Basic Maths: Test 8

This is an assessment test.
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

$\displaystyle 8\sqrt{?}\div 14\times 3+9=29$
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