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Quandaries & Queries
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 Topic: a 5-digit number
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 Two questions from math class 2009-06-18 From Con:Hello, My name is Con and my son is required to answer the following questions for his maths class. He has attempted Q1 through trial and error and has found the answer to 72453. Is this correct? He has attempted to draw the triangles described in Q2 in a number of ways and has found that BE can not equal ED and is dependent of angle BAC. Therefore, he claims that the triangle can not be drawn/practical. Is this correct or is there a slolution? Q1. Digits 2, 3, 4, 5 and 7 are each used once to compose a 5-digit number abcde such that 4 divides a 3-digit number abc, 5 divides a 3-digit number bcd and 3 divides a 3-digit number cde. Find the 5-digit number abcde. Q2. Let ABC be a triangle with AB=AC. D is a point on AC such that BC=BD. E is a point on AB such that BE = ED = AD. Find the size of the angle EAD. ConAnswered by Chris Fisher.

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