Basic Maths: Test 6

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These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
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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

$\displaystyle {{2}^{2p-1}}=\frac{1}{{{8}^{p-3}}}$ ,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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