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Difficulty: Very hardNumerical, Proportion, and Statistical Inferences

From 2015 to 2025, solar power generation in Country X expanded rapidly, growing from supplying 5 percent of the nation's total electricity consumption to 20 percent. Over the same ten-year period, the average greenhouse gas emissions per megawatt-hour of electricity generated from non-solar sources decreased by 10 percent. Total electricity consumption in Country X increased by 50 percent between 2015 and 2025.

If the statements above are true, which of the following must also be true on the basis of them?

  1. The total volume of greenhouse gas emissions produced by non-solar electricity generation in Country X was greater in 2025 than it was in 2015.Answer
  2. B
    Because the proportion of non-solar energy in the grid fell from 95 percent to 80 percent and its emission rate dropped by 10 percent, non-solar electricity generation emitted fewer total tons of greenhouse gases in 2025 than in 2015.
  3. C
    In 2025, non-solar energy sources generated a smaller total number of megawatt-hours of electricity than they did in 2015.
  4. D
    Total greenhouse gas emissions from all electricity generation in Country X decreased overall between 2015 and 2025 because of the quadrupling of solar capacity.
  5. E
    Solar power generation prevented a larger quantity of greenhouse gas emissions in 2025 than all technological improvements in non-solar power plants combined.

Answer

The total volume of greenhouse gas emissions produced by non-solar electricity generation in Country X was greater in 2025 than it was in 2015.
The conclusion that non-solar greenhouse gas emissions were greater in 2025 than in 2015 is mathematically inescapable. Setting 2015 total consumption to 100 units yields 95 non-solar units at rate RR (95R95R emissions). A 50 percent growth in total electricity by 2025 yields 150 units, 80 percent of which is non-solar (120 units). At a reduced rate of 0.90R0.90R, non-solar emissions equal 120×0.90R=108R120 \times 0.90R = 108R, which exceeds 95R95R.

Step-by-Step Solution

1
Calculate 2015 baseline non-solar production and emissions
If 2015 Total Electricity = 100 units, Non-Solar Electricity = 95 units (95%). With emission rate RR, 2015 Emissions = 95R95R.
Establishes the quantitative starting point based on stimulus premises.
2
Calculate 2025 total electricity and non-solar production
2025 Total Electricity = 100×1.50=150100 \times 1.50 = 150 units. Non-Solar Share = 100%−20%=80%100\% - 20\% = 80\%. Non-Solar Electricity = 150×0.80=120150 \times 0.80 = 120 units.
Combines total consumption growth (+50%) with the new solar grid proportion (20%).
3
Calculate 2025 non-solar emissions rate and total non-solar emissions
2025 Emission Rate = 0.90R0.90R. 2025 Non-Solar Emissions = 120×0.90R=108R120 \times 0.90R = 108R.
Applies the 10% rate reduction to the new non-solar production volume.
4
Compare 2015 and 2025 absolute emissions
108R>95R108R > 95R, proving non-solar emissions increased by 13.68%.
Identifies the logically inescapable deduction.

Key Concept

Disentangling Percentage Proportions from Absolute Quantities
Estimated Time:2m 30s
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Topics

Numerical, Proportion, and Statistical Inferences

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