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Difficulty: EasyCannot Be True Questions

If a student takes Advanced Physics, they must have already completed Calculus. No student who has completed Calculus is eligible for the introductory math seminar. Julian is currently taking Advanced Physics.

Based on the information above, which one of the following cannot be true?

  1. Julian is eligible for the introductory math seminar.Answer
  2. B
    A student who has completed Calculus is not taking Advanced Physics.
  3. C
    A student who is not taking Advanced Physics has completed Calculus.
  4. D
    Julian is currently enrolled in courses other than Advanced Physics.
  5. E
    Most students taking Advanced Physics are not eligible for the introductory math seminar.

Answer

The correct answer is the statement that Julian is eligible for the introductory math seminar.
The stimulus states that taking Advanced Physics guarantees that a student has completed Calculus, and completing Calculus guarantees that a student is not eligible for the introductory math seminar. Therefore, taking Advanced Physics guarantees ineligibility for the introductory math seminar. Since Julian is taking Advanced Physics, it is a proven fact that he is not eligible for the seminar. The correct option contradicts this proven fact, making it impossible to be true.

Step-by-Step Solution

1
Identify the first conditional relationship.
Taking Advanced Physics requires completing Calculus (Advanced Physics -> Calculus).
This establishes the necessary condition for taking Advanced Physics.
2
Identify the second conditional relationship.
Completing Calculus means a student is not eligible for the introductory math seminar (Calculus -> Not Eligible for Intro Math).
This establishes what happens once Calculus is completed.
3
Chain the conditionals together.
Advanced Physics -> Calculus -> Not Eligible for Intro Math.
Transitive logic allows us to connect the first and second statements.
4
Apply the rule to the specific case of Julian.
Because Julian is taking Advanced Physics, he must not be eligible for the introductory math seminar.
Julian triggers the sufficient condition of the chained conditionals.
5
Evaluate the options to find the one that contradicts the deduction.
The statement claiming Julian is eligible for the introductory math seminar is logically impossible.
A 'cannot be true' question asks for the option that directly violates the facts established in the stimulus.

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Cannot Be True Questions
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Cannot Be True Questions

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