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

\text{What approximate value will come in place of question mark (?) in following Question?}\45\% \times 299.99 + \sqrt{399.99} \times \frac{4}{5} = ?

  1. 240

  2. 151

  3. 218

  4. 122

  5. 162
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We need to calculate 45% × 299.99 + √399.99 × 4/5. Approximating: 45% × 300 = 135 (since 45% = 0.45, and 0.45 × 300 = 135). √400 = 20. 20 × 4/5 = 20 × 0.8 = 16. Total = 135 + 16 = 151. This matches option B. The question asks for approximate value, so using 300 instead of 299.99 and 400 instead of 399.99 is the correct approach.

Multiple choice

What approximate value will come in place of question mark (?) in following Question?( (215.98)^{1/3} \times \sqrt{120.6} -? = 35\% \times 698 )
  1. $-167$
  2. $-179$
  3. $-209$
  4. $-245$
  5. $-130$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We need to find ? in (215.98)^(1/3) × √120.6 - ? = 35% × 698. Rearranging: ? = (215.98)^(1/3) × √120.6 - 35% × 698. Approximating: ³√216 = 6 (since 6³ = 216). √121 = 11 (since 11² = 121). 35% × 700 = 0.35 × 700 = 245. So ? ≈ 6 × 11 - 245 = 66 - 245 = -179. This matches option B. The calculation is straightforward with proper approximations.

Multiple choice

What approximate value should come in place of question mark. प्रश्नवाचक चिन्ह के स्थान पर लगभग कितना मान आना चाहिए। √{(29.98% of 779.95) + (25.05% of 219.97)} = ? √{(779.95 का 29.98% ) + (219.97 का 25.05%)} = ?

  1. 28

  2. 17

  3. 35

  4. 24

  5. none of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Approximate: 29.98% of 779.95 ≈ 30% of 780 = 0.30 × 780 = 234. And 25.05% of 219.97 ≈ 25% of 220 = 0.25 × 220 = 55. Sum = 234 + 55 = 289. Now √289 ≈ 17 (since 17² = 289). The answer is approximately 17.

Multiple choice

Find the value of the square root of (?) ( 6.25\% \text{ of } 25 + 25\% \text{ of } 50 - 14\% \text{ of } 25 = ? )
  1. $\(\frac{12}{25}\)$
  2. $\(\frac{144}{25}\)$
  3. $\(\frac{13}{3}\)$
  4. $\(\frac{5}{71}\)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

6.25% of 25 = 1.5625, 25% of 50 = 12.5, 14% of 25 = 3.5. So 1.5625 + 12.5 - 3.5 = 10.5625. √10.5625 = 3.25 = 13/4. Wait, let me recalculate: 6.25% = 1/16, so (1/16) × 25 = 25/16. 25% × 50 = 12.5 = 25/2. 14% × 25 = 3.5 = 7/2. Expression = 25/16 + 25/2 - 7/2 = 25/16 + 18/2 = 25/16 + 9 = 169/16. √(169/16) = 13/4. But 13/3 = 4.33, 13/4 = 3.25. Let me verify: 169/16 = 10.5625, √10.5625 = 3.25 = 13/4. Option C is 13/3, not 13/4. There's a discrepancy. Actually, let me check the expression again: 25/16 + 25/2 - 7/2 = 25/16 + (25-7)/2 = 25/16 + 18/2 = 25/16 + 9 = 25/16 + 144/16 = 169/16. √(169/16) = 13/4. This doesn't match 13/3. However, the question asks for √(6.25% of 25 + 25% of 50 - 14% of 25). Let me recalculate: 6.25% = 0.0625 = 1/16, 0.0625 × 25 = 1.5625. 0.25 × 50 = 12.5. 0.14 × 25 = 3.5. Sum: 1.5625 + 12.5 - 3.5 = 10.5625. √10.5625 = 3.25 = 13/4. The answer should be 13/4, not 13/3. But given the options, 13/3 is marked correct. There might be an error in the question or my calculation.

Multiple choice

What approximate value will come in place of question mark in following questions? (250.87 × 8.12 × 6.829) ÷ 25 = 11.86 + ?

  1. 662

  2. 504

  3. 548

  4. 448

  5. 580
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Calculate: (250.87 × 8.12 × 6.829) ÷ 25 = ? × 11.86. Approximation: (251 × 8.1 × 6.8) ÷ 25 ≈ 251 × 8.1 × 0.272 ≈ 251 × 2.2 ≈ 552. Then 552 - 11.86 ≈ 540. Option C (548) is closest. Precise calculation: 250.87 × 8.12 = 2037.0664, then × 6.829 = 13911.47, then ÷ 25 = 556.46. Then 556.46 - 11.86 = 544.6. Option C (548) is closest.

Multiple choice

$(\text{What approximate value will come in place of the question mark(?) in following equation?})$ $((10.998)^2 + (16.221)^2 – (14.441)^2 =?)$
  1. $180$
  2. $220$
  3. $130$
  4. $240$
  5. $165$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Approximating: (10.998)² ≈ 11² = 121, (16.221)² ≈ 16² = 256, (14.441)² ≈ 14² = 196. So 121 + 256 - 196 = 181. The closest approximation is 180. This tests ability to round decimals to nearest integers and compute quickly.