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Difficulty: Very hardMust Be True Questions

According to the federal health regulations, every new pharmaceutical compound approved by the Federal Health Board (FHB) has demonstrated efficacy in phase III trials and has a negligible risk of severe side effects. If a pharmaceutical compound has a negligible risk of severe side effects, it is classified as safe for outpatient distribution, unless it requires intravenous administration. Furthermore, all compounds that require intravenous administration are restricted to hospital use only, while no compound classified as safe for outpatient distribution is restricted to hospital use only.

Based on the information above, which of the following statements must be true? (Select all that apply.)

  1. No compound approved by the Federal Health Board is both classified as safe for outpatient distribution and requires intravenous administration.Answer
  2. B
    Any pharmaceutical compound that has demonstrated efficacy in phase III trials has a negligible risk of severe side effects.
  3. Any pharmaceutical compound restricted to hospital use only does not have a negligible risk of severe side effects, unless it requires intravenous administration.Answer
  4. D
    Any pharmaceutical compound classified as safe for outpatient distribution has a negligible risk of severe side effects.
  5. E
    At least one pharmaceutical compound approved by the Federal Health Board is restricted to hospital use only.

Answer

The correct statements are that no approved compound can be both safe for outpatient use and require IV administration, and that any hospital-restricted compound without an IV requirement does not have a negligible risk.
The correct answers are the statements that 'no compound approved by the Federal Health Board is both classified as safe for outpatient distribution and requires intravenous administration' and 'any pharmaceutical compound restricted to hospital use only does not have a negligible risk of severe side effects, unless it requires intravenous administration'. The first is correct because any compound that is safe for outpatient distribution cannot be restricted to hospital use, while any intravenous compound MUST be restricted to hospital use. Thus, these two classifications are mutually exclusive for all compounds. The second is correct based on the contrapositive of the second premise: if a compound has a negligible risk, it is safe for outpatient OR intravenous. If it is restricted to hospital use, it is NOT safe for outpatient. If it is also NOT intravenous, then both conditions of the 'OR' statement fail, meaning the compound cannot logically have a negligible risk.

Step-by-Step Solution

1
Translate the text into formal logical conditional statements.
1. Approved -> Efficacy AND Negligible Risk. 2. Negligible Risk -> Safe for Outpatient OR Intravenous (IV). 3. IV -> Hospital Only. 4. Safe for Outpatient -> NOT Hospital Only.
Translating to formal logic ensures that deductive inferences are strictly governed by structural rules, preventing real-world assumptions.
2
Combine the rules regarding hospital restrictions to find constraints on IV and outpatient status.
Since 'IV -> Hospital Only' and 'Safe for Outpatient -> NOT Hospital Only', a compound cannot be both IV and Safe for Outpatient. They are mutually exclusive.
Identifying mutually exclusive outcomes allows you to identify statements that represent impossible combinations.
3
Form the contrapositive of the rule concerning negligible risk and outpatient safety.
The rule 'Negligible Risk -> Safe for Outpatient OR IV' translates into the contrapositive: 'NOT Safe for Outpatient AND NOT IV -> NOT Negligible Risk'.
LSAT 'must be true' questions heavily rely on the contrapositive of compound sufficient or necessary conditions.
4
Evaluate the answer choices against these deduced relationships.
The statement prohibiting any compound from being both safe for outpatient and IV is true (proving the first correct option). The contrapositive formed in Step 3 directly proves that if a compound is Hospital Only (meaning NOT Safe for Outpatient) and NOT IV, it must NOT have a negligible risk (proving the second correct option).
Correct answers in this question type must be 100% provable without relying on outside information or assuming unstated existence.

Key Concept

Conditional Logic Chaining and Contrapositives with Compound Statements
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