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Rational number properties

Source: 2014-2015 SDML Middle School 1a Problem 11

August 28, 2016

Problem Statement

Phillip and Paula both pick a rational number, and they notice that Phillip's number is greater than Paula's number by 1212. They each square their numbers to get a new number, and see that the sum of these new numbers is half of 169169. Finally, they each square their new numbers and note that Phillip's latest number is now greater than Paula's by 50705070. What was the sum of their original numbers?
(A) −4(B) −3(C) 1(D) 2(E) 5\text{(A) }-4\qquad\text{(B) }-3\qquad\text{(C) }1\qquad\text{(D) }2\qquad\text{(E) }5
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