Simplification - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{According to question,}} \cr & \frac{{\frac{5}{3} \times \frac{7}{{51}}{\text{ of }}\frac{17}{5} - \frac{1}{3}}}{{\frac{2}{9} \times \frac{5}{7}{\text{ of }}\frac{{28}}{5} - \frac{2}{3}}}\, \cr & \Rightarrow \frac{{\frac{5}{3} \times \frac{7}{{51}} \times \frac{17}{5} - \frac{1}{3}}}{{\frac{2}{9} \times \frac{5}{7} \times \frac{{28}}{5} - \frac{2}{3}}}\, \cr & \Rightarrow \frac{{\frac{5}{3} \times \frac{7}{{15}} - \frac{1}{3}}}{{\frac{2}{9} \times 4 - \frac{2}{3}}} \cr & \, \Rightarrow \frac{{\frac{7}{9} - \frac{1}{3}}}{{\frac{8}{9} - \frac{2}{3}}} \cr & \, \Rightarrow \frac{{\frac{{7 - 3}}{9}}}{{\frac{{8 - 6}}{9}}} \cr & \Rightarrow \frac{4}{2} \cr & \Rightarrow 2 \cr} $$

1 - [5 - {2 + (- 5 + 6 - 2) 2}]
= 1 - [5 - {2 + (- 1) 2}]
= 1 - [5 - {2 - 2}]
= 1 - [5 - 0]
= 1 - 5
= -4

According to the question,
$$\eqalign{ & \sqrt {1.3} + \sqrt {1300} + \sqrt {0.013} \cr & \Rightarrow \sqrt {\frac{{130}}{{100}} }+ \sqrt {1300} + \sqrt {\frac{{130}}{{10000}}} \cr & \Rightarrow \frac{{11.4}}{{10}} + 36.05 + \frac{{11.4}}{{100}} \cr & \Rightarrow 1.14 + 36.05 + 0.114 \cr & \Rightarrow 37.304 \cr} $$

$$\eqalign{ & 1888 \div 32 \div 8 \cr & = \frac{{1888}}{{32}} \div 8 \cr & = 59 \div 8 \cr & = \frac{{59}}{8} \cr & = 7.375 \cr} $$

$$\eqalign{ & \frac{{4848}}{{24}} \times 11 - 222 \cr & = 202 \times 11 - 222 \cr & = 2222 - 222 \cr & = 2000 \cr} $$

Let the missing number is x.
then, $$\frac{{354750}}{{4096 + x}}$$   = 55
⇒ 55( 4096 + x ) = 354750
⇒ 55x = 354750 - 225280
⇒ 55x = 129470
⇒ x = 2354

$$\eqalign{ & {\text{According to question}} \cr & \frac{{\frac{5}{3} \times \frac{7}{{51}}{\text{of}}\frac{17}{5} - \frac{1}{3}}}{{\frac{2}{9} \times \frac{5}{7}{\text{of}}\frac{{28}}{5} - \frac{2}{3}}}\, \cr & \Rightarrow \frac{{\frac{5}{3} \times \frac{7}{{51}} \times \frac{17}{5} - \frac{1}{3}}}{{\frac{2}{9} \times \frac{5}{7} \times \frac{{28}}{5} - \frac{2}{3}}}\, \cr & \Rightarrow \frac{{\frac{5}{3} \times \frac{7}{{15}} - \frac{1}{3}}}{{\frac{2}{9} \times 4 - \frac{2}{3}}} \cr & \, \Rightarrow \frac{{\frac{7}{9} - \frac{1}{3}}}{{\frac{8}{9} - \frac{2}{3}}} \cr & \, \Rightarrow \frac{{\frac{{7 - 3}}{9}}}{{\frac{{8 - 6}}{9}}} \cr & \Rightarrow \frac{4}{2} \cr & \Rightarrow 2 \cr} $$

$$\eqalign{ & {\text{Let,}} \cr & {\text{853 + }}x \div 17 = 1000 \cr & {\text{Then,}} \cr & {\text{853 + }}\frac{x}{{17}} = 1000 \cr & \Leftrightarrow \frac{x}{{17}} = 1000 - 853 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 147 \cr & \Leftrightarrow x = 147 \times 17 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 2499 \cr} $$

$$\eqalign{ & {\text{Let,}} \cr & \left( {x - 968} \right) \div 79 \times 4 = 512 \cr & {\text{Then,}} \cr & \frac{{x - 968}}{{79}} \times 4 = 512 \cr & \Rightarrow x - 968 = \frac{{512 \times 79}}{4} \cr & \Rightarrow x - 968 = 10112 \cr & \Rightarrow x = 10112 + 968 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 11080 \cr} $$

Given Expression
= 1 - [ 1 - { 1 - ( 1 - 0 ) } ]
= 1 - [ 1 - ( 1 - 1 ) ]
= 1 - [ 1 - 0 ]
= 0