Quantitative Aptitude

Simplification and Approximation

647 Questions
All Approximate with option-sensitive rounding 386 Percentage calculation 112 Calculate squares and identify square roots 38 Simplify surds and indices 29 VBODMAS 27 Recognize algebraic identity patterns 23 Use cube patterns and perfect cube roots 15 Fraction and mixed number reduction 13 Mixed recurring decimals 3 Integer division and remainders 1

Simplification and Approximation Questions

Multiple choice

What approximate value should come in place of the question mark (?) in the following question? (16.2\% \text{ of } 986 \times 12.8\% \text{ of } 963 = ?)

  1. 19450

  2. 19435

  3. 20450

  4. 19950

  5. 18650
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Calculate: 16.2% of 986 ≈ 0.162 × 986 ≈ 159.7. Then 12.8% of 963 ≈ 0.128 × 963 ≈ 123.3. Multiply: 159.7 × 123.3 ≈ 19686. The closest option is 19435 (Option B). The approximation accounts for rounding in intermediate steps.

Multiple choice

What approximate value will come in place of the question mark (?) in the following questions? (38.9)2 ÷ 12.95×29=?–795

  1. 4100

  2. 4200

  3. 4600

  4. 4400

  5. 4000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Approximate: (38.9)² ÷ 12.95 × 29 = ? - 795. 38.9² ≈ 1510. Then 1510 ÷ 13 ≈ 116. Then 116 × 29 ≈ 3364. So ? ≈ 3364 + 795 = 4159. Among options, 4200 (B) is closest. Option A is too low. Option C is too high. Option D is too high. Option E is too low.

Multiple choice

\text{What approximate value will come in place of the question mark (?) in the following questions?}\\text{(97.1)}^{2} - \text{(87.2)}^{2} - \text{(13.01)}^{2} = ?

  1. 1670

  2. 1700

  3. 1650

  4. 1750

  5. 1800
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use difference of squares: a² - b² = (a+b)(a-b). (97.1)² - (87.2)² = (97.1+87.2)(97.1-87.2) = (184.3)(9.9) ≈ 1824.6. Then subtract (13.01)² ≈ 169.2, giving ≈ 1655.4. Rounding to nearest 50 gives 1670. Option A is correct. Option B is slightly high. Option C is too low. Option D is too high. Option E is much too high.

Multiple choice

What approximate value will come in place of question mark (?) in the following question? 20300 ÷ 36.14 × 176.120 = ? + 38.72

  1. 96850

  2. 90770

  3. 98700

  4. 89800

  5. 100000
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Approximating: 20300 ≈ 20000, 36.14 ≈ 36, 176.120 ≈ 176, 38.72 ≈ 39. So: (20000/36)×176 ≈ 555.56×176 ≈ 97778. Then 97778 - 39 ≈ 97739, which rounds to approximately 100000. The exact calculation: 20300÷36.14 × 176.120 - 38.72 ≈ 561.8×176.12 - 38.72 ≈ 98963 - 38.72 ≈ 98924, closest to 100000 among options.