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Here is the eligibility criterion
There is no specific eligibility criterion for GRE. However, various universities that accept GRE scores have their own criteria of admission.

Here is the GRE exam pattern
Section No. of questions
Analytical Writing
(One section with two separately timed tasks) Task 1 - Analyse an Issue
Task 2 - Analyse an Argument task
Verbal Reasoning
(Two sections) 20 questions per section

Quantitative Reasoning
(Two sections) 20 questions per section

Unscored Varies

Research Varies

Score required in the section to clear GRE exam
Sections Score
Verbal Reasoning 130-170, in 1 point increments

Quantitative Reasoning 130-170, in 1 point increments

Analytical Writing 0-6, in half point increments

Schedule of the exam

The computer-based GRE can be taken once every 21 days, up to five times within any continuous period of 12 months.

This includes test attempts in which the score was cancelled by the candidate.

Here is the syllabus of the exam

In Analytical section you will get the logical and strategical questions to solve by the help of your skill and presence of mind.

List of topics in GRE Quantitative Reasoning Syllabus
Maths Formulas List
Number properties
Order of operations
Percentage
Ratio and proportion
Profit and loss
Simple and compound interest
Speed, distance and time
Permutation & combination
Linear equations
Quadratic equations
Sets
Statistics: Average, Median, Mode, Range, Standard deviation
Powers and roots
Probability
Pipes, cisterns, work, time
Lines and angles
Triangles
Polygon
Quadrilateral
Circles
Co-ordinate geometry
Volume and surface area

List of topics in GRE Verbal Reasoning Syllabus
Basic Sentence structure: Nouns, Pronouns, Adjectives
Verb Tense
Idioms & Idiomatic Expressions
Pronoun Agreement
Subject Verb Agreement
Modifiers
Parallelism