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GATE CSE 2015 Set 3 | Question: GA-7

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The head of 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 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?

  1. $P$-Home, $Q$-Power, $R$-Defense, $S$-Telecom, $T$-Finance
  2. $R$-Home, $S$-Power, $P$-Defense, $Q$-Telecom, $T$-Finance
  3. $P$-Home, $Q$-Power, $T$-Defense, $S$-Telecom, $U$-Finance
  4. $Q$-Home, $U$-Power, $T$-Defense, $R$-Telecom, $P$-Finance
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"$U$ does not want any portfolio if $S$ gets one of the five"

So, $S$ and U cannot come together. Option $C$ eliminated.

"$R$ wants either Home or Finance or no portfolio"

So, options $A$ and $D$ eliminated. 

So, answer is B. 

Just to confirm: 

$Q$ says that if $S$ gets Power or Telecom, then she must get the other one

In $B$, $S$ gets Power and $Q$ gets Telecom

"T insists on a portfolio if $P$ gets one"

In $B$, $T$ is getting a portfolio.

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(A) P-Home, Q-Power, R-Defense, S-Telecom, T-Finance : X (R wants either Home or Finance or no portfolio)

(B) R-Home, S-Power, P-Defense, Q-Telecom, T-Finance: Valid

(c) P-Home, Q-Power, T-Defense, S-Telecom, U-Finance: X (U does not want if S gets one of the five)

(d) Q-Home, U-Power, T-Defense, R-Telecom, P-Finance: X( R wants either Home or Finance or no portfolio)

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we can do this easily by option elimination.

option a) it is false because R is assign to Defence where as the condition was R wants either home or finance or no portfolio.

option c) is false because S and U both got portfolio where the condition is if S gets some portfolio U does not want any portfolio. So S and U can’t go together .

option D) is false because R is assign to Telecom where as the condition was R wants either home or finance or no portfolio.

so option (B) is the answer because its was a valid distribution and every condition is satisfied.
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