Question 1

The HCF of two numbers is 12 and their LCM is 360. If one of the numbers is 60, what is the other number?

Accepted Answer

Step 1: Use the relation — Product of two numbers = HCF × LCM. Step 2: First number × Second number = 12 × 360 = 4320. Step 3: Second number = 4320 ÷ 60 = 72. Therefore, the other number is 72.

Question 2

Simplify: (144 ÷ 12) × 8 + 36 ÷ 4 - 15

Accepted Answer

Step 1: Solve division and multiplication from left to right: 144 ÷ 12 = 12. Step 2: 12 × 8 = 96. Step 3: 36 ÷ 4 = 9. Step 4: Now we have 96 + 9 - 15. Step 5: 96 + 9 = 105. Step 6: 105 - 15 = 90. Therefore, the answer is 90.

Question 3

Simplify: (∛64)² ÷ (√16)³ × (⁴√81)

Accepted Answer

Step 1: Evaluate each term separately.
(∛64)² = (4)² = 16  [since ∛64 = 4]
(√16)³ = (4)³ = 64  [since √16 = 4]
(⁴√81) = 3  [since 3⁴ = 81]

Step 2: Substitute into the expression:
16 ÷ 64 × 3

Step 3: Perform division and multiplication from left to right:
(16 ÷ 64) × 3 = (1/4) × 3 = 3/4

Therefore, the answer is 3/4 or 0.75

Question 4

A number series follows the pattern where the difference between consecutive terms increases by 2 each time. If the first term is 3 and the second term is 6, what is the 6th term?

Accepted Answer

Step 1: Term 1 = 3, Term 2 = 6. Difference d₁ = 6 − 3 = 3. Step 2: The next difference increases by 2, so d₂ = 3 + 2 = 5. Term 3 = 6 + 5 = 11. Step 3: d₃ = 5 + 2 = 7. Term 4 = 11 + 7 = 18. Step 4: d₄ = 7 + 2 = 9. Term 5 = 18 + 9 = 27. Step 5: d₅ = 9 + 2 = 11. Term 6 = 27 + 11 = 38. Therefore, the 6th term is 38.

Question 5

In a number series, the nth term is given by the formula: aₙ = n² + 2n − 1. What is the difference between the 5th term and the 3rd term?

Accepted Answer

Step 1: Calculate the 5th term: a₅ = 5² + 2(5) − 1 = 25 + 10 − 1 = 34. Step 2: Calculate the 3rd term: a₃ = 3² + 2(3) − 1 = 9 + 6 − 1 = 14. Step 3: Difference = a₅ − a₃ = 34 − 14 = 20. Therefore, the difference is 20.

Question 6

In a number series, the first term is 5 and each subsequent term is obtained by multiplying the previous term by 2 and then subtracting 3. What is the 5th term of this series?

Accepted Answer

Step 1: Term 1 = 5. Step 2: Term 2 = 5 × 2 − 3 = 10 − 3 = 7. Step 3: Term 3 = 7 × 2 − 3 = 14 − 3 = 11. Step 4: Term 4 = 11 × 2 − 3 = 22 − 3 = 19. Step 5: Term 5 = 19 × 2 − 3 = 38 − 3 = 35. Therefore, the 5th term is 35.

RRB Group D Number System Questions

RRB Group D Number System — Past Exam Questions

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