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Quantitative Aptitude — Simplification
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Quantitative Aptitude — Simplification

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19 mins
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25
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1
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Quantitative Aptitude — Simplification — Questions with Answers Open after you finish the quiz — all 25 questions, with answers and explanations.
Q1. What is the value of 15 + [25 - (10 * 2)]?
  1. 20
  2. 25
  3. 30
  4. 35
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Answer: A. 20
Following BODMAS rule: 1. Brackets first: (10 * 2) = 20 2. Next bracket: [25 - 20] = 5 3. Finally, addition: 15 + 5 = 20
Q2. Simplify: 36 ÷ 6 * 3 + 5 - 2
  1. 18
  2. 21
  3. 24
  4. 27
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Answer: B. 21
Following BODMAS rule (Division and Multiplication from left to right, then Addition and Subtraction from left to right): 1. Division: 36 ÷ 6 = 6 2. Multiplication: 6 * 3 = 18 3. Addition: 18 + 5 = 23 4. Subtraction: 23 - 2 = 21
Q3. Evaluate: 1/2 + 3/4 * 8/9
  1. 1
  2. 5/6
  3. 7/6
  4. 4/3
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Answer: C. 7/6
Following BODMAS rule: 1. Multiplication first: 3/4 * 8/9 = (3*8)/(4*9) = 24/36 = 2/3 2. Addition: 1/2 + 2/3 = 3/6 + 4/6 = 7/6
Q4. Simplify: 50 - [20 + {30 - (15 - 5)}]
  1. 0
  2. 5
  3. 15
  4. 10
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Answer: D. 10
Following BODMAS rule (innermost brackets first): 1. Parentheses: (15 - 5) = 10 2. Curly brackets: {30 - 10} = 20 3. Square brackets: [20 + 20] = 40 4. Subtraction: 50 - 40 = 10
Q5. What is the value of 4^2 + 3 * (10 - 2)?
  1. 40
  2. 32
  3. 28
  4. 48
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Answer: A. 40
Following BODMAS rule: 1. Brackets: (10 - 2) = 8 2. Orders (Exponents): 4^2 = 16 3. Multiplication: 3 * 8 = 24 4. Addition: 16 + 24 = 40
Q6. Simplify: 120 ÷ 10 * 5 - 15 + 7
  1. 48
  2. 52
  3. 55
  4. 60
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Answer: B. 52
Following BODMAS rule: 1. Division: 120 ÷ 10 = 12 2. Multiplication: 12 * 5 = 60 3. Subtraction: 60 - 15 = 45 4. Addition: 45 + 7 = 52
Q7. Evaluate: 25% of 200 + 15 * 3
  1. 85
  2. 90
  3. 95
  4. 100
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Answer: C. 95
Following BODMAS rule: 1. 'Of' (multiplication): 25% of 200 = (25/100) * 200 = 50 2. Multiplication: 15 * 3 = 45 3. Addition: 50 + 45 = 95
Q8. Simplify: 72 ÷ 9 + 4 * 5 - 12
  1. 12
  2. 14
  3. 18
  4. 16
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Answer: D. 16
Following BODMAS rule: 1. Division: 72 ÷ 9 = 8 2. Multiplication: 4 * 5 = 20 3. Addition: 8 + 20 = 28 4. Subtraction: 28 - 12 = 16
Q9. What is the value of 18 - 3 * 4 + (6 + 2) ÷ 2?
  1. 10
  2. 8
  3. 12
  4. 14
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Answer: A. 10
Following BODMAS rule: 1. Brackets: (6 + 2) = 8 2. Multiplication: 3 * 4 = 12 3. Division: 8 ÷ 2 = 4 4. Subtraction: 18 - 12 = 6 5. Addition: 6 + 4 = 10
Q10. Simplify: 60 ÷ [5 * {16 - (8 + 2)}]
  1. 1
  2. 2
  3. 3
  4. 4
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Answer: B. 2
Following BODMAS rule (innermost brackets first): 1. Parentheses: (8 + 2) = 10 2. Curly brackets: {16 - 10} = 6 3. Square brackets: [5 * 6] = 30 4. Division: 60 ÷ 30 = 2
Q11. What is the value of (70 + 5 × 2 ÷ 10 + 15 − 10) / (25 × 6 + 2)?
  1. 5/18
  2. 1/2
  3. 19/50
  4. 53/114
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Answer: B. 1/2
Numerator: 70 + 5×2÷10 + 15 - 10 = 70 + 1 + 15 - 10 = 76. Denominator: 25×6 + 2 = 150+2 = 152. So 76/152 = 1/2.
Q12. Simplify: (√144/6) × (√121/8) × (132/√484).
  1. 3/4
  2. 4
  3. 33/2
  4. 155/36
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Answer: C. 33/2
(12/6) × (11/8) × (132/22) = 2 × (11/8) × 6 = (11/4) × 6 = 66/4 = 33/2.
