Quiz 3: Algebra Challenge

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Created by Isabelle Yeong on April 19th 2015

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Question 1: Two different positive real numbers x and y each differ from their reciprocals by 1.

Evaluate x+y.

√5

√6

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Question 2: The product of three consecutive positive integers is 8 times their sum. Find the sum of their squares.

110

194

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Question 3: Positive integers a, b and c are chosen such that c>b>a and the system of equations y=|x-a|+x-b|+x-c| and 2x+y=1999 has exactly one solution.

Find the least possible value of c.

666

668

999

1000

1999

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