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 at the place of question mark (?) in following questions (you are not expected to calculate exact value)?}\ \text{12\% of }[(298.98) + (16.01)^2] + (12.01)^2 = ?

  1. 210

  2. 220

  3. 190

  4. 195

  5. 200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

298.98 ≈ 299. 16.01² = 256.08 ≈ 256. Sum = 299 + 256 = 555. 12.01² ≈ 144. 12% of 555 = 0.12 × 555 = 66.6. Adding 144: 66.6 + 144 = 210.6 ≈ 210. The answer 210 matches option A.

Multiple choice

$( \text{What approximate value will come in place of question mark (?) in the following questions?} )$ $( (99867)^{\frac{1}{2}} + (65547)^{\frac{1}{4}} + (19712)^{\frac{1}{3}} + (1314)^{\frac{1}{4}} = (6571)^{\frac{1}{4}} + ? )$

  1. 365

  2. 340

  3. 356

  4. 345

  5. 375
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Approximating using roots: (99867)^(1/2) = √99867 ≈ 316, (65547)^(1/4) = √(√65547) ≈ √256 = 16, (19712)^(1/3) = ∛19712 ≈ 27, (1314)^(1/4) = √(√1314) ≈ √36 = 6. LHS = 316 + 16 + 27 + 6 = 365. RHS = (6571)^(1/4) + ? ≈ √(√6571) ≈ √81 = 9. So: 365 = 9 + ?, giving ? = 356. Option C is 356. Let me verify: √99867 = 315.99, ⁴√65547 = 15.97, ∛19712 = 27.02, ⁴√1314 = 6.01. LHS = 315.99 + 15.97 + 27.02 + 6.01 = 365. ⁴√6571 = 8.99. So: 365 = 8.99 + ?, ? = 356.01 ≈ 356. This confirms option C is correct.

Multiple choice

(\text{What approximate value will come in place of question mark (?) in the following questions?})( (82)^{8} \div (735)^{8} \times (731)^{6} \times 81 = 730^{?} )

  1. 9

  2. 6

  3. 5

  4. 4

  5. 8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given: (82)^8 ÷ (735)^8 × (731)^6 × 81 = 730^?. This can be rewritten as: (82/735)^8 × (731)^6 × 81 = 730^?. Notice that 82/735 ≈ 1/9 (since 735 ÷ 82 ≈ 9), 731 ≈ 730, and 81 = 3^4. So: (1/9)^8 × 730^6 × 3^4 = 730^?. Simplifying: (1/9)^8 × 3^4 = (1/3^2)^8 × 3^4 = 1/3^16 × 3^4 = 1/3^12. But we need to express this in terms of base 730. Actually, let me think differently. Since 82/735 ≈ 1/9 = 3^(-2), we have: (3^(-2))^8 × 730^6 × 3^4 = 730^? 3^(-16) × 730^6 × 3^4 = 730^? 730^6 × 3^(-12) = 730^?. This doesn't simplify nicely to 730^4. Let me reconsider. Perhaps the question means: 82^8 ÷ 735^8 × 731^6 × 81 = (82/735)^8 × 731^6 × 81. If 82/735 ≈ 1/9, then (1/9)^8 × 730^6 × 81 = 3^(-16) × 730^6 × 3^4 = 730^6 × 3^(-12). For this to be a power of 730, the 3^(-12) must somehow cancel or convert. Actually, if 3^(-12) ≈ 730^(-2) (since 730^2 ≈ 532900, which is not close to 3^12 = 531441, they're very close!), then 730^6 × 730^(-2) = 730^4. Yes! 3^12 = 531441 and 730^2 = 532900, which are very close. So 3^(-12) ≈ 730^(-2). Therefore: 730^6 × 730^(-2) = 730^4. So ? = 4, which is option D.

Multiple choice

(\text{what approximate value should come in place of question mark in the following questions? (You are not expected to calculate the exact value).})(459\% \text{ of } 849.947 + 266\% \text{ of } 6284.012 - 1486.002 =?)
  1. $20330$
  2. $12640$
  3. $15000$
  4. $22160$
  5. $19130$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Approximating: 459% ≈ 4.6, 849.947 ≈ 850, 266% ≈ 2.7, 6284.012 ≈ 6280. 4.6 × 850 = 3910, 2.7 × 6280 = 16956. Sum = 3910 + 16956 - 1486 ≈ 19130. Option E (19130) is closest.

Multiple choice

\text{What approximate value should come in place of question mark in the following questions? (You are not expected to calculate the exact value).}\ 7.09\% \text{ of } 8500 - 3.51\% \text{ of } 5500 = 1.6 \% \text{ of } ?

  1. 23000

  2. 24000

  3. 24500

  4. 25500

  5. 25000
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Calculate: 7.09% of 8500 ≈ 7% of 8500 = 595. 3.51% of 5500 ≈ 3.5% of 5500 = 192.5. 595 - 192.5 = 402.5. So 1.6% of X = 402.5. Therefore X ≈ 402.5 / 0.016 ≈ 25156, closest to 25000. Option E is correct.

Multiple choice

what approximate value should come in place of question mark in the following questions? (You are not expected to calculate the exact value). (118.07 \times 13.49 + 169.8\% \text{ of } 784 =?)

  1. 2520

  2. 2610

  3. 2750

  4. 2870

  5. 2930
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Approximate: 118 × 13.5 = 1593 and 170% of 784 = 1.7 × 784 = 1333. Adding: 1593 + 1333 = 2926, which rounds to 2930 (option E). The calculation checks out: 118.07 × 13.49 ≈ 1592 and 169.8% of 784 ≈ 1331, sum ≈ 2923.