Q13. If x : y = 2 : 3, find the ratio (4x + 3y) : (2x + 5y).
  1. 17 : 19
  2. 13 : 11
  3. 19 : 17
  4. 11 : 13
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Answer: A. 17 : 19
Let x=2k, y=3k. (4×2k + 3×3k)/(2×2k + 5×3k) = (8k+9k)/(4k+15k) = 17k/19k = 17:19.
Q14. Evaluate √((544)² − (256)²).
  1. 480
  2. 400
  3. 288
  4. 144
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Answer: A. 480
Using a²-b² = (a+b)(a-b). √((544-256)(544+256)) = √(288×800) = √230400 = 480.
Q15. Simplify the expression: 2 − [2 − {2 − 2(2 + 2)}].
  1. 4
  2. -4
  3. -6
  4. 6
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Answer: C. -6
Step by step: 2-[2-{2-2(4)}] = 2-[2-{2-8}] = 2-[2-(-6)] = 2-[2+6] = 2-8 = -6.
Q16. Find the value of '?' in the equation: 47^7.5 ÷ 47^(3/2) × 47^(-3) = (√47)^?.
  1. 2^(1/2)
  2. 6
  3. 5
  4. 4
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Answer: B. 6
47^(7.5 - 1.5 - 3) = 47^3. Also, (√47)^? = (47^(1/2))^? = 47^(?/2). So, 3 = ?/2, which means ? = 6.
Q17. What is the result of simplifying 105 ÷ 5 × 3 + 39 − 46?
  1. 56
  2. 10
  3. 65
  4. 0
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Answer: A. 56
Using BODMAS: 105÷5×3 + 39 - 46 = 21×3 + 39 - 46 = 63 + 39 - 46 = 102 - 46 = 56.
Q18. In the equation (2a³ − 3)(5a³ − 2) = 10a⁶ + ? + 6, what term replaces the question mark?
  1. 19a³
  2. 19a²
  3. 19
  4. -19a³
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Answer: D. -19a³
Expanding LHS: (2a³)(5a³) + (2a³)(-2) + (-3)(5a³) + (-3)(-2) = 10a⁶ - 4a³ - 15a³ + 6 = 10a⁶ - 19a³ + 6. Comparing with RHS, ? = -19a³.
Q19. Calculate the value of 20 − [15 − {4 − (8 − 6 + 3)}].
  1. 4
  2. 8
  3. 5
  4. 6
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Answer: A. 4
20-[15-{4-(8-6+3)}] = 20-[15-{4-(2+3)}] = 20-[15-{4-5}] = 20-[15-(-1)] = 20-[15+1] = 20-16 = 4.
Q20. Given √2916 = 54, find the value of √29.16 + √0.2916 + √0.002916 + √0.00002916.
  1. 5.999
  2. 6.00
  3. 5.9994
  4. 5.90
Show answer
Answer: C. 5.9994
√29.16 = 5.4, √0.2916 = 0.54, √0.002916 = 0.054, √0.00002916 = 0.0054. Sum = 5.4 + 0.54 + 0.054 + 0.0054 = 5.9994.
Q21. What is the value of 12 + 8 − 5 × (1/2) × 12 − {45 ÷ (34-19)}?
  1. 13
  2. -10
  3. -25
  4. -13
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Answer: D. -13
12 + 8 - 5 × 6 - {45 ÷ 15} = 20 - 30 - 3 = -10 - 3 = -13.
Q22. Simplify √(8 − 2√15).
  1. 3 - √5
  2. √5 + √3
  3. √5 - √3
  4. 5 - √3
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Answer: C. √5 - √3
We can write 8 - 2√15 as 5 + 3 - 2√5√3, which is (√5)² + (√3)² - 2√5√3 = (√5 - √3)². Therefore, √(8 - 2√15) = √5 - √3.
Q23. Calculate the value of (2/5) × 350 + 30% of 250.
  1. 115
  2. 125
  3. 215
  4. 225
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Answer: C. 215
(2/5) × 350 = 2 × 70 = 140. 30% of 250 = (30/100) × 250 = 3 × 25 = 75. Sum = 140 + 75 = 215.
Q24. Find the value of √(36.1/102.4).
  1. 6.1/34
  2. 19/34
  3. 19/32
  4. 19/31
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Answer: C. 19/32
√(36.1/102.4) = √(361/1024). Since 19² = 361 and 32² = 1024, the value is 19/32.
Q25. Which of the following is NOT a rational number?
  1. √(3²+4²)
  2. √12.96
  3. √125
  4. √900
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Answer: C. √125
√(3²+4²) = √25 = 5 (rational). √12.96 = 3.6 (rational). √125 = 5√5 (irrational). √900 = 30 (rational).
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