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Basic Maths: Test 45

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Question 1
Which of the following is greater than $\left( 1-\frac{1}{100} \right)\,\left( 1-\frac{1}{101} \right)\,\left( 1-\frac{1}{102} \right)\,......\left( 1-\frac{1}{200} \right)$ :
A
0.2
B
0.3
C
0.4
D
0.5
Question 1 Explanation:
$\begin{align} & \left( 1-\frac{1}{100} \right)\,\left( 1-\frac{1}{101} \right)\,\left( 1-\frac{1}{102} \right)\,......\left( 1-\frac{1}{200} \right) \\ & =\frac{99}{100}\times \frac{100}{101}\times \frac{101}{102}\times .....\frac{199}{200}=\frac{99}{200} \\ \end{align}$
Is less than 0.5
Question 2
${{\left( \sqrt{3}+\frac{1}{\sqrt{3}} \right)}^{2}}$ is equal to:
A
$2\frac{1}{3}$
B
$3\frac{1}{3}$
C
$4\frac{1}{3}$
D
$5\frac{1}{3}$
Question 2 Explanation:
$\begin{align} & {{\left( \sqrt{3}+\frac{1}{\sqrt{3}} \right)}^{2}} \\ & =3+\frac{1}{3}+2\times \sqrt{3}\times \frac{1}{\sqrt{3}}=5\frac{1}{3} \\ \end{align}$
Question 3
The value of ${{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11-1$ is:
A
1.98
B
1.09
C
1
D
0
Question 3 Explanation:
Expression
$\begin{align} & {{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11-1 \\ & ={{\left( .89 \right)}^{3}}+{{\left( 0.11 \right)}^{3}}+3\times .89\times .11\left( 0.89+0.11 \right)-1 \\ & ={{\left( 0.89+0.11 \right)}^{3}}-1=1-1=0 \\ \end{align}$
Question 4
$7.4\overline{2}+0.\overline{8}+0.00\overline{3}$ is equal to
A
$8.\overline{313}$
B
$8.3\overline{13}$
C
$8.31\overline{3}$
D
$8.3\overline{13}$
Question 4 Explanation:
5
Question 5
The value of $\frac{4}{5}\times \frac{5}{\frac{7}{9}\div \frac{5}{3}\,\,of\,\,1\frac{6}{15}}$ is
A
2.5
B
12
C
10
D
5
Question 5 Explanation:
Expression
\[\begin{align} & =\frac{4}{5}\times \frac{5}{\frac{7}{9}\div \frac{5}{3}\times \frac{21}{15}} \\ & =\frac{4}{5}\times 15=12 \\ \end{align}\]
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