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GRE Numerical Ability - Data Sufficiency Sample Question with Solutions

(#M40165917) GRE QUESTION Keep an EYE

Compare the two quantities:
There are 50 students in a class. 27 of them play cricket, 18 play hockey and 10 play neither cricket nor hockey.
Quantity A: The number of students who play both cricket and hockey.
Quantity B: 5

A) Quantity A is greater B) Quantity B is greater C) The two quantities are equal D) The relationship cannot be determined from the information given.

Asked In GRE Devendra Marghade (4 years ago)

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(#M40165881) GRE QUESTION Keep an EYE

A club of 36 people includes permanent and temporary members. Of the 20 temporary members, 14 are men. Exactly 12 women are permanent members, then
(A) Total number of men are greater than total number of women.
(B) Total number of women are greater than total number of men.
(C) Total number of men and total number of women are equal.
(D) The relationship cannot be determined.

Asked In GRE Devendra Marghade (4 years ago)

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(#M40151782) GRE QUESTION Non empty subset Keep an EYE

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

Asked In GRE Aashu (7 years ago)

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(#M40151781) GRE QUESTION Sets has the greatest cardinality Keep an EYE

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

Asked In GRE Aashu (7 years ago)

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(#M40151778) GRE QUESTION Matrices Keep an EYE

Suppose A and B are n*n invertible matrices, where n >1, and I is the n*n identity matrix. If A and B are similar matrices, which of the following statements must be true?
I. A - 2I and B – 2I are similar matrices.
II. A and B have the same trace.
III. A^-1 and B^-1 are similar matrices.
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III

Asked In GRE Aashu (7 years ago)

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(#M40151774) GRE QUESTION Matrix Keep an EYE

Let A be a real 2*2 matrix. Which of the following statements must be true?
I. All of the entries of A^2 are nonnegative.
II. The determinant of A^2 is nonnegative.
III. If A has two distinct eigenvalues, then A^2 has two distinct eigenvalues.
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III

Asked In GRE Aashu (7 years ago)

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(#M40151772) GRE QUESTION Consider the theorem Keep an EYE

Consider the theorem: If f and f’ are both strictly increasing real-valued functions on the interval (0, infinite) then lim f(x) = infinite (x -> infinite). The following argument is suggested as a proof of this theorem.
(1) By the Mean Value Theorem, there is a c1 in the interval (1, 2) such that
f’(c1) = {f(2)-f(1)}/ (2-1) = f(2) – f(1) > 0.
(2) For each x > 2, there is a c(x) in (2, x) such that {f(x) – f(2)}/(x-2) = f’{c(x)}
(3) For each x > 2, {f(x)-f(2)}/(x-2) = f’(c(x)) > f’(c1) since f’ strictly incrasing
(4) For each x > 2, f(x) > f(2) + (x-2) f’(c1)
(5) lim f(x) = infinite (x -> infinite)
Which of the following statements is true?
(A) The argument is valid.
(B) The argument is not valid since the hypotheses of the Mean Value Theorem are not satisfied in (1) and (2).
(C) The argument is not valid since (3) is not valid.
(D) The argument is not valid since (4) cannot be deduced from the previous steps.
(E) The argument is not valid since (4) does not imply (5).

Asked In GRE Aashu (7 years ago)

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(#M40151770) GRE QUESTION Complex number Keep an EYE

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

Asked In GRE Aashu (7 years ago)

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(#M40151769) GRE QUESTION Circular region divide 5 sector Keep an EYE

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

Asked In GRE Aashu (7 years ago)

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(#M40151763) GRE QUESTION Matrix Keep an EYE

Let M be a 5*5 real matrix. Exactly four of the following five conditions on M are equivalent to each other. Which of the five conditions is equivalent to NONE of the other four?
(A) For any two distinct column vectors u and v of M, the set {u, v} is linearly independent.
(B) The homogeneous system Mx = 0 has only the trivial solution.
(C) The system of equations M x = b has a unique solution for each real 5*1 column vector b.
(D) The determinant of M is nonzero.
(E) There exists a 5*5 real matrix N such that NM is the 5*5 identity matrix.

Asked In GRE Aashu (7 years ago)

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