Question 1

Find the LCM of 12, 18, and 24.

Accepted Answer

Step 1: Prime factorize each number. 12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. Step 2: LCM = product of each prime factor with the highest power = 2³ × 3² = 8 × 9 = 72. Therefore, answer is 72.

Question 2

Simplify: (8 × 15) ÷ (6 × 4) + 12

Accepted Answer

Step 1: Calculate numerator: 8 × 15 = 120. Step 2: Calculate denominator: 6 × 4 = 24. Step 3: Divide: 120 ÷ 24 = 5. Step 4: Add: 5 + 12 = 17. Therefore, the answer is 17.

Question 3

What is the missing term in the series: 100, 90, 81, 73, 66, ?

Accepted Answer

Step 1: Calculate the differences between consecutive terms: 100−90=10, 90−81=9, 81−73=8, 73−66=7. Step 2: The differences form the sequence 10, 9, 8, 7 (decreasing by 1 each time). Step 3: The next difference should be 6. Step 4: 66 − 6 = 60. Therefore, the missing term is 60.

Question 4

What is the value of √256 + ∛27 − √100?

Accepted Answer

Step 1: Calculate √256 = 16 (since 16 × 16 = 256). Step 2: Calculate ∛27 = 3 (since 3 × 3 × 3 = 27). Step 3: Calculate √100 = 10 (since 10 × 10 = 100). Step 4: Combine: 16 + 3 − 10 = 9. Therefore, the answer is 9.

Question 5

Simplify: (3^4)^2 ÷ 3^5

Accepted Answer

Step 1: Using the power rule, (3^4)^2 = 3^(4×2) = 3^8. Step 2: 3^8 ÷ 3^5 = 3^(8-5) = 3^3 = 27.

Question 6

A number is divisible by both 4 and 9. Which of the following must also divide this number?

Accepted Answer

Step 1: A number divisible by both 4 and 9 must be divisible by their LCM. Step 2: Since 4 = 2² and 9 = 3², and gcd(4,9) = 1, we have LCM(4,9) = 4 × 9 = 36. Step 3: Therefore, any number divisible by both 4 and 9 must be divisible by 36. Step 4: Checking the options: 36 divides the number, so 12 (a factor of 36) also divides it. The answer is 12.

Question 7

If 3/5 of a number is 45, what is the number?

Accepted Answer

Step 1: Let the number be x. Step 2: Set up equation: (3/5) × x = 45. Step 3: Multiply both sides by 5/3: x = 45 × (5/3). Step 4: Calculate: x = (45 × 5) ÷ 3 = 225 ÷ 3 = 75. Therefore, the answer is 75.

Question 8

Simplify: (8 × 9) ÷ (6 ÷ 2) + 5

Accepted Answer

Step 1: Solve the numerator: 8 × 9 = 72. Step 2: Solve the denominator: 6 ÷ 2 = 3. Step 3: Divide: 72 ÷ 3 = 24. Step 4: Add 5: 24 + 5 = 29. Therefore, the answer is 29.

Question 9

What is the missing number in the series: 5, 10, 20, 40, ?, 160?

Accepted Answer

Step 1: Observe the pattern between consecutive terms. Step 2: 10÷5 = 2, 20÷10 = 2, 40÷20 = 2. Step 3: This is a geometric series with common ratio 2. Step 4: The missing term = 40 × 2 = 80. Step 5: Verify: 80 × 2 = 160 ✓. Therefore, the answer is 80.

Question 10

What is the next number in the series: 1, 4, 9, 16, 25, ?

Accepted Answer

Step 1: Recognize that each term is a perfect square: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25. Step 2: The series consists of consecutive perfect squares. Step 3: The next term should be 6² = 36. Therefore, the answer is 36.

Question 11

Find the next term in the series: 2, 5, 10, 17, 26, ?

