GRE Exam Numerical Ability Number System

For which of the following rings is it possible for the product of two nonzero elements to be zero?
(A) The ring of complex numbers
(B) The ring of integers modulo 11
(C) The ring of continuous real-valued functions on [0, 1]
(D) The ring {a + b Sqrt 2 : a and b are rational numbers}
(E) The ring of polynomials in x with real coefficients

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GRE Other Question

In the complex z-plane, the set of points satisfying the equation z^2 = |z|^2 is a
(A) pair of points
(B) circle
(C) half-line
(D) line
(E) union of infinitely many different lines Suppose X is a discrete random variable on the set of positive integers such that for each positive integer n, the probability that X = n is 1/2^n. If Y is a random variable with the same probability distribution and X and Y are independent, what is the probability that the value of at least one of the variables X and Y is greater than 3 ?
(A) 1/64
(B) 15/64
(C) 1/4
(D) 3/8
(E) 4/9