GRE - Quantitative Reasoning

QuickStudy Laminated Reference Guide

• Publisher: QuickStudy Reference Guides
• Year: 2018
• ISBN:
  9781423240631
• Topic: Study Aids
• Subtopic: Study Guides

Increase your score on the GRE with a tool that is easy to review and less expensive than any other study aid. Whether taking the exam while in college, after your undergrad, or with some time in-between, a 6-page laminated guide can go anywhere for review of concepts you will learn in exam prep courses or through test-taking books. This thorough and slick breakdown of the mathematical and reasoning concepts for conquering this section of the test is so handy and concise that you can review anywhere in record time.
6-page laminated guide includes:

• Exam Overview
• Arithmetic
  • Integers, Exponents, Order of Operations
  • Scientific Notation
  • Adding Radicals
  • Fractions, Percents, Absolute Value
  • Rounding Numbers, Proportions & Ratios
  • Distance, Speed & Time
  • Averages
• Algebra
  • Solving Algebraic Equations
  • Binomials & Trinomials
• Geometry
  • Angles, Points, Lines
  • Shapes
  • Areas & Perimeters
  • Volumes & Surface Area
• Data Interpretation
  • Graphs, Standard Deviation
  • Probability
  • Independent vs. Dependent Variables
  • Mean, Median, Mode & Range
  • Word Problems
• Measurement
• Scoring

Suggested uses:

• Review Anywhere – exam prep books are huge, with much space used for sample questions, this guide focuses on how to answer – keep in your bag or car to review any place, any time
• The Whole Picture – with 6 pages, it is easy to jump to one section or another to go straight to the core of the concept you need for answering questions
• Last Review – many people use our guides as a last review before they enter an exam

Arithmetic

Topics include integers, such as divisibility, factorization, prime numbers, remainders, and odd and even integers; arithmetic operations, exponents, and roots; and concepts such as estimation, percent, ratio, rate, absolute value, the number line, decimal representation, and sequences of numbers.

Integers Properties of Integers

• Integer: Number with no fraction or decimal.
• An integer can be positive, negative, or 0.
  EX: -2, 0, 18

Identity Properties

• A number will not change when adding 0 to the number.
  EX: 8 + 0 = 8
  EX: y + 0 = y
• A number will not change when multiplying it by 1.
  EX: 6 × 1 = 6
  EX: y × 1 = y

Properties of Zero

• Any number multiplied by 0 is 0.
• If the product is 0, one or more of the factors must equal 0.
  EX: a × b × c × d = 0

  a, b, c, or d must equal 0.
• If the product is not equal to 0, none of the factors equals 0.
  EX: a × b × c × d ≠ 0

  a, b, c, and d ≠ 0.

Divisibility

• An integer is divisible by 2 if the last digit in the integer is divisible by 2.
  EX: 8,542,634

  4 is divisible by 2.

  Therefore, 8,542,634 is divisible by 2.
• An integer is divisible by 3 if the sum of the digits in the integer is divisible by 3.
  EX: 865,257

  8 + 6 + 5 + 2 + 5 + 7 = 33

  33 is divisible by 3.

  Therefore, 865,257 is divisible by 3.
• An integer is divisible by 4 if the last digit in the integer is divisible by 4.
  EX: 5,243,624

  24 is divisible by 4.

  Therefore, 5,243,624 is divisible by 4.
• An integer is divisible by 5 if the last digit in the integer is 0 or 5.
  EX: 6,842,570

  The last digit is 0.

  Therefore, 6,842,570 is divisible by 5.
• An integer is divisible by 6 if the integer is divisible by both 2 and 3.
  EX: 358,416

  3 + 5 + 8 + 4 + 1 + 6 = 27

  27 is divisible by 3.

  6 is divisible by 2.

  Therefore, 358,416 is divisible by 6.
• An integer is divisible by 9 if the sum of the digits in the integer is divisible by 9.
  EX: 620,874

  6 + 2 + 0 + 8 + 7 + 4 = 27

  27 is divisible by 9.

  Therefore, 620,874 is divisible by 9.

Odd & Even Integers

• A number is even if the last digit in the number is 0, 2, 4, 6, or 8.
  EX: 6,584,298

  The last digit of the number is 8.

  Therefore, 6,584,298 is even.
• A number is odd if the last digit in the number is 1, 3, 5, 7, or 9.
  EX: 2,451,869

  The last digit of the number is 9.

  Therefore, 2,451,869 is odd.
• An even integer can be represented as 2k, where k is an integer.
• An odd integer can be represented as 2k + 1 or 2k – 1, where k is an integer.

Rules for Adding & Multiplying Odd & Even Numbers

1. Odd + Odd = Even
2. Even + Even = Even
3. Odd + Even = Odd
4. Odd × Odd = Odd
5. Even × Even = Even
6. Odd × Even = Even

Prime Numbers & Factors

• Factors of an integer are integers that can be divided evenly into the integer.
  EX: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
• Prime number: Number that can only be divided evenly by itself and 1.
  EX: 19 is a prime number.
• The prime numbers up to twenty are 2, 3, 5, 7, 11, 13, 17, and 19.
• 0 and 1 are never prime numbers.
• 2 is the only even prime number.

Least Common Multiple

• The least common multiple of two or more numbers is the smallest number that is a multiple of each of the original numbers.
  EX: The least common multiple of 3 and 13 is 39.

  The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, etc.

  The multiples of 13 are 13, 26, 39, etc.

  39 is the smallest number that intersects these lists.

Exponents

• When multiplying two numbers with the same base, add the exponents.
  EX: 8³ × 8⁴ = 8 × 8 × 8 × 8 × 8 × 8 × 8 = 8⁷
• When dividing two numbers with the same base, subtract the exponents.
  EX: 7⁶ ÷ 7² = (7 × 7 × 7 × 7 × 7 × 7) ÷ (7 × 7) = 7⁴
• When multiplying two num...