Question 1

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.

Question 2

Convert 0.625 to a fraction in simplest form.

Accepted Answer

Step 1: Write 0.625 as 625/1000. Step 2: Find GCD(625, 1000). 625 = 5⁴ and 1000 = 2³ × 5³, so GCD = 5³ = 125. Step 3: Divide both numerator and denominator by 125: 625÷125 = 5 and 1000÷125 = 8. Step 4: Answer is 5/8.

Question 3

Solve: 50 − 15 + 20 ÷ 4 × 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 20 ÷ 4 = 5, then 5 × 2 = 10. Step 2: Expression becomes 50 − 15 + 10. Step 3: Subtraction and Addition (left to right): 50 − 15 = 35, then 35 + 10 = 45.

Question 4

Evaluate: 72 ÷ 8 + 6 × 3 − 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first. 72 ÷ 8 = 9 and 6 × 3 = 18. Step 2: Expression becomes 9 + 18 − 2. Step 3: Addition and Subtraction (left to right): 9 + 18 = 27, then 27 − 2 = 25.

Question 5

If 2/5 of a number is 24, what is the number?

Accepted Answer

Step 1: Let the number be x. Step 2: Set up equation: (2/5) × x = 24. Step 3: Multiply both sides by 5/2: x = 24 × (5/2) = (24 × 5)/2 = 120/2 = 60. Step 4: Verify: (2/5) × 60 = 24 ✓

Question 6

Which digit should replace * in 5*3 to make it divisible by 3?

Accepted Answer

Step 1: A number is divisible by 3 if the sum of its digits is divisible by 3. Step 2: Sum of known digits = 5 + 3 = 8. Step 3: We need 8 + * to be divisible by 3. Step 4: If * = 1, sum = 9, which is divisible by 3. Therefore, * = 1.

Question 7

Which of the following numbers is divisible by both 4 and 6?

Accepted Answer

Step 1: A number divisible by both 4 and 6 must be divisible by their LCM. Step 2: LCM(4, 6) = 12. Step 3: Check 144: 144 ÷ 12 = 12 (exactly divisible). Therefore, 144 is the answer.

Question 8

A number when divided by 9 leaves remainder 0. Which of the following is definitely true about this number?

Accepted Answer

Step 1: If a number is divisible by 9 (remainder 0), then by the divisibility rule of 9, the sum of its digits must be divisible by 9. Step 2: A number divisible by 9 is also divisible by 3 (since 9 = 3²). Step 3: Therefore, the number must be divisible by 3. The answer is that the number is divisible by 3.

Question 9

A number is divisible by 11 if the difference between the sum of digits at odd positions and the sum of digits at even positions is divisible by 11. Using this rule, which number is divisible by 11?

Accepted Answer

Step 1: For divisibility by 11, calculate (sum of odd-position digits) − (sum of even-position digits). Step 2: Test 4587: Odd positions (1st, 3rd) = 4 + 8 = 12. Even positions (2nd, 4th) = 5 + 7 = 12. Difference = 12 − 12 = 0. Step 3: 0 is divisible by 11. Therefore, 4587 is divisible by 11.

Question 10

Which of the following numbers is NOT divisible by 8?

Accepted Answer

Step 1: A number is divisible by 8 if its last three digits form a number divisible by 8. Step 2: Test 2456: Last three digits = 456. 456 ÷ 8 = 57 (exactly divisible). Step 3: Test 3264: Last three digits = 264. 264 ÷ 8 = 33 (exactly divisible). Step 4: Test 5432: Last three digits = 432. 432 ÷ 8 = 54 (exactly divisible). Step 5: Test 6218: Last three digits = 218. 218 ÷ 8 = 27.25 (NOT exactly divisible). Therefore, 6218 is NOT divisible by 8.

Question 11

A number is divisible by 6 if it is divisible by both 2 and 3. Which of the following is divisible by 6?

Accepted Answer

Step 1: For divisibility by 6, the number must be even (divisible by 2) AND the sum of digits must be divisible by 3. Step 2: Test 318: It is even (ends in 8). Sum of digits = 3 + 1 + 8 = 12, which is divisible by 3. Step 3: Since 318 is divisible by both 2 and 3, it is divisible by 6. Therefore, 318 is the answer.

Question 12

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 13

Simplify: 2 + 8 × 3 − 10 ÷ 2

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 8 × 3 = 24 and 10 ÷ 2 = 5. Step 2: Expression becomes 2 + 24 − 5. Step 3: Addition and Subtraction (left to right): 2 + 24 = 26, then 26 − 5 = 21.

Question 14

Calculate: 36 ÷ 3 × 2 + 4 − 1

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 36 ÷ 3 = 12, then 12 × 2 = 24. Step 2: Expression becomes 24 + 4 − 1. Step 3: Addition and Subtraction (left to right): 24 + 4 = 28, then 28 − 1 = 27.

Question 15

How many numbers between 100 and 300 are divisible by 7 but NOT divisible by 3?

Accepted Answer

Step 1: Count multiples of 7 between 100 and 300. Smallest: 105 (7×15), Largest: 294 (7×42). Count = 42-15+1 = 28. Step 2: Count multiples of both 7 and 3 (i.e., multiples of 21) between 100 and 300. Smallest: 105 (21×5), Largest: 294 (21×14). Count = 14-5+1 = 10. Step 3: Numbers divisible by 7 but NOT by 3 = 28 - 10 = 18.

Question 16

A number when divided by 11 leaves remainder 7. What is the remainder when the square of this number is divided by 11?

Accepted Answer

Step 1: Let the number be N. Given: N ≡ 7 (mod 11). Step 2: We need N² (mod 11). Step 3: N² ≡ 7² ≡ 49 (mod 11). Step 4: 49 = 11×4 + 5, so 49 ≡ 5 (mod 11). Therefore, remainder is 5.

Question 17

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 18

Evaluate: 5 + 3 × 2² − 8 ÷ 4 + 1

Accepted Answer

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

Question 19

Simplify: 100 − 20 × 3 + 15 ÷ 5 − 2

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right): 20 × 3 = 60 and 15 ÷ 5 = 3. Step 2: Rewrite as 100 − 60 + 3 − 2. Step 3: Subtraction and Addition (left to right): 100 − 60 = 40, 40 + 3 = 43, 43 − 2 = 41. Therefore, answer is 41.

Question 20

Calculate: 6 × 8 − 24 ÷ 3 + 10 − 5 × 2

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right): 6 × 8 = 48, 24 ÷ 3 = 8, and 5 × 2 = 10. Step 2: Rewrite as 48 − 8 + 10 − 10. Step 3: Addition and Subtraction (left to right): 48 − 8 = 40, 40 + 10 = 50, 50 − 10 = 40. Therefore, answer is 40.

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