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Difficulty: MediumChaining Conditional Statements

The symphony orchestra will perform Mahler's Symphony No. 8 this season only if they hire additional brass musicians. Furthermore, the orchestra can hire additional brass musicians only if they secure the City Arts Grant. The terms of the City Arts Grant dictate that any recipient must host a free community concert. However, if the main concert hall's scheduled renovations are delayed, the orchestra will be unable to host a free community concert this season.

Which one of the following conclusions can be properly drawn from the information above?

  1. If the main concert hall's scheduled renovations are delayed, the symphony orchestra will not perform Mahler's Symphony No. 8.Answer
  2. B
    If the symphony orchestra secures the City Arts Grant, they will perform Mahler's Symphony No. 8 this season.
  3. C
    If the symphony orchestra does not perform Mahler's Symphony No. 8, they will be unable to host a free community concert.
  4. D
    Hosting a free community concert is sufficient to guarantee that the orchestra will hire additional brass musicians.
  5. E
    The City Arts Grant is the most difficult funding source for the symphony orchestra to secure this season.

Answer

If the main concert hall's scheduled renovations are delayed, the symphony orchestra will not perform Mahler's Symphony No. 8.
The stimulus establishes a linear chain of conditional logic: Performing Mahler requires hiring brass, which requires the grant, which requires a free concert. Thus, performing Mahler fundamentally requires hosting a free concert. The final sentence provides a trigger: if renovations are delayed, the free concert cannot happen. By taking the contrapositive of the main chain, if the free concert cannot happen, then the orchestra cannot perform Mahler. Therefore, a renovation delay logically guarantees that Mahler will not be performed.

Step-by-Step Solution

1
Diagram the first two conditional premises.
Perform Mahler -> Hire Brass -> Secure Grant
The phrase 'only if' introduces a necessary condition. Performing Mahler requires hiring brass, and hiring brass requires securing the grant.
2
Diagram the final two conditional premises.
Secure Grant -> Host Free Concert. Renovations Delayed -> NOT Host Free Concert.
The grant dictates the concert, making it a necessary condition. The delay prevents the concert, making the delay a sufficient condition for not hosting the concert.
3
Chain all the conditional statements together.
Perform Mahler -> Hire Brass -> Secure Grant -> Host Free Concert
Connecting the shared terms creates a complete logical chain of necessary conditions for performing Mahler.
4
Take the contrapositive of the entire chain and apply the final premise.
NOT Host Free Concert -> NOT Secure Grant -> NOT Hire Brass -> NOT Perform Mahler. Since Renovations Delayed -> NOT Host Free Concert, then Renovations Delayed -> NOT Perform Mahler.
If the final necessary condition in a chain fails, the initial sufficient condition cannot occur. A renovation delay triggers this failure.

Key Concept

Chaining Conditional Statements and applying Contrapositives
Estimated Time:1m 30s
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Topics

Chaining Conditional Statements

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