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Basic Maths: Test 8

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Question 1
$\displaystyle 8\sqrt{?}\div 14\times 3+9=29$
What is the value of P
A
7
B
49
C
64
D
None of these
Question 1 Explanation:
$ \displaystyle \begin{array}{l}Let\,\,\,?\,=p\\8\sqrt{p}\div 14\times 3+9=29\\\frac{24\sqrt{p}}{14}+9=29\\\frac{24\sqrt{p}}{14}=20\\24\sqrt{p}=280\\p=1225/9=136.11\end{array}$
Question 2
$ \displaystyle \sqrt{p}+{{\left( 14 \right)}^{2}}\times 18\div 6-1029=-83\times \left( 12-7 \right)$
What is the value of P
A
676
B
567
C
26
D
24
Question 2 Explanation:
$ \displaystyle \begin{array}{l}\sqrt{p}+{{\left( 14 \right)}^{2}}\times 18\div 6-1029=-83\times \left( 12-7 \right)\\\sqrt{p}+196\times 3-1029=-83\times 5\\\sqrt{p}+588-1029=-415\\\sqrt{p}=1029-415-588\\\sqrt{p}=26\\\therefore \,\,p=676\end{array}$
Question 3
$ \displaystyle {{83}^{27.3}}\div {{83}^{14}}\times {{83}^{46.8}}={{83}^{31.9+p}}$
What is the value of P
A
64.1
B
41.9
C
28.2
D
39.1
Question 3 Explanation:
$ \displaystyle \begin{array}{l}{{\left( 83 \right)}^{27.3}}\div {{\left( 83 \right)}^{14}}\times {{\left( 83 \right)}^{46.8}}={{\left( 83 \right)}^{31.9+p}}\\\Rightarrow {{\left( 83 \right)}^{27.3-14+46.8}}={{\left( 83 \right)}^{31.9+p}}\\\Rightarrow {{\left( 83 \right)}^{60.1}}={{\left( 83 \right)}^{31.9+p}}\\\Rightarrow p+31.9=60.1\\\Rightarrow p=60.1-31.9=28.2\end{array}$
Question 4
40% of 586 = 341.2 -p
What is the value of P
A
76.28
B
49.53
C
82.99
D
none
Question 4 Explanation:
$ \displaystyle \begin{array}{l}\frac{586\times 40}{100}=341.2-p\\\Rightarrow \text{234}\text{.4}=341.2-p\\\Rightarrow p=341.2-234.4=106.8\end{array}$
Question 5
$ \displaystyle \left( 504.14\div 14 \right)\div 13=p$
What is the value of P
A
2.77
B
2.56
C
3.14
D
2.17
Question 5 Explanation:
$ \displaystyle p=\frac{504.14}{14\times 13}=2.77$
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