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Basic Maths: Test 41

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Question 1
$\frac{\frac{1}{7}.\frac{1}{7}.\frac{1}{7}+\frac{1}{2}.\frac{1}{2}.\frac{1}{2}-3.\frac{1}{7}.\frac{1}{2}.\frac{1}{5}.+\frac{1}{5}.\frac{1}{5}.\frac{1}{5}}{\frac{1}{7}.\frac{1}{7}+\frac{1}{2}.\frac{1}{2}+\frac{1}{5}.\frac{1}{5}-\left( \frac{1}{7}.\frac{1}{2}+\frac{1}{2}.\frac{1}{5}+\frac{1}{5}.\frac{1}{7} \right)}$ is equal to:
A
$\frac{2}{3}$
B
$\frac{39}{40}$
C
$\frac{59}{60}$
D
$\frac{59}{70}$
Question 1 Explanation:
$\begin{align} & Let\,\,\frac{1}{7}\,\,=a,\frac{1}{2}\,=b\,\,\,and\,\frac{1}{5}\,\,=c \\ & Therefore\,\,\,\,\,\exp ression \\ & =\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-ac-bc} \\ & =\frac{\left( a+b+c \right)\left( {{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-ac-bc \right)}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-ac-bc}=a+b+c \\ & =\frac{1}{7}+\frac{1}{2}+\frac{1}{5} \\ & =\frac{10+35+14}{70} \\ & =\frac{59}{70} \\ \end{align}$
Question 2
The value of $\frac{27-0.064}{9+1.2+0.16}$is:
A
3.6
B
3.4
C
2.6
D
2.4
Question 2 Explanation:
$\begin{align} & =\frac{{{\left( 3 \right)}^{3}}-{{\left( 0.4 \right)}^{3}}}{{{\left( 3 \right)}^{2}}+3\times 0.4+{{\left( 0.4 \right)}^{2}}} \\ & Let\,\,3\,\,=a,\,0.4\,=b \\ & Therefore\,\,\,\,\exp ression \\ & =\frac{{{a}^{3}}-{{b}^{3}}}{{{a}^{2}}+ab+{{b}^{2}}} \\ & =\frac{\left( a-b \right)\left( {{a}^{2}}+ab+{{b}^{2}} \right)}{{{a}^{2}}+ab+{{b}^{2}}} \\ & =a-b=3-0.4=2.6 \\ \end{align}$
Question 3
$10.9-\left[ 9.8-\left\{ 8.7-\left( 7.6-\overline{6.5-4} \right)\, \right\}\, \right]$is simplified to:
A
2.7
B
3.7
C
4.7
D
5.7
Question 3 Explanation:
$\begin{align} & =10.9-\left[ 9.8-\left\{ 8.7-\left( 7.6-\overline{6.5-4} \right)\, \right\}\, \right] \\ & =10.9-\left[ 9.8-\left\{ 8.7-\left( 7.6-2.5 \right)\, \right\}\, \right] \\ & =10.9-\left[ 9.8-\left\{ 8.7-4.1\, \right\}\, \right] \\ & =10.9-\left[ 9.8-4.6\, \right] \\ & =10.9-5.2 \\ & =5.7 \\ \end{align}$
Question 4
$\frac{1\frac{1}{10}\div 1\frac{1}{5}}{\left( \frac{11}{12}+1-\frac{5}{6} \right)}$ is equal to:
A
11/15
B
13/11
C
11/13
D
15/17
Question 4 Explanation:
$\begin{align} & =\frac{1\frac{1}{10}\div 1\frac{1}{5}}{\left( \frac{11}{12}+1-\frac{5}{6} \right)} \\ & =\frac{\frac{11}{10}\times \frac{5}{6}}{\left( \frac{11+12-10}{12} \right)} \\ & =\frac{\frac{11}{10}\times \frac{5}{6}}{\frac{13}{12}}=\frac{11}{12}\times \frac{12}{13}=\frac{11}{13} \\ \end{align}$
Question 5
The greatest number among $0.9+\sqrt{.09,}\,\,1.4\,\,-\frac{1.2}{24},\,\,1.5\times 0.89\,\,and\,\,\sqrt{1.21}$ is:
A
$0.9+\sqrt{0.09}$
B
$\sqrt{1.21}$
C
$1.5\times 0.89$
D
$1.4-\frac{1.2}{24}$
Question 5 Explanation:
$\begin{align} & 0.9+\sqrt{0.09} \\ & =0.9+0.3=1.2 \\ & 1.4-\frac{1.2}{24} \\ & =1.4-0.05 \\ & =1.35 \\ & 1.5\times 0.89=1.335 \\ & \sqrt{1.21}=1.1 \\ & Hence,\,\,\,the\,\,\,greatest\,\,\,\,number \\ & =1.4-\frac{1.2}{24} \\ \end{align}$
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