Six family members P, Q, R, S, T, and U have distinct weights. The third heaviest person weighs 40 kg. Q's weight is an odd number and Q is lighter than S but heavier than R. The count of people lighter than S is one more than the count of people lighter than P. T is heavier than both R and U. T weighs 20 kg more than P, and P is heavier than Q. The second lightest person is not Q.

What is the possible weight of S?

Question

Six family members P, Q, R, S, T, and U have distinct weights. The third heaviest person weighs 40 kg. Q's weight is an odd number and Q is lighter than S but heavier than R. The count of people lighter than S is one more than the count of people lighter than P. T is heavier than both R and U. T weighs 20 kg more than P, and P is heavier than Q. The second lightest person is not Q.

What is the possible weight of S?

Accepted Answer

**Solution:** 1. The third heaviest person weighs 40 kg. 2. Q's weight is an odd number, and Q is lighter than S but heavier than R, so the order among these three is: R < Q < S. 3. The number of persons lighter than S is one more than the number of persons lighter than P. 4. T is heavier than R and U. 5. T weighs 20 kg more than P, and P is heavier than Q. 6. The second lightest person is not Q. Let's arrange the weights step-by-step: - Since the third heaviest weighs 40 kg, the weights in descending order are: 1st heaviest > 2nd heaviest > 40 kg (3rd heaviest) > 4th heaviest > 5th heaviest > 6th heaviest - Let’s assign the 3rd heaviest weight (40 kg) to the person who fits logically. - From the conditions, Q is lighter than S but heavier than R, so S must be heavier than Q and R. - P is heavier than Q, and T is heavier than R and U. - T = P + 20 kg. - The number of persons lighter than S is one more than those lighter than P. Try to assign weights: - Suppose S is the 2nd heaviest. - Then T is the heaviest (since T is heavier than R and U, and T = P + 20). - P is heavier than Q, so P is heavier than Q but lighter than T. - Q is odd and lighter than S but heavier than R. - The third heaviest is 40 kg, so assign 40 kg to P (3rd heaviest). - Then T = P + 20 = 40 + 20 = 60 kg. - S is heavier than Q and lighter than T, so S could be 53 kg (between 40 and 60). - Q is lighter than S but heavier than R, so Q could be 39 kg (odd number), R lighter than Q, say 34 kg. - U is lighter than T, and T is heavier than U and R, so U could be 30 kg. Check the number of persons lighter than S: - Lighter than S (53 kg): Q (39), R (34), U (30) → 3 persons Number of persons lighter than P (40 kg): Q (39), R (34), U (30) → 3 persons But the condition says number lighter than S is one more than number lighter than P. So, adjust weights: If P is 40 kg (3rd heaviest), then number lighter than P is 3. Number lighter than S should be 4. So S must be heavier than P and have 4 persons lighter than S. Assign S = 53 kg. Persons lighter than S: P (40), Q (39), R (34), U (30) → 4 persons Persons lighter than P: Q (39), R (34), U (30) → 3 persons This satisfies the condition. Thus, the possible weight of S is **53 kg**. **Answer:** 53 kg

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