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P, Q, R, S and T have different weights. Only one person is heavier than Q and lighter than P. S is heavier than R. Who is the lightest among all?
R
T
Cannot be determined
P
Cannot be determined
Map the fixed positions first and identify the floating variables; if the lowest position is occupied by either of two variables, the answer is indeterminate.
Map the fixed positions first and identify the floating variables; if the lowest position is occupied by either of two variables, the answer is indeterminate.
Analyze the fixed sequence
Given that only one person is heavier than Q and lighter than P, the relative order must be P > X > Q, where X is one of the five individuals (S, R, or T). This confirms three fixed slots in the weight hierarchy.
Evaluate the remaining variables
We have 5 people: P, Q, R, S, T. The sequence P > X > Q uses 3 people. The remaining 2 people are S, R, and T (minus the one used as X). We know S > R. The position of T relative to S, R, and the group P-X-Q is not defined, making it impossible to fix the last position.
A: R could be the lightest, but T or the person in the middle could also occupy that spot. B: T is not uniquely positioned; if T is lighter than R, R cannot be the lightest. D: P is established as being heavier than Q and X, so P cannot be the lightest.
C is correct because the relative weight of T and the exact identity of the person between P and Q (and their relation to the lightest) cannot be uniquely determined from the given information.
In ranking problems with fewer constraints than participants, look for 'floating' variables that have no defined relationship with the extremes; these almost always lead to 'Cannot be determined'.
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