GATE CS 2015 Set 3 QGA-7 — General Aptitude

To find the valid distribution of portfolios, let us analyze the given constraints and test each option against them:

1. Constraint 1: If $S$ gets a portfolio, then $U$ must not get any portfolio (i.e., $S$ and $U$ cannot both have portfolios).
2. Constraint 2: $R$ must get either Home, Finance, or no portfolio.
3. Constraint 3: If $S$ gets Power, then $Q$ must get Telecom (and vice versa).
4. Constraint 4: If $P$ gets a portfolio, then $T$ must also get a portfolio.

Let us evaluate each option:

• Option A: $P$-Home, $Q$-Power, $R$-Defense, $S$-Telecom, $T$-Finance
  • Violates Constraint 2 because $R$ is assigned Defense.
• Option B: $R$-Home, $S$-Power, $P$-Defense, $Q$-Telecom, $T$-Finance
  • Constraint 1: $S$ has a portfolio, and $U$ has none. (Satisfied)
  • Constraint 2: $R$ is assigned Home. (Satisfied)
  • Constraint 3: $S$ has Power and $Q$ has Telecom. (Satisfied)
  • Constraint 4: $P$ has a portfolio (Defense), and $T$ also has a portfolio (Finance). (Satisfied)
  • All constraints are satisfied.
• Option C: $P$-Home, $Q$-Power, $T$-Defense, $S$-Telecom, $U$-Finance
  • Violates Constraint 1 because both $S$ and $U$ are assigned portfolios.
• Option D: $Q$-Home, $U$-Power, $T$-Defense, $R$-Telecom, $P$-Finance
  • Violates Constraint 2 because $R$ is assigned Telecom.

Thus, only Option B represents a valid distribution.