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Ratios, Rates, and Proportions
A free GRE Quantitative Reasoning note on setting up ratios and rates, solving proportions by cross-multiplication, and avoiding the unit mistakes that cost easy points.
- Write a comparison as a ratio or a rate, and decide which one a problem is describing.
- Reduce a ratio and find a unit rate so quantities are easy to compare.
- Solve a proportion for an unknown using cross-multiplication.
Formulas covered: Proportion solved by cross-multiplication · Unit rate
Read the Ratios, Rates, and Proportions noteExponents and Roots
A free GRE Quantitative Reasoning note on the exponent rules, negative and fractional exponents, simplifying roots, rationalizing denominators, and the sign traps that catch test takers.
- Apply the product, quotient, and power properties of exponents to expressions with a common base.
- Rewrite negative exponents as reciprocals and fractional exponents as roots.
- Simplify square roots and rationalize a denominator containing a radical.
Formulas covered: Product and power properties of exponents · Negative and fractional exponents
Read the Exponents and Roots noteProbability and Counting
A free GRE Quantitative Reasoning note on basic probability, the complement rule, independent versus dependent events, and choosing between combinations and permutations.
- Compute a basic probability as favorable outcomes over equally likely total outcomes.
- Use the complement rule to handle "at least one" and "not" questions in one subtraction.
- Decide whether events are independent or dependent, and multiply probabilities accordingly.
Formulas covered: Complement rule · Multiplication rule for independent events · Permutations and combinations of n items taken r at a time
Read the Probability and Counting noteDescriptive Statistics
A free GRE Quantitative Reasoning note on mean, median, mode, range, standard deviation as a measure of spread, quartiles and percentiles, and the normal distribution facts the GRE actually uses.
- Compute and compare the mean, median, and mode of a small data set.
- Locate quartiles and interpret percentiles as positions in ordered data, not scores.
- Compare standard deviations of data sets by their spread around the mean without calculating them.
Formulas covered: Arithmetic mean · Range and interquartile range
Read the Descriptive Statistics noteQuantitative Comparison Strategy
A free GRE Quantitative Reasoning note on the Quantitative Comparison format, its four fixed answer choices, disciplined number plugging with negatives, zero, fractions, and extremes, and when the relationship cannot be determined.
- State the four fixed Quantitative Comparison answer choices and what each asserts about all allowed values.
- Test algebraic quantities with a deliberate spread of numbers: zero, negatives, fractions between 0 and 1, and large values.
- Recognize when two test values with different results settle the answer as "cannot be determined."
Formulas covered: Sign-of-the-difference test
Read the Quantitative Comparison Strategy noteText Completion Strategy
A free GRE Verbal Reasoning note on the Text Completion format — one to three blanks, no partial credit — and the method: read for the sentence's logical direction, predict your own word before the choices, and dodge the difficult-word trap.
- Identify the structurally significant words in a sentence and state whether they signal continuation or contrast.
- Predict a plain-language filler for each blank from the sentence's own clues before reading the choices.
- Work multi-blank questions one blank at a time, starting with the most constrained blank rather than the first one.
Formulas covered: Blank-count to choice-count map
Read the Text Completion Strategy noteSentence Equivalence Strategy
A free GRE Verbal Reasoning note on the Sentence Equivalence format — one blank, six choices, pick two — and the method: predict from the sentence's logical direction and avoid the synonym-pair trap among the wrong answers.
- State the Sentence Equivalence format — one blank, six choices, select two, no partial credit — and what "alike in meaning" requires.
- Use the sentence's structural words to fix its logical direction before evaluating any choice.
- Predict your own word for the blank and select by matching choices to the prediction rather than to each other.
Formulas covered: Sentence Equivalence answer pattern
Read the Sentence Equivalence Strategy noteReading Comprehension Strategy
A free GRE Verbal Reasoning note on Reading Comprehension: the three answer formats, the recurring question jobs (main idea, inference, strengthen/weaken, author's purpose), reading for structure over detail, and justifying every answer from the passage text alone.
- Name the three Reading Comprehension answer formats and the recurring question jobs: main idea, inference, strengthen/weaken, and author's purpose.
- Map a passage's structure — claim, evidence, objection, reply — in a few words per paragraph before answering.
- Separate the author's own position from positions the passage merely reports, and answer purpose questions from that separation.
Formulas covered: Answer-selection test
Read the Reading Comprehension Strategy note