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Question

Difficulty: MediumNumerical, Proportion, and Statistical Inferences

In 2022, organic crop protection treatments accounted for exactly 25 percent of all crop protection treatments applied in Region Z. By 2025, organic treatments accounted for 40 percent of all crop protection treatments in the region. During the same 2022–2025 period, the total number of non-organic crop protection treatments applied in Region Z decreased by 20 percent. If the statements above are true, which of the following must also be true regarding crop protection treatments in Region Z?

  1. The total number of crop protection treatments applied in Region Z was the same in 2025 as it was in 2022.Answer
  2. B
    The total volume of synthetic chemicals used in non-organic treatments decreased by more than 20 percent between 2022 and 2025.
  3. C
    The total number of organic crop protection treatments applied in Region Z was lower in 2025 than in 2022.
  4. D
    Farmer satisfaction with organic crop protection treatments increased significantly in Region Z between 2022 and 2025.
  5. E
    The percentage increase in organic treatments from 2022 to 2025 was equal to the percentage decrease in non-organic treatments.

Answer

The total number of crop protection treatments applied in Region Z was the same in 2025 as it was in 2022.
The option stating that total crop protection treatments remained the same in 2025 as in 2022 is logically inescapable. In 2022, non-organic treatments accounted for 75%75\% of total applications. A 20%20\% decrease in non-organic treatments leaves 0.75×0.80=60%0.75 \times 0.80 = 60\% of the original 2022 total volume. Since non-organic treatments represent 60%60\% of the 2025 total volume (as organic is 40%40\%), 60%60\% of the 2025 total equals 60%60\% of the 2022 total. Thus, the total overall volume did not change.

Step-by-Step Solution

1
Define total treatments in 2022 as T2022T_{2022} and express 2022 non-organic treatments.
Non-organic treatments in 2022 equaled 75%75\% of T2022T_{2022}, or 0.75⋅T20220.75 \cdot T_{2022}.
Since organic treatments were 25%25\%, non-organic treatments comprised the remaining 75%75\%.
2
Calculate the absolute number of non-organic treatments in 2025.
Non-organic treatments in 2025 equaled 0.75⋅T2022⋅(1−0.20)=0.60⋅T20220.75 \cdot T_{2022} \cdot (1 - 0.20) = 0.60 \cdot T_{2022}.
The stimulus states that non-organic treatments decreased by 20%20\% from 2022 to 2025.
3
Relate the 2025 non-organic treatment count to the total 2025 treatments (T2025T_{2025}).
In 2025, non-organic treatments were 60%60\% of T2025T_{2025}, so 0.60⋅T2025=0.60⋅T20220.60 \cdot T_{2025} = 0.60 \cdot T_{2022}, which simplifies to T2025=T2022T_{2025} = T_{2022}.
Because organic treatments were 40%40\% of T2025T_{2025}, non-organic treatments accounted for 60%60\% of T2025T_{2025}.

Key Concept

Calculating absolute values from relative percentages and percentage changes
Estimated Time:2m 0s
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Topics

Numerical, Proportion, and Statistical Inferences

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