Percent problems

2010018205

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.
\(73\%\)
\(70\%\)
\(30\%\)
\(27\%\)

2000016301

Level: 
C
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.

2010008304

Level: 
A
At the beginning of the therapy, three monitored patients were of the same weight. Their weights were changing as follows: (a) Patient A gained \(6\%\) of his weight and then his weight did not change. (b) Patient B lost \(2\%\) of his weight first, but later he gained \(8\%\) of his weight. (c) Patient C gained \(2\%\) of his weight and later he gained another \(4\%\) of his weight. Which patient has the lowest weight after the therapy?
Patient B
Patient A
Patient C
After described weight changes everyone will weigh the same.

2010008303

Level: 
A
Three merchants were selling the same product for the same price. Successively they adjusted the prices as follows: (a) Merchant A first increased the price of the product by \(5\%\), but later reduced it by \(10\%\). (b) Merchant B first reduced the price of the product by \(2\%\) and later reduced it again, this time by \(3\%\). (c) Merchant C adjusted the price of the product only once. He cheapened the product by \(10\%\). Which merchant offers the product for the highest price after price adjustments?
Merchant B
Merchant A
Merchant C
All merchants will sell the product for the same price.

2010008302

Level: 
A
During epidemic the towns reported the ratios of ill citizens (see the table). Which town had the biggest number of ill citizens on 1$^{\mathrm{st}}$ July. \[\begin{array}{|c|c|c|} \hline \text{Town} & \text{Total population} & \text{Ratio of ill citizens on 1\(^{\mathrm{st}}\) July 2020} \\\hline A & 8\,000 & 4.0\% \\\hline B & 64\,000 & 0.5\% \\\hline C & 320\,000 & 0.1\% \\\hline \end{array}\]
All towns had the same number of ill citizens.
The biggest number of ill citizens was in the town A.
The biggest number of ill citizens was in the town B.
The biggest number of ill citizens was in the town C.

2010008301

Level: 
A
Three companies made a commitment to donate a portion of their annual profit to charity (see the table). Which company did donate the biggest sum? \[\begin{array}{|c|c|c|} \hline \text{Company} & \text{Annual profit} & \text{Ratio from annual profit} \\\hline A & 6\,000\,000 & 4.0\% \\\hline B & 12\,000\,000 & 2.0\% \\\hline C & 48\,000\,000 & 0.5\% \\\hline \end{array}\]
All companies donated the same sum.
The biggest donor was the company A.
The biggest donor was the company B.
The biggest donor was the company C.