GATE CS 2015 Set 3 — Question 10
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General Aptitude → Analytical Aptitude → Deduction & Induction
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Question
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, Defense, 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 or Telecom, then she must get the other one. T insists on a portfolio if P gets one.
Which is the valid distribution of portfolios?
Which is the valid distribution of portfolios?
Correct answer
(B) (B) R-Home, S-Power, P-Defense, Q-Telecom, T-Finance
Solution
There are 6 members (P, Q, R, S, T, U) and 5 portfolios (Home, Power, Defense, Telecom, Finance). This means one member will not be assigned a portfolio.Let's analyze the constraints:
1.U does not want any portfolio if S gets one: This implies if S is assigned a portfolio, U is the one left out. If S is not assigned, S is the one left out.
2.R wants either Home or Finance or no portfolio: R can get Home, Finance, or be unassigned.
3.Q says that if S gets either Power or Telecom, then she must get the other one: This means S and Q must be assigned the Power and Telecom portfolios, one each.
4.T insists on a portfolio if P gets one: If P is assigned, T must also be assigned.
From constraint 3, S must be assigned a portfolio (either Power or Telecom). Therefore, from constraint 1, U must be the member who does not get a portfolio.So, the five members assigned portfolios are P, Q, R, S, T.Now let's re-evaluate the constraints with U being unassigned:- Members assigned: P, Q, R, S, T.
- Constraint 2: R must get Home or Finance (since R is assigned).
- Constraint 3: S and Q get Power and Telecom (one each).
- Constraint 4: Since P is assigned, T must also be assigned (which is consistent).
- R gets Defense. This violates constraint 2 (R must get Home or Finance). So (A) is incorrect.
- U is unassigned (consistent).
- R gets Home (consistent with constraint 2).
- S gets Power, Q gets Telecom (consistent with constraint 3).
- P gets Defense, T gets Finance. Both P and T are assigned (consistent with constraint 4).
- All constraints are satisfied. So (B) is correct.
- U gets Finance. This violates our deduction that U is unassigned. So (C) is incorrect.
- U gets Power. This violates our deduction that U is unassigned. So (D) is incorrect.
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