Question 95
Is $$x = y$$?
A. $$(x+y)(1/x + 1/y) = 4$$
B. $$(x-50)^2 = (y-50)^2$$
Solution
Consider statement 1:$$(x+y)(1/x + 1/y) = 4$$
$$(x+y)^2/xy = 4$$
$$x^2+y^2+2xy = 4xy$$
$$x^2+y^2+2xy-4xy = 0$$
$$(x-y)^2 = 0$$
x = y.
Consider statement 2:$$(x-50)^2 = (y-50)^2$$
(x-y)(x+y-100) = 0
Either x = y or x+y = 100.
Statement 1 is sufficient whereas statement 2 is not sufficient to answer the question.
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