Seven persons P, Q, R, S, T, U, and V have different weights. Find the third heaviest person among them.

Statements:

I. R is heavier than at least two persons. S is heavier than R but lighter than U.

II. Three persons have weight between P and U. Q is just lighter than U.

III. Neither T nor V is the heaviest person. R is not heavier than U.

Which of the following options is correct regarding the sufficiency of the statements to answer the question?

Question

Seven persons P, Q, R, S, T, U, and V have different weights. Find the third heaviest person among them.

Statements:

I. R is heavier than at least two persons. S is heavier than R but lighter than U.

II. Three persons have weight between P and U. Q is just lighter than U.

III. Neither T nor V is the heaviest person. R is not heavier than U.

Which of the following options is correct regarding the sufficiency of the statements to answer the question?

Accepted Answer

**Solution:**

1. From statement I:
   - R is heavier than at least two persons, so R's position is at least 3rd heaviest or better.
   - S is heavier than R but lighter than U, so order among these three is: U > S > R.
   - This gives partial order but does not fix the third heaviest person.

2. From statement II:
   - Three persons are between P and U.
   - Q is just lighter than U.
   - This means if U is at position x, then P is at position x+4 or x-4 (depending on who is heavier).
   - Q is immediately after U in weight.
   - This gives a relative position for U, Q, and P but not the full order.

3. Combining statements I and II:
   - From I, U > S > R.
   - From II, Q is just lighter than U, and three persons lie between P and U.
   - Since Q is just lighter than U, and S and R are lighter than U, we can place Q, S, and R accordingly.
   - This allows us to deduce the order of weights sufficiently to find the third heaviest person.

4. Statement III:
   - States T and V are not the heaviest.
   - R is not heavier than U.
   - This information is not necessary once I and II are combined.

**Answer:** Statements I and II together are sufficient to determine the third heaviest person.

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