Simplification - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & - 7 \div \left[ {5 + 1 \div 2 - \left\{ {4 + \left( {4{\text{ of }}2 \div 4} \right) + \left( {4 \div 4{\text{ of }}2} \right)} \right\}} \right] \cr & = - 7 \div \left[ {5 + \frac{1}{2} - \left\{ {4 + 2 + \frac{1}{2}} \right\}} \right] \cr & = - 7 \div \left[ {5\frac{1}{2} - 6\frac{1}{2}} \right] \cr & = - 7 \div \left( { - 1} \right) \cr & = 7 \cr} $$

$$\eqalign{ & {\text{A}} = \left[ {\frac{3}{7}{\text{ of }}4\frac{1}{5} \div \frac{{18}}{{25}} + \frac{{17}}{{24}}} \right]{\text{ of }}\left[ {\frac{{289}}{{16}} \div {{\left( {\frac{3}{4} + \frac{2}{3}} \right)}^2}} \right] \cr & {\text{A}} = \left[ {\frac{3}{7}{\text{ of }}\frac{{21}}{5} \div \frac{{18}}{{25}} + \frac{{17}}{{24}}} \right]{\text{ of }}\left[ {\frac{{289}}{{16}} \div \frac{{{{17}^2}}}{{{{12}^2}}}} \right] \cr & {\text{A}} = \left[ {\frac{9}{5} \times \frac{{25}}{{18}} + \frac{{17}}{{24}}} \right]{\text{ of }}\left[ {\frac{{289}}{{16}} \times \frac{{144}}{{289}}} \right] \cr & {\text{A}} = \left[ {\frac{5}{2} + \frac{{17}}{{24}}} \right]{\text{ of 9}} \cr & {\text{A}} = \frac{{77}}{{24}} \times 9 \cr & {\text{8A}} = 8 \times \frac{{77}}{{24}} \times 9 \cr & {\text{8A}} = 231 \cr} $$

$$\eqalign{ & \frac{1}{{15}} + \frac{1}{{35}} + \frac{1}{{63}} + \frac{1}{{99}} + \frac{1}{{143}} \cr & = \frac{1}{2}\left[ {\frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7}\,.\,.\,.\,.\,.\,\frac{1}{{11}} - \frac{1}{{13}}} \right] \cr & = \frac{1}{2}\left[ {\frac{1}{3} - \frac{1}{{13}}} \right] \cr & = \frac{1}{2} \times \frac{{10}}{{39}} \cr & = \frac{5}{{39}} \cr} $$

$$\eqalign{ & 1 - 3 \div 6\,{\text{of }}2 + \left( {4 \div 4\,{\text{of }}\frac{1}{4}} \right) \div 8 + \left( {4 \times 8 \div \frac{1}{4}} \right) \times \frac{1}{8} \cr & = 1 - \frac{3}{{12}} + \left( {\frac{4}{1}} \right) \times \frac{1}{8} + \frac{{4 \times 8 \times 4}}{8} \cr & = 1 - \frac{1}{4} + \frac{1}{2} + 16 \cr & = \frac{{69}}{4} \cr} $$

$$\eqalign{ & 3 \div 18{\text{ of }}3 \times 6 + 21 \times 6 \div 18 - 3 \div 2 + 3 - 3 \div 9{\text{ of }}3 \times 9 \cr & = \frac{3}{{54}} \times 6 + \frac{{21 \times 6}}{{18}} - \frac{3}{2} + 3 - \frac{3}{{27}} \times 9 \cr & = \frac{1}{3} + 7 - \frac{3}{2} + 3 - 1 \cr & = 9 + \frac{1}{3} - \frac{3}{2} \cr & = \frac{{54 + 2 - 9}}{6} \cr & = \frac{{47}}{6} \cr} $$

$$\eqalign{ & \frac{{16 - 0.002}}{{8 + 0.4 + 0.02}} \cr & = \frac{{16000 - 2}}{{8000 + 400 + 20}} \cr & = \frac{{15098}}{{8420}} \cr & = 1.9{\text{ Answer}} \cr} $$

$$\eqalign{ & 11760 \times \frac{1}{3} \times \frac{1}{5} \times \frac{3}{8} \cr & = \frac{{1176}}{4} \cr & = 294 \cr} $$

2.1 + 2.25 ÷ [63 - {7.5 × 8 + (13 - 2.5 × 5)}]
= 2.1 + 2.25 ÷ [63 - {60 + 0.5}]
= 2.1 + 2.25 ÷ [63 - 60.5]
= 2.1 + $$\frac{{2.25}}{{2.50}}$$
= 2.1 + 0.9
= 3.0

$$\eqalign{ & x = \sqrt {30 + \sqrt {30 + \sqrt {30 + \sqrt {30\,........\,\infty } } } } \cr & 5 \times 6 = 30 \cr & {\text{Hence }}x = 6 \cr} $$

$$\eqalign{ & {\text{Let two numbers}} = a{\text{ and }}b \cr & a > b \cr & a - b = 1564{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & 6b + 19 = a \cr & a - 6b = 19{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & {\text{From equation }}\left( {\text{i}} \right){\text{ and }}\left( {{\text{ii}}} \right) \cr & a - b = 1564 \cr & a - 6b = 19 \cr & - \,\,\,\,\, + \,\,\,\,\, - \cr & \overline {\,\,\,\,\,\,\,5b = 1545\,} \cr & b = 309 \cr & {\text{Smaller number}} = 309 \cr} $$