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Global Stats
If \(w, x, y,\) and \(z\) are positive integers and \(\dfrac{w}{x}<\dfrac{y}{z}<1,\) what is the proper order, increasing from left to right, of the following quantities: \(\dfrac{x}{w}, \dfrac{z}{y}, \dfrac{x^2}{w^2}, \dfrac{xz}{wy}, \dfrac{x+z}{w+y}, 1?\)
(A) \(1, \dfrac{z}{y}, \dfrac{x}{w}, \dfrac{x+z}{w+y}, \dfrac{x^2}{w^2}, \dfrac{xz}{wy}\)
(B) \(1, \dfrac{z}{y}, \dfrac{x+z}{w+y}, \dfrac{x}{w}, \dfrac{xz}{wy}, \dfrac{x^2}{w^2}\)
(C) \(1, \dfrac{z}{y}, \dfrac{x}{w}, \dfrac{x+z}{w+y}, \dfrac{xz}{wy}, \dfrac{x^2}{w^2}\)
(D) \(1, \dfrac{z}{y}, \dfrac{x}{w}, \dfrac{xz}{wy}, \dfrac{x+z}{w+y}, \dfrac{x^2}{w^2}\)
(E) \(1, \dfrac{z}{y}, \dfrac{x+z}{w+y}, \dfrac{xz}{wy}, \dfrac{x^2}{w^2}, \dfrac{x}{w}\)
Answer: B
Source: Manhattan GMAT
(A) \(1, \dfrac{z}{y}, \dfrac{x}{w}, \dfrac{x+z}{w+y}, \dfrac{x^2}{w^2}, \dfrac{xz}{wy}\)
(B) \(1, \dfrac{z}{y}, \dfrac{x+z}{w+y}, \dfrac{x}{w}, \dfrac{xz}{wy}, \dfrac{x^2}{w^2}\)
(C) \(1, \dfrac{z}{y}, \dfrac{x}{w}, \dfrac{x+z}{w+y}, \dfrac{xz}{wy}, \dfrac{x^2}{w^2}\)
(D) \(1, \dfrac{z}{y}, \dfrac{x}{w}, \dfrac{xz}{wy}, \dfrac{x+z}{w+y}, \dfrac{x^2}{w^2}\)
(E) \(1, \dfrac{z}{y}, \dfrac{x+z}{w+y}, \dfrac{xz}{wy}, \dfrac{x^2}{w^2}, \dfrac{x}{w}\)
Answer: B
Source: Manhattan GMAT
