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 will come in place of the question mark (?) in the following question? $22.05% of 249.99 =?$

  1. 46

  2. 65

  3. 12

  4. 55

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find 22.05% of 249.99, we can approximate: 22.05% ≈ 22% and 249.99 ≈ 250. Then 22% of 250 = 0.22 × 250 = 55. For a more precise calculation: 0.2205 × 249.99 ≈ 55.12. Among the options, 55 is the closest. The other options (46, 65, 12) are too far from the calculated value to be reasonable approximations.

Multiple choice

\text{What approximate value will come at place of question mark (?) in the following questions?}\\text{89}^2 + 45^2 = 36^2 + ?^2

  1. 93

  2. 86

  3. 81

  4. 99

  5. 112
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculate 89^2 + 45^2 = 7921 + 2025 = 9946. We have 9946 = 36^2 + ?^2, so ?^2 = 9946 - 1296 = 8650. Taking square root gives approximately 93.02, so ? ≈ 93. This is an exact calculation: 93^2 = 8649, which when added to 36^2 (1296) gives 9945, very close to 9946. Option A (93) is the correct answer.

Multiple choice

(\text{What approximate value should come in place of question mark (?) in the following question?}\19.99\% \text{ of } 789.907 \times 15.08 + 111.999 \div 4.034 - 45\% \text{ of } 399.998 = ?)

  1. 2220

  2. 2290

  3. 2190

  4. 1320

  5. 2480
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculate: 19.99% of 789.907 ≈ 20% of 790 = 158; 158 × 15.08 ≈ 158 × 15 = 2370; 111.999 ÷ 4.034 ≈ 112 ÷ 4 = 28; 45% of 399.998 ≈ 45% of 400 = 180. Final = 2370 + 28 - 180 = 2218 ≈ 2220. Answer A (2220) is correct.

Multiple choice

What approximate value will come in place of question mark (?) in the question given below ? (21.7\% \text{ of } 514.9 - 43.44 =? \div 5.5)

  1. 385

  2. 410

  3. 340

  4. 450

  5. 490
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculate 21.7% of 514.9 ≈ 111.73. Then 111.73 - 43.44 = 68.29. The expression (68.29) ÷ 5.5 = 12.4. But this doesn't match any option. Alternatively, reading '?' as the variable: (21.7% of 514.9 - 43.44) = ? ÷ 5.5 means ? = (111.73 - 43.44) × 5.5 = 374.6. Option A (385) is closest to this approximate calculation.

Multiple choice

What approximate value should come in place of question mark (?) in the following questions? $699.989÷7.05-4.998×17.96+14.05×3.99-12.09=?$

  1. 54

  2. 60

  3. 48

  4. 42

  5. 64
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Approximate and solve: 699.989 ≈ 700, 7.05 ≈ 7, so 700 ÷ 7 = 100. Next, 4.998 ≈ 5, 17.96 ≈ 18, so 5 × 18 = 90. Then, 14.05 ≈ 14, 3.99 ≈ 4, so 14 × 4 = 56. Finally: 100 - 90 + 56 - 12 = 10 + 56 - 12 = 66 - 12 = 54. This matches option A exactly. Remember to follow the order of operations: division and multiplication before addition and subtraction.

Multiple choice

What approximate value should come in place of question mark (?) in the following questions? $( (12.05)^2 - (8.99)^2 + (13.99)^2 - (17.08)^2 = ? )$

  1. -20

  2. -40

  3. -30

  4. -50

  5. -10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Use difference of squares formula: a² - b² = (a+b)(a-b). Round the values: (12.05)² - (8.99)² ≈ (12+9)(12-9) = 21 × 3 = 63. For the second pair: (13.99)² - (17.08)² ≈ (14-17)(14+17) = (-3) × 31 = -93. Total: 63 - 93 = -30. Option C is correct. The key insight is recognizing the difference of squares pattern rather than calculating each square individually.

Multiple choice

\text{What approximate value should come in place of question mark (?) in the following questions?}\\sqrt{3970} \div 2.998 + 5.098 \times 268.99 + 433.908 =?

  1. 1800

  2. 2000

  3. 1700

  4. 2100

  5. 2400
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Approximate: √3970 ≈ √3969 = 63 (since 63² = 3969). Then: 63 ÷ 2.998 ≈ 63 ÷ 3 = 21. Next: 5.098 × 268.99 ≈ 5 × 269 = 1345. Finally: 21 + 1345 + 433.908 ≈ 21 + 1345 + 434 = 1800. Option A is correct. The strategy is to round each term to numbers that are easy to work with while maintaining accuracy.

Multiple choice

\text{What approximate value should come at place of question mark (?) in the following questions?}\(\frac{2}{7} \times \frac{1}{8} + \frac{3}{7} \div \frac{6}{14} = ?)
  1. $\frac{2}{56}$
  2. $\frac{3}{56}$
  3. $1$
  4. $5$
  5. $\frac{50}{60}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Calculate: (2/7)×(1/8) = 2/56 = 1/28. And: (3/7)÷(6/14) = (3/7)×(14/6) = 42/42 = 1. Sum: 1/28 + 1 = 1/28 + 28/28 = 29/28 ≈ 1.04. But wait, let me recalculate the second part: (3/7)÷(6/14) = (3/7)×(14/6) = 42/42 = 1. So total = 1/28 + 1 = 1 + 1/28, not exactly 1. Let me check the first part again: (2/7)×(1/8) = 2/(7×8) = 2/56 = 1/28. Sum = 1/28 + 1 = 29/28. Hmm, none of the options match 29/28. Option C is 1, which is approximately 29/28 ≈ 1.036. But the question asks for approximate value? Looking at the question again: 'What approximate value should come...' So the answer 1 is approximately correct. Actually wait, let me re-read: (2/7)×(1/8) + (3/7)÷(6/14). First term: 2/56 = 1/28. Second term: 3/7 ÷ 6/14 = 3/7 × 14/6 = 42/42 = 1. Total: 1 + 1/28 = 29/28 ≈ 1.04. Among options, 1 is closest. But actually, 29/28 rounds to 1, so C is correct.

Multiple choice

What approximate value should come at place of question mark (?) in the following questions?(24^3 + 95^2 = ?^3 + 115^2)

  1. 16

  2. 19

  3. 21

  4. 24

  5. 13
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Calculate: 24³ + 95² = 13,824 + 9,025 = 22,849. Also: ?³ + 115². So: ?³ = 22,849 - 13,225 = 9,624. Find cube root: 9,261 is 21³, which is very close to 9,624. Checking options: 16³ = 4,096 (too low), 19³ = 6,859 (too low), 21³ = 9,261 (closest), 24³ = 13,824 (too high). Answer 'C' (21) is correct.