Basic Maths: Test 20

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Basic Maths: Test 20

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Question 1

$ \displaystyle \frac{{{\left( 0.05 \right)}^{2}}+{{\left( 0.41 \right)}^{2}}+{{\left( 0.073 \right)}^{2}}}{{{\left( 0.005 \right)}^{2}}+{{\left( 0.041 \right)}^{2}}+{{\left( 0.0073 \right)}^{2}}}$

A	10
B	100
C	1000
D	None of these

Question 1 Explanation:

$ \displaystyle \begin{array}{l}Let\,\,0.05=x\,Therefore\,\,0.005=\frac{x}{10}\\0.41=c\,\,Therefore\,\,0.041=\frac{c}{10}\\and\,\,\,\,0.073\,\,=v\,\,therefore\,\,\,\,\,0.0073=\frac{v}{10}\\Therefore\,\,\exp ression\\=\frac{{{x}^{2}}+{{c}^{2}}+{{v}^{2}}}{{{\left( \frac{x}{10} \right)}^{2}}+{{\left( \frac{c}{10} \right)}^{2}}+{{\left( \frac{v}{10} \right)}^{2}}}\\=\frac{{{x}^{2}}+{{c}^{2}}+{{v}^{2}}}{\frac{1}{100}\left( {{x}^{2}}+{{c}^{2}}+{{v}^{2}} \right)}=100\end{array}$

Question 2

$ \displaystyle \frac{\left( 3\frac{1}{3}-2\frac{1}{2} \right)\div \frac{1}{2}\,\,of\,\,1\frac{1}{4}}{\frac{1}{3}+\frac{1}{5}\,\,of\,\,\frac{1}{9}}$

A	1
B	15/4
C	1/5
D	1/2

Question 2 Explanation:

$ \displaystyle \begin{array}{l}\,\frac{\left( \frac{10}{3}-\frac{5}{2} \right)\div \frac{5}{4}\,\times \frac{1}{2}}{\frac{1}{3}+\frac{1}{9}\,\times \frac{1}{5}}\\\frac{\left( \frac{20-15}{6} \right)\div \frac{5}{8}}{\frac{1}{3}+\frac{1}{45}}\\\frac{\frac{5}{6}\times \frac{8}{5}}{\frac{15+1}{45}}=\frac{45}{16}\times \frac{4}{3}=15/4\end{array}$

Question 3

$ \displaystyle \frac{9}{2}-\left[ 2\frac{1}{4}\div \left\{ 1\frac{1}{4}-\frac{1}{2}\left( 1\frac{1}{2}-\frac{1}{3}-\frac{1}{6} \right) \right\} \right]$ is

A	$ 1\frac{1}{2}$
B	$ \displaystyle 2\frac{1}{2}$
C	$ \displaystyle 3\frac{1}{2}$
D	$ \displaystyle 9\frac{1}{2}$

Question 3 Explanation:

$ \displaystyle \begin{array}{l}=\frac{9}{2}-\left[ \frac{9}{4}\div \left\{ \frac{5}{4}-\frac{1}{2}\left( \frac{3}{2}-\frac{1}{3}-\frac{1}{6} \right) \right\} \right]\\=\frac{9}{2}-\left[ \frac{9}{4}\div \left\{ \frac{5}{4}-\frac{1}{2}\left( \frac{9-2-1}{6} \right) \right\} \right]\\=\frac{9}{2}-\left[ \frac{9}{4}\div \left\{ \frac{5}{4}-\frac{1}{2} \right\} \right]\\=\frac{9}{2}-\left[ \frac{9}{4}\div \left\{ \frac{5-2}{4} \right\} \right]\\=\frac{9}{2}-\left[ \frac{9}{4}\div \frac{3}{4} \right]\\=\frac{9}{2}-\frac{9}{4}\times \frac{4}{3}\\=\frac{9}{2}-3\\=\frac{3}{2}\\=1\frac{1}{2}\end{array}$

Question 4

$ \displaystyle \frac{5}{8}\,\,of\,\,\frac{2}{3}\,\,of\,\frac{3}{7}\,\,of\,\,22=?$

A	42/14
B	43/14
C	39/14
D	55/14

Question 4 Explanation:

$ \displaystyle \begin{array}{l}?=\frac{5}{8}\,\,of\,\,\frac{2}{3}\,\,of\,\,\frac{3}{7}\,\,of\,\,22\\=\frac{5}{8}\times \frac{2}{3}\times \frac{3}{7}\times 22=\frac{55}{14}\end{array}$

Question 5

$ \displaystyle \left[ {{\left( 165 \right)}^{2}}\div 75\times 12 \right]\div 24=\left( ? \right)$