GRE
Exam
Numerical Ability
Data Sufficiency
A circular region is divided by 5 radii into sectors. Twenty-one points are chosen in the circular region, none of which is on any of the 5 radii. Which of the following statements must be true?
I. Some sector contains at least 5 of the points.
II. Some sector contains at most 3 of the points.
III. Some pair of adjacent sectors contains a total of at least 9 of the points.
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
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GRE Other Question
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
Let G be the group of complex numbers {1, i, -1, -i} under multiplication. Which of the following statements are true about the homomorphism of G into itself?
I. z -> z defines one such homomorphism, where z denotes the complex conjugate of z,
II. z -> z^2 defines one such homomorphism.
III. For every such homomorphism, there is an integer k such that the homomorphism has the form z -> z^k .
(A) None
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III