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Any municipality that adopts the Comprehensive Water Management protocol must install smart meters in all its commercial buildings. Installing smart meters in all commercial buildings guarantees that a municipality will demonstrate a reduction in peak usage rates. Furthermore, a municipality cannot secure a Regional Infrastructure Grant unless it demonstrates a reduction in peak usage rates. Most municipalities in the Arid Basin region have adopted the Comprehensive Water Management protocol. However, most municipalities in the Arid Basin region failed to secure a Regional Infrastructure Grant.

Which one of the following statements must be true on the basis of the information above?

  1. A
    Most municipalities that have adopted the Comprehensive Water Management protocol are located in the Arid Basin region.
  2. B
    Any municipality that fails to adopt the Comprehensive Water Management protocol will fail to demonstrate a reduction in peak usage rates.
  3. C
    Any municipality that demonstrates a reduction in peak usage rates is guaranteed to secure a Regional Infrastructure Grant.
  4. At least some municipalities that demonstrated a reduction in peak usage rates failed to secure a Regional Infrastructure Grant.Answer
  5. E
    The percentage of municipalities that demonstrated a reduction in peak usage rates is higher in the Arid Basin region than in any other region.

Answer

At least some municipalities that demonstrated a reduction in peak usage rates failed to secure a Regional Infrastructure Grant.
The stimulus establishes that adopting the protocol guarantees a reduction in peak usage rates. Since most municipalities in the Arid Basin adopted the protocol, it must be true that most municipalities in the Arid Basin demonstrated this reduction. The stimulus also explicitly states that most municipalities in the Arid Basin failed to secure a grant. Whenever 'most' (more than 50%) of a specific group has property X, and 'most' of that same group has property Y, there must be at least some overlap between the two subgroups. Therefore, there must be at least some municipalities that have both demonstrated the reduction and failed to secure the grant.

Step-by-Step Solution

1
Diagram the absolute conditional statements established in the stimulus.
Protocol → Smart Meters; Smart Meters → Reduction; Grant → Reduction.
This establishes the necessary and sufficient relationships, allowing us to chain the first two rules: Protocol → Reduction.
2
Analyze the quantifier statements applying to the Arid Basin region.
Arid Basin (most) → Protocol. Arid Basin (most) → No Grant.
Tracking these group-specific quantities is essential for finding overlapping characteristics.
3
Combine the quantifier statements with the established conditional chain.
Because 'Arid Basin (most) → Protocol' and 'Protocol → Reduction', it follows logically that 'Arid Basin (most) → Reduction'.
A conditional rule applies to any member of a group that meets the sufficient condition.
4
Synthesize the two resulting majorities for the Arid Basin region.
More than half of the Arid Basin municipalities demonstrated a Reduction, and more than half of the Arid Basin municipalities received No Grant.
When two 'most' statements apply to the exact same finite group, they must mathematically intersect. Therefore, there is at least one municipality with both characteristics (Reduction AND No Grant).

Key Concept

Combining formal conditional chains with overlapping logical quantifiers (the 'Most + Most = Some' intersection rule).

Alternative Method

You can visualize this mathematically: If there are 100 municipalities in the Arid Basin, 'most' means at least 51. So, at least 51 achieved a reduction. At the same time, at least 51 failed to secure a grant. 51 + 51 = 102, which is greater than 100. This mathematically proves that at least 2 municipalities must fall into both categories.
Estimated Time:2m 0s
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