Study the following information carefully and answer the questions given below:
Six persons are arranged in descending order according to their weight from left to right. Only T is lighter than Q whose weight is 17kg. S is twice heavier than Q and 14 kg lighter than N. Two persons between M and S. R is not the second heaviest among all.
How many persons are lighter than S?
Correct Answer :
Two
Solution :
The correct answer is Two.
Let's analyze the given information step-by-step to determine the order of the six persons arranged in descending order of their weight from left to right (heaviest to lightest).
Let the six positions from left to right be: Position 1 (Heaviest) > Position 2 > Position 3 > Position 4 > Position 5 > Position 6 (Lightest).
1. Analyze the position of Q and T:
"Only T is lighter than Q whose weight is 17kg."
This implies T is the lightest person of all, so T is at Position 6.
Since only T is lighter than Q, Q must be placed immediately before T at Position 5.
So, Q = 17 kg, and the arrangement so far from right to left is: _ > _ > _ > _ > Q (17 kg) > T.
2. Determine the weight and position of S and N:
"S is twice heavier than Q..."
Weight of S = 2 × Weight of Q = 2 × 17 kg = 34 kg.
"...and 14 kg lighter than N."
Weight of N = Weight of S + 14 kg = 34 kg + 14 kg = 48 kg.
3. Place S and M:
"Two persons between M and S."
Since Q and T occupy positions 5 and 6, S can be at position 4, 3, 2, or 1.
If S is at position 4, then M must be at position 1 (since 2 persons are between position 1 and position 4).
If S is at position 3, M would have to be at position 6 (which is occupied by T) or beyond position 1, which is invalid.
If S is at position 2, M would be beyond the available 6 positions.
Therefore, S must be at Position 4, and M must be at Position 1.
4. Place N and R:
Currently, the filled positions are: Position 1 = M, Position 4 = S, Position 5 = Q, Position 6 = T.
The remaining available positions are Position 2 and Position 3 for N and R.
We know "R is not the second heaviest among all."
Position 2 is the second heaviest position, so R cannot be at Position 2. Thus, N is at Position 2 and R is at Position 3.
Final Arrangement from heaviest to lightest:
Position 1: M
Position 2: N (48 kg)
Position 3: R
Position 4: S (34 kg)
Position 5: Q (17 kg)
Position 6: T
Conclusion:
The persons lighter than S are the ones positioned to the right of S, which are Q and T.
Therefore, there are Two persons lighter than S.
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