Simplification - Aptitude MCQ Questions and Solutions with Explanations

Answer: Option A

$$\eqalign{ & {\text{According to the question}} \cr & {\text{ }}\frac{{{{\left( {3.4567} \right)}^2} - {{\left( {3.4533} \right)}^2}}}{{0.0034}} \cr & \left[ {\because {a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)} \right] \cr & \Rightarrow \frac{{\left( {3.4567 + 3.4533} \right)\left( {3.4567 - 3.4533} \right)}}{{0.0034}} \cr & \Rightarrow \frac{{6.91 \times 0.0034}}{{0.0034}} \cr & \Rightarrow 6.91 \cr} $$

Answer: Option A

$$\eqalign{ & {\text{According to the question,}} \cr & \frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}} + \left[ {0.75 + {{\left( {0.75} \right)}^2} + 1} \right] \cr & \Rightarrow \frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}} + \frac{{{1^3} - {{\left( {0.75} \right)}^3}}}{{1 - 0.75}}\, \cr & \left[ {\because {a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + {b^2} + ab} \right)} \right] \cr & \Rightarrow \frac{{{{\left( {0.75} \right)}^3} + 1 - {{\left( {0.75} \right)}^3}}}{{0.25}} \cr & \Rightarrow \frac{1}{{0.25}} \cr & \Rightarrow 4 \cr} $$

Answer: Option C

$$\eqalign{ & {\text{According to the question,}} \cr & \sqrt {4 + \sqrt {44 + \sqrt {10000} } } \cr & \Rightarrow \sqrt {4 + \sqrt {44 + 100} } \cr & \Rightarrow \sqrt {4 + \sqrt {144} } \cr & \Rightarrow \sqrt {4 + 12} \cr & \Rightarrow \sqrt {16} \cr & \Rightarrow 4 \cr} $$

Answer: Option C

$$\eqalign{ & {\text{Let,}} \cr & 45 - \left[ {28 - \left\{ {37 - \left( {15 - x} \right)} \right\}} \right] = 58 \cr & {\text{then,}} \cr & {\text{45}} - \left[ {28 - \left\{ {37 - 15 + x} \right\}} \right] = 58 \cr & \Rightarrow 45 - \left[ {28 - \left\{ {22 + x} \right\}} \right] = 58 \cr & \Rightarrow 45 - \left[ {28 - 22 - x} \right] = 58 \cr & \Rightarrow 45 - \left[ {6 - x} \right] = 58 \cr & \Rightarrow 45 - 6 + x = 58 \cr & \Rightarrow 39 + x = 58 \cr & \Rightarrow x = 58 - 39 \cr & \Rightarrow x = 19 \cr} $$

Answer: Option A

$$\eqalign{ & \frac{{113 \times 4 - x \times 2}}{{13 \times 9 - 5 \times 7}} = 5 \cr & \Rightarrow \frac{{452 - 2x}}{{117 - 35}} = 5 \cr & \Rightarrow \frac{{452 - 2x}}{{82}} = 5 \cr & \Rightarrow 452 - 2x = 410 \cr & \Rightarrow 2x = 452 - 410 = 42 \cr & \Rightarrow x = 21 \cr} $$