Simplification

Quantitative Aptitude Questions and Answers section on “Simplification” with solution and explanation for competitive examinations such as CAT, MBA, SSC, Bank PO, Bank Clerical and other examinations.

1.

Simplify : 6010-6000\div 10
[A]1
[B]5400
[C]0
[D]5410

5410
Given expression –
6010-6000\times \frac{1}{10}
=>6010-600=5410
Hence option [D] is the right answer.

2.

Simplify: 18800\div 470\div 20
[A]800
[B]2
[C]23.5
[D]None of these

2
Given expression :
\frac{18800}{470}\div 20
=>40\div 20=\frac{40}{20}=2
So the correct option is [B].

3.

If a*b = \left ( a^{2}+b^{2}-ab \right ), Then 6*9 =
[A]66
[B]63
[C]64
[D]62

63
\because 6*9=\left ( 6^{2}+9^{2}-6\times 9 \right )
=>(36+81-54)=63
Hence option [B] is the right answer.

4.

5-\left [ 4-\left \{ 3-(3-3-6) \right \} \right ] is equal to :
[A]0
[B]4
[C]6
[D]10

10
Given,5-\left [ 4-\left \{ 3-(3-3-6) \right \} \right ]
= 5-\left [ 4-\left \{ 3-\left ( -6 \right ) \right \} \right ]
= 5-\left [ 4-\left \{ 3+6 \right \} \right ]
= 5-\left [ 4-9 \right ]
= 5+5 = 10
Hence option [D] is right answer.

5.

Evaluate :
\frac{9|3-5|-5|4|\div 10}{-3(5)-2\times 4\div 2}
[A]\frac{4}{7}
[B]-\frac{16}{19}
[C]-\frac{8}{17}
[D]\frac{9}{10}

\mathbf{-\frac{16}{19}}
= \frac{9|3-5|-5|4|\div 10}{-3(5)-2\times 4\div 2}
= \frac{9\times 2 - 5\times 4\div 10}{-15-8\div 2}
= \frac{18-2}{-19} = -\frac{16}{19}
Hence option [B] is right answer.

6.

Evaluate :
\frac{-(4-6)^{2}-3(-2)+|-6|}{18-9\div 3\times 5}
[A]\frac{7}{4}
[B]\frac{3}{8}
[C]\frac{8}{3}
[D]\frac{4}{7}

\mathbf{\frac{8}{3}}
Given Expression,
= \frac{-(4-6)^{2}-3(-2)+|-6|}{18-9\div 3\times 5}
= \frac{-(-2)^{2}+6+6}{18-15}
= \frac{-4+12}{3} = \frac{8}{3}
Hence option [C] is right answer.

7.

Simplify
\frac{1}{2+\frac{1}{2+\frac{1}{2+\frac{1}{2-\frac{1}{2}}}}} :
[A]\frac{5}{16}
[B]\frac{7}{18}
[C]\frac{8}{19}
[D]\frac{9}{16}

\mathbf{\frac{8}{19}}Given Expression :
\frac{1}{2+\frac{1}{2+\frac{1}{2+\frac{1}{2-\frac{1}{2}}}}}
=>\frac{1}{2+\frac{1}{2+\frac{2}{3}}}
=> \frac{1}{2+\frac{3}{8}}
=>\frac{8}{19}
Hence option [c] is the right answer.

8.

The Simplification of
\frac{5}{3+\frac{3}{1-\frac{2}{3}}} gives:
[A]\frac{5}{12}
[B]5
[C]\frac{5}{3}
[D]\frac{3}{5}

\mathbf{\frac{5}{12}}
Given Expression,
\frac{5}{3+\frac{3}{\frac{3-2}{3}}}
=>\frac{5}{3+\frac{3}{\frac{1}{3}}}
=>\frac{5}{3+3\times 3}
=>\frac{5}{3+9}
=>\frac{5}{12}
Hence option [A] is the right answer.

9.

The value of
\frac{1}{3+\frac{1}{2-\frac{1}{\frac{7}{9}}}}+\frac{17}{22} is :
[A]\frac{12}{22}
[B]\frac{22}{5}
[C]1
[D]\frac{5}{22}

1
Given Expression,
\frac{1}{3+\frac{1}{2-\frac{1}{\frac{7}{9}}}}+\frac{17}{22}
=>\frac{1}{3+\frac{1}{2-\frac{9}{7}}}+\frac{17}{22}
=>\frac{1}{3+\frac{1}{\frac{14-9}{7}}}+\frac{17}{22}
=>\frac{1}{3+\frac{1}{\frac{5}{7}}}+\frac{17}{22}=\frac{1}{3+\frac{7}{5}}+\frac{17}{22}
=>\frac{1}{\frac{15+7}{5}}+\frac{17}{22}
=>\frac{5}{22}+\frac{17}{2}=\frac{22}{22}=1
Hence option [C] is the right answer.

10.

Find the value of
\frac{2}{1+\frac{1}{1-\frac{1}{2}}}\times \frac{3}{\frac{5}{6}of\frac{3}{2}of\div 1\frac{1}{4}} :
[A]4
[B]2
[C]8
[D]6

2
Given Expression,
\frac{2}{1+\frac{1}{\frac{1}{2}}}\times \frac{3}{\left [ \frac{5}{6}\times \frac{3}{2} \right ]\div \frac{5}{4}}
=>\frac{2}{1+2}\times\frac{3}{\frac{5}{4}\div \frac{5}{4}}
=>\frac{2}{3}\times \frac{3}{\frac{5}{4}\times \frac{4}{5}}
=>\frac{2}{3}\times 3=2
Hence option [B] is the right answer.



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