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Twenty Typical GRE Math Problems with Solutions
3) In the diagram above, AD = BE = 6 and CD = 3(BC). If AE = 8, then BC = ?
(A) 6
(B) 4
(C) 3
(D) 2
(E) 1
Answer: Choice E is correct. Since AE is a line segment and all the lengths are additive, AE = AD + DE. We know that AD = 6 and AE = 8. So DE = AE  AD = 8  6 = 2. We also know that BE = 6. So BD = BE  DE = 6  2 = 4. We know BD is 4, but need to find BC.
Since CD = 3(BC), we can solve for BC: x + 3x = 4. x = 1.
