The head of a newly formed government desires to appoint five of the six…

2015

The head of a newly formed government desires to appoint five of the six selected members P, Q, R, S, T and U to portfolios of Home, Power, Defence, Telecom, and Finance. U does not want any portfolio if S gets one of the five. R wants either Home or Finance or no portfolio. Q says that if S gets either Power of telecom, then she must get the other one. T insists on a portfolio if P gets one.

Which is the valid distribution of portfolios?

  1. A.

    P-Home, Q-Power, R-Defence, S-Telecom, T-Finance

  2. B.

    R-Home, S-Power, P-Defence, Q-Telecom, T-Finance

  3. C.

    P-Home, Q-Power, T-Defence, S-Telecom, U-Finance

  4. D.

    Q-Home, U-Power, T-Defence, R-Telecom, P-Finance

Attempted by 23 students.

Show answer & explanation

Correct answer: B

Correct distribution: R-Home, S-Power, P-Defence, Q-Telecom, T-Finance

Check each constraint against this distribution:

  • If S gets a portfolio, U must not get any portfolio. S has Power and U has no portfolio, so this is satisfied.

  • R wants either Home or Finance or no portfolio. R has Home, so this requirement is satisfied.

  • If S gets Power or Telecom, then Q must get the other one. S has Power and Q has Telecom, so this condition is satisfied.

  • If P gets a portfolio, then T must also have one. P has Defence and T has Finance, so this is satisfied.

Why the other distributions fail:

  • P-Home, Q-Power, R-Defence, S-Telecom, T-Finance fails because R is assigned Defence, violating R's requirement to have Home or Finance if given a portfolio.

  • P-Home, Q-Power, T-Defence, S-Telecom, U-Finance fails because S has a portfolio while U is also assigned Finance; U must not have a portfolio when S does.

  • Q-Home, U-Power, T-Defence, R-Telecom, P-Finance fails because R is assigned Telecom, violating R's requirement to have Home or Finance if given a portfolio.

Therefore the only valid distribution is R-Home, S-Power, P-Defence, Q-Telecom, T-Finance.

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