Question 1

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 2

Evaluate: 60 ÷ 5 + 4 × 3 − 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first. 60 ÷ 5 = 12 and 4 × 3 = 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 3

Calculate: 36 ÷ 3 × 2 + 10 − 4

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 36 ÷ 3 = 12, then 12 × 2 = 24. Step 2: Now we have 24 + 10 − 4. Step 3: Addition and Subtraction (left to right): 24 + 10 = 34, then 34 − 4 = 30.

Question 4

Solve: 5 × 6 − 8 ÷ 2 + 3

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first. 5 × 6 = 30 and 8 ÷ 2 = 4. Step 2: Now we have 30 − 4 + 3. Step 3: Subtraction and Addition (left to right): 30 − 4 = 26, then 26 + 3 = 29.

Question 5

Rationalize: 1/(√7 − √2)

Accepted Answer

Step 1: Multiply numerator and denominator by the conjugate (√7 + √2). Step 2: Numerator becomes √7 + √2. Step 3: Denominator becomes (√7)² − (√2)² = 7 − 2 = 5. Step 4: Result is (√7 + √2)/5.

Question 6

If 2^(x+2) = 64, find the value of x.

Accepted Answer

Step 1: Rewrite 64 as a power of 2: 64 = 2⁶. Step 2: Set exponents equal: 2^(x+2) = 2⁶, so x + 2 = 6. Step 3: Solve: x = 4.

Question 7

Simplify: (3⁴ × 3⁻²) ÷ 3¹

Accepted Answer

Step 1: Apply product rule: 3⁴ × 3⁻² = 3^(4−2) = 3². Step 2: Apply quotient rule: 3² ÷ 3¹ = 3^(2−1) = 3¹ = 3.

Question 8

If 5^(2x) = 125, find x.

Accepted Answer

Step 1: Express 125 as a power of 5: 125 = 5³. Step 2: Set exponents equal: 5^(2x) = 5³, so 2x = 3. Step 3: Solve: x = 3/2 = 1.5.

Question 9

Simplify: ∛(27) + ∜(16) − √(4)

Accepted Answer

Step 1: ∛(27) = ∛(3³) = 3. Step 2: ∜(16) = ∜(2⁴) = 2. Step 3: √(4) = 2. Step 4: Add and subtract: 3 + 2 − 2 = 3.

Question 10

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: Now we have 100 − 5 + 15. Step 3: Subtraction and Addition (left to right): 100 − 5 = 95, then 95 + 15 = 110.

Question 11

Simplify: 2 + 8 × 3 − 12 ÷ 4

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 8 × 3 = 24 and 12 ÷ 4 = 3. Step 2: Now we have 2 + 24 − 3. Step 3: Addition and Subtraction (left to right): 2 + 24 = 26, then 26 − 3 = 23.

Question 12

Simplify: (16^(3/4) × 8^(2/3)) / 4^(1/2)

Accepted Answer

Step 1: Convert to prime base 2: 16 = 2⁴, 8 = 2³, 4 = 2². Step 2: Rewrite: (2⁴)^(3/4) × (2³)^(2/3) / (2²)^(1/2) = 2³ × 2² / 2¹. Step 3: Combine exponents: 2^(3+2−1) = 2⁴ = 16.

Question 13

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, then 36 − 5 = 31, then 31 + 2 = 33. Therefore, answer is 33.

Question 14

Evaluate: 5 + 3 × 4 − 2 ÷ 2 + 6

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right): 3 × 4 = 12 and 2 ÷ 2 = 1. Step 2: Rewrite as 5 + 12 − 1 + 6. Step 3: Addition and Subtraction (left to right): 5 + 12 = 17, then 17 − 1 = 16, then 16 + 6 = 22. Therefore, answer is 22.

Question 15

Calculate: 8 + 6 ÷ 2 × 4 − 3 + 9

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right): 6 ÷ 2 = 3, then 3 × 4 = 12. Step 2: Rewrite as 8 + 12 − 3 + 9. Step 3: Addition and Subtraction (left to right): 8 + 12 = 20, then 20 − 3 = 17, then 17 + 9 = 26. Therefore, answer is 26.

Question 16

Solve: 72 ÷ 8 + 5 × 6 − 4 × 2 + 3

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right): 72 ÷ 8 = 9, 5 × 6 = 30, and 4 × 2 = 8. Step 2: Rewrite as 9 + 30 − 8 + 3. Step 3: Addition and Subtraction (left to right): 9 + 30 = 39, then 39 − 8 = 31, then 31 + 3 = 34. Therefore, answer is 34.

Question 17

Evaluate: 2 × 3 + 4 × 5 − 6 ÷ 2 + 7

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right): 2 × 3 = 6, 4 × 5 = 20, and 6 ÷ 2 = 3. Step 2: Rewrite as 6 + 20 − 3 + 7. Step 3: Addition and Subtraction (left to right): 6 + 20 = 26, then 26 − 3 = 23, then 23 + 7 = 30. Therefore, answer is 30.

Question 18

Simplify: 100 − 20 × 3 + 15 ÷ 3 − 10

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right): 20 × 3 = 60 and 15 ÷ 3 = 5. Step 2: Rewrite as 100 − 60 + 5 − 10. Step 3: Subtraction and Addition (left to right): 100 − 60 = 40, then 40 + 5 = 45, then 45 − 10 = 35. Therefore, answer is 35.

Question 19

If 2^(x+1) × 4^(x−1) = 8, find the value of x.

Accepted Answer

Step 1: Rewrite all terms as powers of 2: 2^(x+1) × (2²)^(x−1) = 2³. Step 2: Simplify: 2^(x+1) × 2^(2x−2) = 2³. Step 3: Combine exponents: 2^(x+1+2x−2) = 2³, so 2^(3x−1) = 2³. Step 4: Equate exponents: 3x − 1 = 3, thus 3x = 4, so x = 4/3.

Question 20

Simplify: ∛(27a⁶b⁹) ÷ √(16a⁴b⁴)

Accepted Answer

Step 1: Simplify ∛(27a⁶b⁹) = ∛27 × ∛(a⁶) × ∛(b⁹) = 3 × a² × b³ = 3a²b³. Step 2: Simplify √(16a⁴b⁴) = √16 × √(a⁴) × √(b⁴) = 4 × a² × b² = 4a²b². Step 3: Divide: (3a²b³) ÷ (4a²b²) = (3/4)b.

IBPS RRB PO Number System Questions

IBPS RRB PO Number System — Past Exam Questions

Study by Subtopic — Number System

Study Next — Quantitative Aptitude Topics