Accepted Answer

Step 1: Find the differences between consecutive terms: 5-2=3, 10-5=5, 17-10=7, 26-17=9. Step 2: The first differences are 3, 5, 7, 9 (odd numbers increasing by 2). Step 3: The next first difference should be 11. Step 4: Therefore, the next term = 26 + 11 = 37. Therefore, the answer is 37.

Question 12

Find the missing number in the series: 5, 10, 20, 40, 80, ?

Accepted Answer

Step 1: Identify the pattern by examining the ratio between consecutive terms. Step 2: 10÷5 = 2, 20÷10 = 2, 40÷20 = 2, 80÷40 = 2. Step 3: Each term is multiplied by 2 to get the next term. Step 4: 80 × 2 = 160. Therefore, the missing number is 160.

Question 13

Simplify: (144 ÷ 12) × 5 + 36 ÷ 6 − 8

Accepted Answer

Step 1: Solve division first: 144 ÷ 12 = 12 and 36 ÷ 6 = 6. Step 2: Substitute: 12 × 5 + 6 − 8. Step 3: Multiply: 12 × 5 = 60. Step 4: Add and subtract left to right: 60 + 6 = 66, then 66 − 8 = 58. Therefore, the answer is 58.

Question 14

Which of the following numbers is divisible by 8?

Accepted Answer

Step 1: Divisibility rule for 8 — check if the last 3 digits of the number are divisible by 8. Step 2: Check each option: (a) 624: 624 ÷ 8 = 78 ✓. (b) 732: 732 ÷ 8 = 91.5 ✗. (c) 514: 514 ÷ 8 = 64.25 ✗. (d) 922: 922 ÷ 8 = 115.25 ✗. Therefore, 624 is divisible by 8.

Question 15

Find the missing number: 3, 9, 27, 81, 243, ?

Accepted Answer

Step 1: Observe the relationship between consecutive terms. Step 2: 9÷3 = 3, 27÷9 = 3, 81÷27 = 3, 243÷81 = 3. Step 3: Each term is multiplied by 3 to get the next term (geometric progression with r = 3). Step 4: 243 × 3 = 729. Therefore, the missing number is 729.

Question 16

What is the value of √256 + √144 − √100?

Accepted Answer

Step 1: Calculate √256 = 16 (since 16 × 16 = 256). Step 2: Calculate √144 = 12 (since 12 × 12 = 144). Step 3: Calculate √100 = 10 (since 10 × 10 = 100). Step 4: Now compute 16 + 12 − 10 = 28 − 10 = 18. Therefore, the answer is 18.

Question 17

Simplify: (7² − 5²) ÷ (7 + 5)

Accepted Answer

Step 1: Calculate 7² = 49. Step 2: Calculate 5² = 25. Step 3: Subtract: 49 − 25 = 24. Step 4: Calculate denominator: 7 + 5 = 12. Step 5: Divide: 24 ÷ 12 = 2. Therefore, the answer is 2. [Note: This uses the difference of squares formula: a² − b² = (a + b)(a − b), so (49 − 25)/(7 + 5) = (7 − 5)(7 + 5)/(7 + 5) = 7 − 5 = 2]

Question 18

Evaluate: √(144) + √(64) - √(36)

Accepted Answer

Step 1: √144 = 12. Step 2: √64 = 8. Step 3: √36 = 6. Step 4: 12 + 8 - 6 = 14.

Question 19

What is the next term in the series: 2, 6, 12, 20, 30, ?

Accepted Answer

Step 1: Find the differences between consecutive terms: 6−2=4, 12−6=6, 20−12=8, 30−20=10. Step 2: The first differences form the series 4, 6, 8, 10 (increasing by 2 each time). Step 3: The next first difference should be 12. Step 4: 30 + 12 = 42. Therefore, the next term is 42.

Question 20

Find the missing number in the series: 2, 6, 18, 54, ?

Accepted Answer

Step 1: Identify the pattern. Each term is multiplied by 3 to get the next term. Step 2: 2 × 3 = 6, 6 × 3 = 18, 18 × 3 = 54, 54 × 3 = 162. Therefore, the missing number is 162.

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