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Zorluk: ZorNumerical, Proportion, and Statistical Inferences

In 2021, Phase III trials constituted exactly 15 percent of all clinical drug trials conducted by Apex BioTech. By 2025, Phase III trials represented 25 percent of the company's total clinical drug trials. If the total number of clinical drug trials conducted by Apex BioTech that were NOT Phase III trials increased by 20 percent from 2021 to 2025, which of the following statements must be true based on the information above?

  1. Apex BioTech conducted a greater total number of Phase III clinical drug trials in 2025 than it did in 2021.Cevap
  2. B
    The absolute expenditure on Phase III clinical trials at Apex BioTech increased by exactly 10 percentage points between 2021 and 2025.
  3. C
    Apex BioTech conducted fewer total clinical drug trials across all phases in 2025 than it conducted in 2021.
  4. D
    Phase III clinical trials conducted in 2025 were significantly more likely to yield successful market approvals than those conducted in 2021.
  5. E
    The proportion of non-Phase III trials that successfully advanced to Phase III status doubled between 2021 and 2025.

Cevap

Apex BioTech conducted a greater total number of Phase III clinical drug trials in 2025 than it did in 2021.
The correct option is mathematically mandatory. Let total trials in 2021 equal 100. Non-Phase III trials in 2021 equal 85, and Phase III trials equal 15. In 2025, non-Phase III trials increased by 20% to 85×1.20=10285 \times 1.20 = 102. Since non-Phase III trials represent 75% of the 2025 total, the total number of trials in 2025 is 1020.75=136\frac{102}{0.75} = 136. Consequently, Phase III trials in 2025 equal 136−102=34136 - 102 = 34. Because 34 is greater than 15, the company undeniably conducted more Phase III trials in 2025 than in 2021.

Adım Adım Çözüm

1
Define variables for the total trial counts in 2021 (T2021T_{2021}) and 2025 (T2025T_{2025}).
In 2021, Phase III trials = 0.15T20210.15 T_{2021} and non-Phase III trials = 0.85T20210.85 T_{2021}. In 2025, Phase III trials = 0.25T20250.25 T_{2025} and non-Phase III trials = 0.75T20250.75 T_{2025}.
Establishing exact mathematical representations of the given proportions allows for direct structural comparison.
2
Relate the non-Phase III trial volume of 2025 to 2021 using the given 20% increase.
0.75T2025=1.20×(0.85T2021)=1.02T20210.75 T_{2025} = 1.20 \times (0.85 T_{2021}) = 1.02 T_{2021}. Solving for T2025T_{2025} yields T2025=1.020.75T2021=1.36T2021T_{2025} = \frac{1.02}{0.75} T_{2021} = 1.36 T_{2021}.
This proves that the total number of clinical trials increased by 36% overall from 2021 to 2025.
3
Calculate the absolute change in the number of Phase III trials.
In 2021, Phase III volume = 0.15T20210.15 T_{2021}. In 2025, Phase III volume = 0.25T2025=0.25×(1.36T2021)=0.34T20210.25 T_{2025} = 0.25 \times (1.36 T_{2021}) = 0.34 T_{2021}.
Comparing 0.34T20210.34 T_{2021} to 0.15T20210.15 T_{2021} shows that the absolute count of Phase III trials increased from 15% to 34% of the 2021 baseline total, confirming an undeniable increase.

Anahtar Kavram

Inferring absolute numerical shifts from proportional changes and base rate adjustments
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Numerical, Proportion, and Statistical Inferences

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