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Among five people named V, W, X, Y and Z, each have a certain age. X is four times the age of Y. V's age is equal to the age of X. Y is one-third the age of Z. W is half the age of V. If the age of Z is 12, what is the age of W?
15
4
8
6
8
Map all ages to a single variable (Y) based on the relationships provided: X=4Y, V=4Y, Z=3Y, W=V/2=2Y. Since Z=12, Y=4, therefore W=2(4)=8.
Map all ages to a single variable (Y) based on the relationships provided: X=4Y, V=4Y, Z=3Y, W=V/2=2Y. Since Z=12, Y=4, therefore W=2(4)=8.
Establish Y as the Base Variable
Given Z = 12. Since Y is one-third of Z, Y = 12 / 3 = 4.
Determine X and V
X is four times Y, so X = 4 * 4 = 16. Since V's age equals X, V = 16.
Calculate W
W is half the age of V, so W = 16 / 2 = 8.
A: 15 is incorrect as it does not follow the derived relationships. B: 4 is the age of Y, not W. D: 6 is an arbitrary value not supported by the equations.
C is correct because according to the provided ratios, if Z=12 then Y=4, X=16, V=16, and W = V/2 = 8.
In age-related problems, always express all variables in terms of one constant or the youngest member to simplify calculations.