Simplification: Aptitude Questions with Answers – Free Practice!

Q. 1 Simplify: \( \frac{(45)^2 – (15)^2}{30} \)

Check Solution

Ans: A

Use $ a^2 – b^2 = (a – b)(a + b) $, then divide: $ \frac{30 \times 60}{30} = 60 $

Q. 2 Simplify: \( \sqrt{2025} + \sqrt{1225} – \sqrt{625} \)

Check Solution

Ans: B

Roots: $ 45 + 35 – 25 = 55 $

Q. 3 Simplify: \( \frac{2}{5} + \frac{3}{10} – \frac{4}{15} \)

Check Solution

Ans: D

LCM = 30 → $ \frac{12+9-8}{30} = \frac{13}{30} $

Q. 4 Simplify: \( \frac{1}{2} \div \left( \frac{3}{4} \times \frac{2}{3} \right) \)

Check Solution

Ans: C

$ \frac{3}{4} \times \frac{2}{3} = \frac{1}{2}, \frac{1}{2} \div \frac{1}{2} = 1 $

Q. 5 Simplify: \( (3.2)^2 – (1.2)^2 \)

Check Solution

Ans: B

$ a^2 – b^2 = (4.4)(2.0) = 8.8 $

Q. 6 Simplify: \( \frac{(2 + \frac{1}{2})^2}{(1 + \frac{1}{4})} \)

Check Solution

Ans: A

$ (\frac{5}{2})^2 = \frac{25}{4}, \div \frac{5}{4} = 5 $

Q. 7 Simplify: \( \frac{3}{2} + \frac{4}{3} – \frac{5}{6} \)

Check Solution

Ans: A

Convert to common denominator → $ \frac{9 + 8 – 5}{6} = \frac{12}{6} = 2 $

Q. 8 Simplify: \( \left( \frac{5}{6} \right)^2 + \left( \frac{1}{2} \right)^2 \)

Check Solution

Ans: D

$ \frac{25}{36} + \frac{9}{36} = \frac{34}{36} = \frac{17}{18} $

Q. 9 Simplify: \( \sqrt{144} + \sqrt{121} – \sqrt{81} \)

Check Solution

Ans: C

$ \sqrt{144} = 12, \sqrt{121} = 11, \sqrt{81} = 9 → 12 + 11 – 9 = 14 $

Q. 10 Simplify: \( \frac{1}{(1 – \frac{1}{2})} + \frac{1}{(1 – \frac{1}{3})} \)

Check Solution

Ans: B

$ \frac{1}{\frac{1}{2}} + \frac{1}{\frac{2}{3}} = 2 + \frac{3}{2} = \frac{7}{2} $

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