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Zorluk: OrtaNumerical, Proportion, and Statistical Inferences

In 2022, synthetic fiber products accounted for exactly 30 percent of the total metric tons of textile exports produced by Country X, with natural fiber products making up the remaining 70 percent. In 2025, synthetic fiber products accounted for 50 percent of Country X's total metric tons of textile exports, while natural fiber products made up the remaining 50 percent. If the total volume (in metric tons) of synthetic fiber textile exports produced by Country X increased by 20 percent from 2022 to 2025, which of the following statements must be true based on the information provided?

  1. The total volume (in metric tons) of natural fiber textile exports produced by Country X was lower in 2025 than in 2022.Cevap
  2. B
    Country X exported a greater total metric tonnage of textiles overall in 2025 than it did in 2022.
  3. C
    In 2025, Country X generated more monetary revenue from synthetic fiber textile exports than from natural fiber textile exports.
  4. D
    The global market demand for natural fiber textiles experienced a significant decline between 2022 and 2025.
  5. E
    The volume (in metric tons) of natural fiber textile exports produced by Country X decreased by more than 60 percent between 2022 and 2025.

Cevap

The total volume (in metric tons) of natural fiber textile exports produced by Country X was lower in 2025 than in 2022.
The option stating that natural fiber export volume was lower in 2025 than in 2022 is logically inescapable. Letting the 2022 synthetic volume be SS, the total 2022 volume is S/0.30S / 0.30, making 2022 natural fiber volume 2.333S2.333S. In 2025, synthetic volume grows by 20 percent to 1.20S1.20S. Because synthetic fiber constitutes 50 percent of the 2025 total, natural fiber must also equal 1.20S1.20S. Comparing 1.20S1.20S to 2.333S2.333S proves a mandatory decline in natural fiber export volume.

Adım Adım Çözüm

1
Express the 2022 volumes in terms of an arbitrary variable for synthetic fiber volume.
Let 2022 synthetic fiber volume equal SS. Total 2022 volume V1=S/0.30=3.333SV_1 = S / 0.30 = 3.333S. 2022 natural fiber volume = 0.70×V1=2.333S0.70 \times V_1 = 2.333S.
Establishing base relationships allows precise mathematical comparison between years.
2
Calculate the 2025 volumes using the given 20 percent increase in synthetic fiber exports.
2025 synthetic fiber volume = 1.20S1.20S. Since synthetic fibers represented 50 percent of total 2025 volume V2V_2, V2=1.20S/0.50=2.40SV_2 = 1.20S / 0.50 = 2.40S. 2025 natural fiber volume = 0.50×2.40S=1.20S0.50 \times 2.40S = 1.20S.
Translating the 20 percent volume increase into 2025 total and category volumes.
3
Compare the 2022 and 2025 natural fiber volumes.
2022 natural fiber volume = 2.333S2.333S, while 2025 natural fiber volume = 1.20S1.20S. Since 1.20S<2.333S1.20S < 2.333S, natural fiber export volume necessarily decreased.
Direct mathematical deduction shows that natural fiber volume was strictly lower in 2025.

Anahtar Kavram

Combining proportions and absolute subgroup growth to derive absolute changes in remaining categories.
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Numerical, Proportion, and Statistical Inferences

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