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Basic Maths: Test 35

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Question 1
$ \displaystyle \frac{2\frac{1}{3}-\frac{5}{7}\,of\,\frac{7}{10}}{3\frac{1}{2}\div \frac{7}{6}\left( \frac{9}{14}+11\frac{1}{7} \right)}-\left[ \left( 2\frac{3}{4}\,of\,2\frac{2}{11} \right)\div 135 \right]$
is equal to
A
1
B
1/135
C
135
D
$15\frac{1}{2}$
Question 1 Explanation:
3
Question 2
The value of $\frac{0.5\times 0.5\times 0.5+0.7\times 0.7\times 0.7+0.9\times 0.9\times 0.9-3\times 0.5\times 0.7\times 0.9}{0.5\times 0.5+0.7\times 0.7+0.9\times 0.9-0.5\times 0.7-0.7\times 0.9-0.9\times 0.5}$ is
A
0.21
B
0.02
C
1
D
2.1  
Question 2 Explanation:
\[\begin{align} & Let\,\,\,0.5\,\,=a,\,\,0.7=b\,\,and\,\,0.9=c \\ & Then,\,\,we\,\,have, \\ & \frac{a\times a\times a+b\times b\times b+c\times c\times c-3abc}{a\times a+b\times b+c\times c-ab-bc-ac} \\ & =\frac{{{a}^{3}}+b{}^{3}+{{c}^{3}}-3abc}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ac} \\ & =\frac{\left( a+b+c \right)\left( {{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ac \right)}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ac} \\ & =a+b+c \\ & =0.5+0.7+0.9=2.1 \\ \end{align}\]
Question 3
The value of $\frac{4.096\times 5241\times 2.167}{49.986\times 1362.114}$is closest to
A
0.062
B
0.62
C
6.2
D
62
Question 3 Explanation:
Taking approximate values, we have $\frac{4\times 5241\times 2}{50\times 1362}=0.61568=0.62$
Question 4
$\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}=?$
A
$12$
B
$\frac{1}{9}$
C
$\frac{5}{27}$
D
$\frac{1}{12}$
Question 4 Explanation:
$\begin{align} & \frac{1}{6\times 7}+\frac{1}{7\times 8}+\frac{1}{8\times 9}+\frac{1}{9\times 10}+\frac{1}{10\times 11}+\frac{1}{11\times 12} \\ & =\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12} \\ & =\frac{1}{6}-\frac{1}{12}=\frac{2-1}{12}=\frac{1}{12} \\ \end{align}$
Question 5
Simplify $\sqrt{\,\left[ \,{{\left( 10.1 \right)}^{2}}-{{\left( 6.1 \right)}^{2}} \right]/\left[ \,{{\left( 0.25 \right)}^{2}}+\left( 0.25 \right)\,\left( 15.95 \right)\, \right]}$
A
1
B
2
C
3
D
4
Question 5 Explanation:
$\begin{align} & \sqrt{\frac{16.2\times 4}{0.25\times 16.2}}=\sqrt{\frac{4}{0.25}} \\ & =\sqrt{\frac{400}{25}}=\sqrt{16}=4 \\ \end{align}$
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