Latest GRE Aptitude Question SOLUTION: Up to isomorphism, how many additive abelian groups G of order 16 have the property that x+x+x+x = 0 for each x in G ? (A) 0 (B) 1 (C) 2 (D) 3 (E) 5

Follow Quotesrain

GRE Question Papers:

GRE Select Another Category Algebra Select Another Topic

Exam

GRE Question Topics

General Ability (3)

General Knowledge(3)

Logical Reasoning (12)

Numerical Ability (407)

Programming (6)

Functions(6)

Verbal Ability (46)

Advertisements

Previous Question: 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). Next Question: 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

(#M40151773) GRE Numerical Ability question Isomorphism Keep an EYE

Up to isomorphism, how many additive abelian groups G of order 16 have the property that x+x+x+x = 0
for each x in G ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5: Asked In GRE Aashu (9 years ago); Unsolved; Is this Puzzle helpful? (0) (0) Submit Your Solution Algebra

Advertisements

Read Solution (0) :

Please Login to Read Solution.

Previous Question: 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). Next Question: 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

Login
Register

Sponsored Links

Advertisements

Challenger of the Day

no image

Dimple

India

Punjab

Time: 00:01:33

Points

19

Maths Quotes

"Obvious" is the most dangerous word in mathematics.

Eric Temple Bell

But mathematics is the sister, as well as the servant, of the arts and is touched with the same madness and genius.

Harold Marston Morse

Placed User Comments

M4Math helped me a lot.

Vipul Chavan 4 years ago

Thanks m4 maths for helping to get placed in several companies.
I must recommend this website for placement preparations.

yash mittal 5 years ago

2526K+Registerd user
1769K+Engineers
757K+MBA Asprirant
3K+Enginnering College
250+Company Exam
150K+Interview Questions

All rights are reserved to @m4maths.com