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Example: 2
• As part of their sports physical, 7 university sportsman's F, G, H, I,J, K and L are being weighed. In announcing the results of the physical exams, the coach has given the following information.
i. None of the sportsman is exactly the same weight as another athlete.
ii: K is heavier than L, but lighter than H.
iii. I is heavier than J
iv. Both F and G are heavier than H.
Solution
• We Can Make Such relations from Given Information
1: 7 university sportsman's are F G H I J K L
i. None of thes portsman is exactly the same weight as anothersportsman. So we can represent as F > G > H > I > J > K > L
ii: K is heavier than L, but lighter than H.
ii: K is heavier than L, but lighter than H.
H > K > L
iii: I is heavier than J : I > J
iv. Both F and G are heavier than H. F > G > H OR G > F > H
• So the overall relation for Given athlete becomes
• So the overall relation for Given athlete becomes
H > K > L
F > G > H > k > L OR G > F > H > k > L
Where I > J can be adjusted anywhere in Above relations Any Single sportsman or more can be possible between I & J Such as I > F > J, I > J > G, I > H > K > J
• Question. 1: Each of the following could be true EXCEPT
A. F is the heaviest.
B. G is the heaviest.
C. I is the heaviest.
D. More than three sportsman are heavier than K.
E. More than three sportsman are lighter than K.
• Answer is E
• As Maximum three sportsman can be lighter than K
• F > G > H > k > L > I > J OR G > F > H > k > L > I > J
• Question.2: Which of the following, if true, would be sufficient to determine which sportsman is the lightest?
A. I is the heaviest
B. I is lighter than K
C. K is heavier than J
D. J is heavier than K
E. Exactly five students are lighter than F.
• Answer is D
• If J is heavier than K then simply L will be the Lightest
• F > G > H > k > L OR G > F > H > k > L and I > J before K.
• Question. 3: If J is heavier than F, how many different rankings by weight, of the sportsman are possible?
A. 1
B. 2
C. 3
D. 4
E. 5
• Answer is D
• As F > G > H > k > L OR G > F > H > k > L & I > J > F
• If J > F then following relations can be possible
• I > J > F > G > H > k > L
• I > J > G > F > H > k > L
• I > G > J > F > H > K > L
• G > I > J > F > H > K > L
• Question. 4: If H is heavier than I, which of the following CANNOT be true?
A. I's weight is equal to the average of F's weight and G's weight.
B. I's weight is equal to the average of K's weight and L's weight
C. J's weight is equal to the average of K's weight and L's weight
D. J is the second lightest.
Answer is A
As H > I so possible relations can be
F > G > H > k > I > L > J OR G > F > H > I > k > J > L
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