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Basic Maths: Test 6

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Your answers are highlighted below.
Question 1
What is the value of p ?
$\displaystyle \frac{p}{\sqrt{130}}=\frac{\sqrt{170}}{p}$
A
196
B
12
C
144
D
16
Question 1 Explanation: 
$ \displaystyle \begin{array}{l}\frac{p}{\sqrt{130}}=\frac{\sqrt{170}}{p}\\{{\left( p \right)}^{2}}=\sqrt{130}\times \sqrt{170}\\=11.40\times 13.03=148.542\\p=\sqrt{148.542}\approx 12\end{array}$
Question 2
$ \displaystyle If\,\,\,\,1.5p=0.04q$,then the value of $ \displaystyle \left( \frac{q-p}{q+p} \right)\,\,is:$
A
730/77
B
73/77
C
7.3/77
D
703/77
Question 2 Explanation: 
$ \displaystyle \begin{array}{l}1.5p=0.04q\\\Rightarrow \frac{p}{q}=\frac{0.04}{1.5}=\frac{4}{150}=\frac{2}{75}\\\therefore \,\,Expression\,\,=\frac{q-p}{q+p}=\frac{1-\frac{p}{q}}{1+\frac{p}{q}}\\=\frac{1-\frac{2}{75}}{1+\frac{2}{75}}=\frac{\frac{75-2}{75}}{\frac{75+2}{75}}\\=\frac{73}{75}\times \frac{75}{77}=\frac{73}{77}\end{array}$
Question 3
If $\displaystyle {{2}^{2p-1}}=\frac{1}{{{8}^{p-3}}}$,then the value of p is:
A
–1
B
–2
C
2
D
3
Question 3 Explanation: 
$ \displaystyle \begin{array}{l}{{2}^{2p-1}}=\frac{1}{{{8}^{p-3}}}={{8}^{-\left( p-3 \right)}}\\\Rightarrow {{2}^{2p-1}}={{8}^{3-p}}={{\left( {{2}^{3}} \right)}^{\left( 3-p \right)}}\\\Rightarrow {{2}^{2p-1}}={{2}^{9-3p}}\\\Rightarrow 2p-1=9-3p\\\Rightarrow 2p+3p=9+1\\\Rightarrow 5p=10\\\Rightarrow p=\frac{10}{5}=2\end{array}$
Question 4
$ \displaystyle 36865+12473+21045-44102=p$
A
114485
B
28081
C
26281
D
114845
Question 4 Explanation: 
$ \displaystyle \begin{array}{l}p=36865+12473+21045-44102\\=70383-44102=26281\end{array}$
Question 5
$\displaystyle 5328\times \frac{3}{4}\times \frac{2}{9}\times p=619$
A
0.69
B
1.5
C
0.2
D
2.4
Question 5 Explanation: 
$ \displaystyle \begin{array}{l}5328\times \frac{3}{4}\times \frac{2}{9}\times p=619\\\Rightarrow 888\times p=619\\\Rightarrow p=\frac{619}{888}=0.69\end{array}$
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