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

Using the differentials, the approximate value of $(627)^{1/4}$ is

  1. 5.002

  2. 5.003

  3. 5.005

  4. 5.004
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using differentials, f(x+dx) is approximately f(x) + f'(x)dx. For (627)^(1/4), let x = 625 and dx = 2. Then 625^(1/4) = 5, and f'(x) = (1/4)x^(-3/4). Calculating 5 + (1/4)(625^(-3/4))(2) gives 5 + 0.5/125 = 5 + 0.004 = 5.004.

Multiple choice

If Mode=$195.2$, Median=$198.4$ then the approximately value of mean is
  1. $200$
  2. $250$
  3. $210$
  4. $225$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The empirical relationship between mean, median, and mode is given by the formula Mode = 3 * Median - 2 * Mean. Substituting the given values, we get 195.2 = 3 * 198.4 - 2 * Mean, which simplifies to 2 * Mean = 400, yielding a Mean of 200.

Multiple choice

Approximate value of $\sqrt[4]{81.04}$
  1. $3.0003$
  2. $3.004$
  3. $3.0046$
  4. $3.0012$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using binomial approximation (x+dx)^(1/n) approx x^(1/n) + (1/n)x^((1/n)-1)*dx. Here x=81, dx=0.04, n=4. 81^(1/4) = 3. Approximation = 3 + (1/4)*81^(-3/4)*0.04 = 3 + (1/4)(1/27)*0.04 = 3 + 0.01/27 = 3 + 0.00037. The closest option is 3.0003.