Explanation
Step 1: Identify the Middle Term
From statement 3, Q is the middle term. This means there are three values lower than Q and three values higher than Q.
Step 2: Analyze the Relationship between U,Q,R, and S
From statement 1: Q−U=R−S.
This implies the distance between Q and U is the same as the distance between R and S.
Step 3: Evaluate the Options using the Constraints
Let's check the given options to see which one satisfies all conditions:
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Checking Option (a) TVPQRSU:
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Q is the middle term? Yes (4th position).
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Q−U=R−S? Here Q is 4th and U is 7th, so Q−U=−3. R is 5th and S is 6th, so R−S=−1. −3=−1. (Incorrect)
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Checking Option (b) TRSQUPV:
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Q is middle? Yes.
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Q−U=R−S? Q(4th)−U(5th)=−1. R(2nd)−S(3rd)=−1. Matches.
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V > U? V is 7th, U is 5th. 7 > 5. Matches.
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P > S? P is 6th, S is 3rd. 6 > 3. Matches.
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However, looking at the letters provided (P,Q,R,S,T,U,V), option (b) contains T,R,S,Q,U,P,V. Let's re-verify the logic for other options.
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Checking Option (c) TUSQRPV:
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Q is middle? Yes.
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Q−U=R−S? Q(4th)−U(2nd)=2. R(5th)−S(3rd)=2. Matches.
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V > U? V is 7th, U is 2nd. Matches.
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P > S? P is 6th, S is 3rd. Matches.
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This satisfies all conditions perfectly.
Conclusion:
In option (c), Q is in the middle. The difference between Q and U (2 positions) is equal to the difference between R and S (2 positions). V (7th) is greater than U (2nd), and P (6th) is greater than S (3rd).
Correct Option: (c)