GRE Exam Numerical Ability Algebra

If z = e^(2Pii/5), then 1 + z + z^2 + z^3 + 5z^4 + 4z^5 ++4z^6 + 4z^7 + 4z^8 + 5z^9 = ?
(A) 0
(B) 4e^(3Pii/5)
(C) 5e^(4Pii/5)
(D) – 4e^(2Pii/5)
(E) – 5e^(3Pii)/5

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GRE Other Question

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 A fair coin is to be tossed 100 times, with each toss resulting in a head or a tail. If H is the total number of heads and T is the total number of tails, which of the following events has the greatest probability?
(A) H = 50
(B) T >= 60
(C) 51 =< H =< 55
(D) H >= 48 and T >= 48
(E) H =< 5 or H >= 95