Percent problems and financial mathematics
7400120041
Submitted by michaela.bailova on Thu, 01/04/2024 - 17:012010018205
Level:
A
The number of traffic accidents in the monitored cities changed year on year. It increased by \(20\%\) in city A and decreased by \(1\%\) in city B. Decide which of the following statements is correct:
\[
\begin{array}{l}
\text{X: The same number of accidents occurred in city A as in city B the last year.} \\
\text{Y: There were more accidents in city A than in city B the last year.} \\
\text{Z: There have been fewer accidents in city B than in city A this year.}\\
\end{array}
\]
The correctness of any of the above statements cannot be verified from the given data.
Only statement X is true.
Only statement Y is true.
Only statement Z is true.
2010018204
Level:
B
The aluminium rod and brass rod have the same length at a given temperature. The material constants of the rods are: \(\alpha_{\mathrm{aluminium}}=24\cdot 10^{-6}\,\mathrm{K}^{-1}\) and \(\alpha_{\mathrm{brass}}=18\cdot 10^{-6}\,\mathrm{K}^{-1}\). Suppose both rods are heated to the same higher temperature. Find the true statement about the extensions of both rods. Round the percentage difference in the rods’ extensions to the whole percent.
\[~\]
Hint: Solid materials expand upon heating. The rod with the initial length \(l_0\) is upon the temperature increasing by \(\Delta t\) extended by the value \(\Delta l = l_0 \cdot \alpha \cdot \Delta t\), where \(\alpha\) is the material constant (coefficient of linear thermal expansion) that is indicative of the extent to which a material expands upon heating.
The extension of the aluminium rod is by \(33\%\) greater than the extension of the brass rod.
The extension of the aluminium rod is by \(67\%\) greater than the extension of the brass rod.
The extension of the aluminium rod is by \(133\%\) greater than the extension of the brass rod.
The extension of the aluminium rod is by \(33\%\) less than the extension of the brass rod.
2010018203
Level:
B
A protective layer of thickness \(d\) reduces the level of harmful radiation by \(10\%\). Determine what is the percentage decrease in the original level of harmful radiation after passing through the layer of thickness \(3d\). Round the result to the whole percent.
\(73\%\)
\(70\%\)
\(30\%\)
\(27\%\)
2010018202
Level:
B
A rectangle is drawn in a scale drawing with the scale factor of \(1:5\). By what percentage is the area of the drawn rectangle smaller than the area of the real unscaled rectangle?
by \(96\%\)
by \(4\%\)
by \(20\%\)
by \(80\%\)
2010018201
Level:
B
We measured the length of a rod to be \(2\,\mathrm{m}\). What is the possible maximum length of the rod, if the percentage error of the measurement was \(5\%\).
\(210\,\mathrm{cm}\)
\(205\,\mathrm{cm}\)
\(200\,\mathrm{cm}\)
\(195\,\mathrm{cm}\)
2000016301
Level:
B
Investors Thomas and Paul invested the same amount. After the first year, the value of Thomas's investments decreased by \(5{\small{{}^\text{o}\mkern-5mu/\mkern-3mu_\text{o}}}\), but after the following year, their value increased by \(5{\small{{}^\text{o}\mkern-5mu/\mkern-3mu_\text{o}}}\). Paul's investments were more stable. After the first year, the value of his investments increased by \(2{\small{{}^\text{o}\mkern-5mu/\mkern-3mu_\text{oo}}}\), but after the second year, it decreased again by \(2{\small{{}^\text{o}\mkern-5mu/\mkern-3mu_\text{oo}}}\). Determine the true statement about the value of Thomas and Paul's investments two years after the investment.
Paul's investments will have a higher value.
Thomas's investments will have a higher value.
The values of both investments will again be the same.
It is not possible to determine the ratio of the values of Paul and Thomas's investments from the given data.