5 = 0.30. Step 2: Remove trailing zero: 0.30 = 0.3. Therefore, the answer is 0.3.

Question 15

Simplify: 48 ÷ 6 + 8 × 2 − 5

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 48 ÷ 6 = 8 and 8 × 2 = 16. Step 2: Now we have 8 + 16 − 5. Step 3: Addition and Subtraction (left to right): 8 + 16 = 24, then 24 − 5 = 19. Therefore, the answer is 19.

Question 16

What is the value of 36 ÷ 3 × 2 + 10 − 4?

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication (left to right). 36 ÷ 3 = 12, then 12 × 2 = 24. Step 2: Expression becomes 24 + 10 − 4. Step 3: Addition and Subtraction (left to right): 24 + 10 = 34, then 34 − 4 = 30. Therefore, the answer is 30.

Question 17

What is 35% of 240?

Accepted Answer

Step 1: To find 35% of 240, multiply 240 by 0.35 (or 35/100). Step 2: 240 × 0.35 = 84. Therefore, 35% of 240 is 84.

Question 18

Simplify: (18 + 12) ÷ 6 + 5 × 2

Accepted Answer

Step 1: Solve the bracket first: 18 + 12 = 30. Step 2: Now we have 30 ÷ 6 + 5 × 2. Step 3: Perform division and multiplication: 30 ÷ 6 = 5 and 5 × 2 = 10. Step 4: Add: 5 + 10 = 15. Therefore, the answer is 15.

Question 19

Simplify: √256 + √144 − √100

Accepted Answer

Step 1: Calculate each square root. √256 = 16, √144 = 12, √100 = 10. Step 2: Substitute: 16 + 12 − 10 = 28 − 10 = 18. Therefore, the answer is 18.

Question 20

A number when divided by 12 leaves remainder 7. What remainder will it leave when divided by 4?

Accepted Answer

Step 1: If a number N leaves remainder 7 when divided by 12, then N = 12k + 7 for some integer k. Step 2: Rewrite: N = 12k + 7 = 4(3k) + 7 = 4(3k + 1) + 3. Step 3: Therefore, N leaves remainder 3 when divided by 4.

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