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Difficulty: MediumMust Be True Questions

Company policy documentation states the following:

All employees who hold a Level 4 security clearance have passed a rigorous background check. No one who has passed a rigorous background check has a history of financial insolvency. Every employee assigned to the Quantum Project holds a Level 4 security clearance. Furthermore, some employees who hold a Level 4 security clearance are recent college graduates.

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

  1. No employee assigned to the Quantum Project has a history of financial insolvency.Answer
  2. At least some recent college graduates have passed a rigorous background check.Answer
  3. C
    Any employee without a history of financial insolvency holds a Level 4 security clearance.
  4. D
    At least some employees assigned to the Quantum Project are recent college graduates.
  5. E
    If an employee is not assigned to the Quantum Project, that employee does not hold a Level 4 security clearance.

Answer

The statements that must be true are: 'No employee assigned to the Quantum Project has a history of financial insolvency' and 'At least some recent college graduates have passed a rigorous background check.'
The correct statements are derived through valid logical deductions directly from the text. First, chaining the premises 'Every employee assigned to the Quantum Project holds a Level 4 security clearance', 'All employees with Level 4 clearance have passed a rigorous background check', and 'No one who has passed a rigorous background check has a history of financial insolvency' logically proves that no Quantum Project employee has a history of financial insolvency. Second, combining the premise 'some employees who hold a Level 4 clearance are recent college graduates' with 'All employees with Level 4 clearance have passed a rigorous background check' guarantees that at least some recent college graduates have passed the rigorous background check.

Step-by-Step Solution

1
Translate the statements into formal logical notation.
1. L4 -> BC
2. BC -> ~FI
3. QP -> L4
4. L4 -some-> RCG
Mapping the premises allows for precise chaining and prevents bringing in outside assumptions.
2
Chain the conditional statements together.
QP -> L4 -> BC -> ~FI
Connecting the sufficient and necessary conditions reveals guaranteed deductions across the entire chain.
3
Evaluate the 'some' statement against the established chain.
Since L4 -some-> RCG, and L4 -> BC, we can deduce RCG -some-> BC.
If a subset (some recent college graduates) possesses a characteristic (Level 4), they must also possess all characteristics guaranteed by that characteristic (Background Check).
4
Evaluate the choices against the established valid deductions and eliminate logical fallacies.
The two correct statements match our deductions perfectly. The other three choices represent an illegal reversal, an unwarranted assumption of set overlap, and an illegal negation.
Must Be True questions require 100% provable answers. Any choice relying on a logical flaw must be eliminated.

Key Concept

Chaining conditional statements and correctly integrating quantifier logic ('some') without making unwarranted assumptions.
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