For the sake of clarity, the word in red should be included in the question stem:
gmatt1476 wrote:
In the figure above, points A, B, C, and D are collinear and AB, BC, and CD are semicircles with diameters d1 cm, d2 cm, and d3 cm, respectively. What is the sum of the
arc lengths of semicircles AB, BC, and CD, in centimeters?
(1) d1:d2:d3 is 3:2:1.
(2) The length of line segment AD is 48 cm.
Arc length of a semicircle = \(\frac{πd}{2}\)
Statement 1:
Case 1: d₁ = 3, d₂ = 2, d₃ = 1
In this case, the sum of the arc lengths \(= \frac{3π}{2} + \frac{2π}{2} + \frac{π}{2} = \frac{6π}{2} = 3π\)
Case 2: d₁ = 30, d₂ = 20, d₃ = 10
In this case, the sum of the arc lengths \(= \frac{30π}{2} + \frac{20π}{2} + \frac{10π}{2} = \frac{60π}{2} = 30π\)
Since the sum can be different values, INSUFFICIENT.
Statement 2:
Case 1: d₁ = 16, d₂ = 16, d₃ = 16
In this case, the sum of the arc lengths \(= \frac{16π}{2} + \frac{16π}{2} + \frac{16π}{2} = \frac{48π}{2} = 24π\)
Case 2: d₁ = 20, d₂ = 20, d₃ = 8
In this case, the sum of the arc lengths \(= \frac{20π}{2} + \frac{20π}{2} + \frac{8π}{2} = \frac{48π}{2} = 24π\)
Since the sum in each case is the same, SUFFICIENT.
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