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Zorluk: OrtaDrawing Inferences and Valid Conclusions

In Region K, agricultural water permits are issued annually based on historical crop yield metrics. In 2024, farms growing low-yield staple crops received 40 percent lower base water allocations than farms cultivating high-yield cash crops. However, regional environmental regulations dictate that any farm reducing its overall synthetic fertilizer usage by at least 25 percent in a given year is automatically granted a 30 percent bonus to its base water allocation for the subsequent year. In 2024, every farm cultivating high-yield cash crops reduced its synthetic fertilizer usage by more than 30 percent.

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

  1. In 2025, every farm that cultivated high-yield cash crops in 2024 will qualify for a 30 percent bonus to its base water allocation.Cevap
  2. B
    In 2024, farms cultivating high-yield cash crops consumed less total water than farms growing low-yield staple crops.
  3. C
    Any farm in Region K that reduced its synthetic fertilizer usage by more than 30 percent in 2024 cultivated high-yield cash crops.
  4. D
    In 2025, farms growing low-yield staple crops will receive lower total water allocations than farms cultivating high-yield cash crops.
  5. E
    Reducing synthetic fertilizer usage is the most effective method for farms in Region K to increase their overall crop yields.

Cevap

In 2025, every farm that cultivated high-yield cash crops in 2024 will qualify for a 30 percent bonus to its base water allocation.
The passage explicitly defines a rule: any farm reducing synthetic fertilizer usage by at least 25 percent in one year receives a 30 percent bonus to its base water allocation the next year. Since every farm cultivating high-yield cash crops reduced fertilizer usage by more than 30 percent in 2024, every such farm met the condition and must qualify for the 30 percent allocation bonus in 2025.

Adım Adım Çözüm

1
Identify the rule governing water allocation bonuses.
A farm qualifies for a 30% water allocation bonus in year N+1 if it reduces synthetic fertilizer usage by at least 25% in year N.
This sets up the conditional requirement for earning the bonus.
2
Apply the 2024 performance facts to the rule.
In 2024, every high-yield cash crop farm reduced fertilizer usage by more than 30%, which satisfies the 'at least 25%' threshold.
Because all high-yield cash crop farms met the necessary requirement, all of them must receive the specified bonus in 2025.
3
Evaluate option choices to find the statement that must be true without external assumptions.
The statement asserting that every high-yield cash crop farm from 2024 qualifies for the 30 percent bonus in 2025 is mathematically and logically sound.
It is a direct deduction requiring no outside information.

Anahtar Kavram

Combining conditional rules and factual premises to derive a logically necessary conclusion.
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