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Difficulty: Very hardIdentifying Must-Be-True Statements and Valid Deductions

A municipal energy commission released a report containing the following facts regarding regional energy infrastructure:

• In any municipality where smart meters were installed in more than 80 percent of residential units, peak-hour electricity demand decreased by at least 15 percent during summer months.
• In every municipality where peak-hour electricity demand decreased by at least 15 percent during summer months, municipal electricity tax revenues fell unless local utility rates were increased.
• Last summer, District X had smart meters installed in 90 percent of its residential units, while its local utility rates were held constant.

If the statements above are true, which of the following must also be true regarding District X last summer?

  1. Municipal electricity tax revenues in District X fell.Answer
  2. B
    Any municipality that experienced a fall in electricity tax revenues last summer must have installed smart meters in more than 80 percent of its residential units.
  3. C
    Overall residential electricity consumption in District X declined during non-summer months last year.
  4. D
    The installation of smart meters in District X directly caused the municipal government to suffer an overall fiscal budget deficit.
  5. E
    If District X increases its local utility rates next summer, peak-hour electricity demand will increase by more than 15 percent.

Answer

Municipal electricity tax revenues in District X fell last summer.
The conclusion that municipal electricity tax revenues in District X fell is strictly guaranteed by combining the premises. First, because District X installed smart meters in 90% of units (exceeding the 80% threshold), peak-hour electricity demand was guaranteed to decrease by at least 15% last summer. Second, the premises state that whenever such a demand decrease occurs, tax revenues fall unless utility rates are raised. Because District X held utility rates constant, tax revenues must have fallen.

Step-by-Step Solution

1
Analyze Premise 1 and apply facts given for District X.
Smart meters were installed in 90% of residential units in District X (> 80%). Therefore, peak-hour electricity demand in District X decreased by at least 15% last summer.
The rule states that Smart Meters > 80% guarantees Peak Demand Decrease ≥ 15% in summer.
2
Analyze Premise 2 and synthesize with the result from Step 1.
Since Peak Demand Decrease ≥ 15% occurred, municipal electricity tax revenues fell UNLESS local utility rates were increased.
Conditional rule: Peak Demand Decrease ≥ 15% ⇒ (Tax Revenue Fell OR Utility Rates Increased).
3
Evaluate the condition regarding utility rates in District X.
Local utility rates were held constant (not increased). Therefore, the 'unless' exception is false, forcing the main clause—municipal electricity tax revenues fell—to be true.
When the alternative condition (rate increase) is explicitly negated, the remaining outcome (revenue fall) must occur.

Key Concept

Identifying Must-Be-True Statements and Valid Deductions
Estimated Time:2m 0s
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Identifying Must-Be-True Statements and Valid Deductions

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