GRE
Exam
Numerical Ability
Data Sufficiency
Let K be a non empty subset of R^n, where n > 1. n where n ! 1. Which of the following statements must be true?
I. If K is compact, then every continuous real-valued function defined on K is bounded.
II. If every continuous real-valued function defined on K is bounded, then K is compact.
III. If K is compact, then K is connected.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
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GRE Other Question
Which of the following sets has the greatest cardinality?
(A) R
(B) The set of all functions from Z to Z
(C) The set of all functions from R to (0, 1)
(D) The set of all finite subsets of R
(E) The set of all polynomials with coefficients in R
Which of the following statements are true about the open interval (0, 1) and the closed interval [0, 1]?
I. There is a continuous function from (0, 1) onto [0, 1].
II. There is a continuous function from [0, 1] onto (0, 1)
III. There is a continuous one-to-one function from (0, 1) onto [0, 1]
(A) None
(B) I only
(C) II only
(D) I and III only
(E) I, II, and III