GRE Exam Numerical Ability Geometry

The minimal distance between any point on the sphere (x-2)^2 + (y-1)^2 + (z-3)^2 = 1 and any point on the sphere (x+3)^2 + (y-2)^2 + (z-4)^2 = 4 is
(A) 0
(B) 4
(C) Sqrt(27)
(D) 2(Sqrt2 + 1)
(E)3(Sqrt3 – 1)

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GRE Other Question

The Euclidean algorithm is used to find the greatest common divisor (gcd) of two positive integers a and b .
input(a)
input(b)
while b>0
begin
r := a mod b
a := b
b := r
end
gcd := a
output(gcd)
When the algorithm is used to find the greatest common divisor of a = 273 and b = 110, which of the
following is the sequence of computed values for r ?
(A) 2, 26, 1, 0
(B) 2, 53, 1, 0
(C) 53, 2, 1, 0
(D) 53, 4, 1, 0
(E) 53, 5, 1, 0 At a banquet, 9 women and 6 men are to be seated in a row of 15 chairs. If the entire seating arrangement is to be chosen at random, what is the probability that all of the men will be seated next to each other in 6 consecutive positions?
(A) 1/(15/6)
(B) 6!/(15/6)
(C) 10!/15!
(D) 6! 9! /14!
(E) 6! 10! / 15!