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Six friends Abby, Bunny, Chan, Dolly, Emma and Fanny have different weights. DollyтАЩs weight is an odd number. Dolly is heavier than Emma but not the heaviest. Chan is heavier than Fanny but lighter than Dolly. Chan is not heavier than Emma but is heavier than Fanny and Abby. AbbyтАЩs weight is not an odd number. The lightest weight is 45 kilograms and the heaviest weight is 80 kilograms. If Chan weighs 68 kilograms, which of the following can be the possible weight of Dolly (in kilograms)?
65
72
71
66
71
Map the weight inequalities (X > Y) and immediately filter values by the constraints of being odd/even and within range.
Map the weight inequalities (X > Y) and immediately filter values by the constraints of being odd/even and within range.
Establish the order of weights
From the text: Dolly > Emma, Chan > Fanny, Dolly > Chan, Emma > Chan, and Chan > Abby. Combining these gives: Dolly > Emma > Chan > Fanny and Chan > Abby. Thus, the order is Dolly > Emma > Chan > (Fanny, Abby).
Apply value constraints
Chan = 68 kg. Since Dolly > Emma > Chan (68), Dolly must be greater than 68. The heaviest is 80, so 68 < Dolly < 80. Dolly must be an odd number.
Evaluate candidates
Possible odd numbers between 68 and 80 are 69, 71, 73, 75, 77, 79. Comparing with the provided options: 65 (too low), 72 (even), 66 (even), 71 (valid).
A: 65 is less than Chan (68) and thus impossible. B: 72 is an even number, violating the constraint that Dolly is an odd number. D: 66 is less than Chan (68) and even, violating both weight and parity constraints.
C is correct because 71 is the only option that is both an odd number and greater than Chan's weight of 68, fitting the deduced hierarchy.
In inequality puzzles, always identify the 'pivot' element (here, Chan at 68) to immediately eliminate impossible range values.
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