GRE General Test: Quantitative, verbal and issue-essay reasoning foundations

Arithmetic: Number Properties, Percents, Ratios, and Exponents

What you must know

This arithmetic practice develops number-property reasoning more than long computation. Be fluent with divisibility rules (3 and 9 by digit sum, 4 by the last two digits, 8 by the last three), prime factorization, greatest common factor and least common multiple, remainders, even/odd and sign rules, fraction–decimal–percent conversions, ratios and proportions, exponent laws, roots, absolute value, and order of operations. Memorize common fraction–percent equivalents (1/6 ≈ 16.7%, 1/8 = 12.5%, 1/7 ≈ 14.3%) to save time under the clock.

Traps that cost points

Percent change is always measured against the base. A 25% increase followed by a 20% decrease returns to the original value; successive percents multiply, they never add.
Distinguish percent of from percent more than, and percent from percentage points.
Never divide both sides by a quantity that could be zero - it silently destroys a case.
Convert units before comparing, and honor any integer constraint the question states.
If a question asks only for the units digit of an integer power, study the base-10 final-digit cycle; do not discard other digits when the question asks for a different quantity.

Worked example

A jacket costs $80. Its price is raised 25%, then the new price is discounted 20%. Final price = 80 × 1.25 × 0.80 = 80 × 1.00 = $80 - unchanged. Rule of thumb: chain percent changes by multiplying factors of the form (1 + r), never by adding percentages.

Algebra: Equations, Inequalities, Quadratics, and Translation

Core skills

Algebra questions reward translation and structure over brute force. You need: solving linear equations and inequalities; systems of two equations (substitution and elimination); quadratic techniques including factoring, the quadratic formula, the discriminant b² − 4 ac, and vertex form; function notation and composition such as f(g(x)); exponent and radical laws; rational expressions; absolute value equations; and modeling word problems - distance/rate/time, combined work rates, mixture and weighted-average setups, and simple sequences.

Traps

Dividing both sides by a variable expression: from x² = 5 x, dividing by x leaves x = 5 and silently drops x = 0. Factor instead.
Multiplying or dividing an inequality by a negative number reverses the inequality sign.
Squaring both sides can introduce extraneous roots; always test candidates in the original equation.
In a quantitative comparison, test permitted cases, including boundary or sign cases where applicable. Values such as 0 or 1 are not valid test substitutions if the stated domain excludes them.
Translated phrases: 5 less than x is x − 5, not 5 − x.
If the question fixes a range such as x > 2, report only the root that satisfies it.

Worked example

Solve x² − 5 x + 6 = 0. Factor: (x − 2)(x − 3) = 0, so x = 2 or x = 3. If the problem also states x > 2.5, the only valid answer is 3. Rule of thumb: move everything to one side, factor, then apply every stated constraint before answering.

Geometry: Figures, Special Triangles, Circles, and Scaling

Core skills

Geometric reasoning compares relationships rather than measurement. Master: angle rules for parallel lines cut by a transversal; triangle properties (angle sum, isosceles base angles, exterior angle, triangle inequality); the Pythagorean theorem and special right triangles 45–45–90 (sides x, x, x√2) and 30–60–90 (x, x√3, 2 x); area and perimeter of standard figures; circles (circumference, area, arcs, sectors, with an inscribed angle equal to half the central angle subtending the same arc); coordinate geometry (slope, distance, midpoint, parallel and perpendicular slopes); and volumes of rectangular solids, cylinders, and spheres.

Traps

Figures are explicitly not drawn to scale: never infer a right angle, equal length, or parallel line from appearance alone.
Similar figures scale lengths by k, areas by k², and volumes by k³.
Area and perimeter are not linked proportionally - doubling a square's perimeter quadruples its area.
The diagonal of a rectangle is not one of its sides; it comes from the Pythagorean theorem.
For sectors, the degree measure and the arc length must use the same fraction of the whole circle.

Worked example

Two similar triangles have corresponding sides in the ratio 3:5. If the smaller triangle's area is 18, the larger area is 18 × (5/3)² = 18 × 25/9 = 50. Rule of thumb: write the similarity ratio first, then apply the correct power - square for area, cube for volume - before computing.

Data Analysis: Statistics, Counting, Probability, and Graphs

Core skills

Data analysis covers descriptive statistics (mean, median, mode, range, standard deviation, quartiles, interquartile range); interpreting bar, line, and circle graphs, scatterplots, and tables - often two or three linked questions per set; the normal distribution's 68–95–99.7 rule; counting via the fundamental counting principle, permutations, and combinations; probability including complements and independent events; and overlapping sets through Total = A + B − Both + Neither.

Traps

With an even number of data values, the median is the average of the two middle values, not one of them.
Adding a constant to every value shifts the mean and median but leaves the standard deviation and range unchanged; multiplying every value by k multiplies the standard deviation by |k|.
Standard deviation measures spread only - two sets can share a mean and have very different spreads.
At least one is almost always fastest as 1 − P(none).
Ask whether order matters: if it does, it is a permutation; if only selection matters, it is a combination.
On graph questions, check axis labels, units, and whether the scale starts at zero before estimating.

Worked example

A set of five numbers has mean 20, so its sum is 100. Adding a sixth value of 32 gives a new mean of (100 + 32)/6 = 132/6 = 22. Rule of thumb: convert every mean back into a sum (sum = mean × count) before combining groups.

Reading Comprehension: Structure, Function, and Inference

Read for structure before detail

A passage may have a structure of claim, evidence, concession or rebuttal; identify what is actually present rather than forcing all four functions onto every text. Before answering anything, summarize in one sentence what the author wants you to believe, and label how the parts move (e.g., phenomenon → rejected explanation → preferred explanation). Most questions, including detail questions, get easier once that skeleton is explicit.

Question types you must recognize

Main idea; function (“in order to”); inference; author's attitude; detail and EXCEPT; strengthen/weaken; vocabulary in context; analogy. For function questions, insert “in order to” before each choice - the correct one completes a statement of purpose, not a paraphrase of the sentence's content.

Traps

True but irrelevant: supported by the passage, yet it does not answer the question asked.
Extreme language: all, never, proves, impossible usually outruns hedged academic prose.
Scope creep: an answer about the wrong paragraph, or one that generalizes a carefully limited claim.
Outside knowledge: your own expertise is never the evidence; only the text is.
Reversed direction: in strengthen/weaken items, choices that do the opposite are common.

Rule of thumb

Phrase your own answer in the author's cautious register before looking at the choices, then eliminate anything stronger or broader than the text. For an inference, require support for the proposed conclusion - a statement that must be true if the passage is.

Worked example

Passage: “Historians once treated guild records as mere administrative residue. Recent work reads them as negotiated documents in which masters and journeymen contested wage norms.” Question: the author mentions “administrative residue” primarily to - the answer names a view the passage then revises. A choice like “to describe medieval bookkeeping practices” is true to the phrase but misses its function, and is wrong.

Text Completion: Logic First, Vocabulary Second

The sentence is a logic puzzle

Each blank is constrained by a signal: contrast (although, yet, paradoxically, despite), support (because, indeed, moreover, so), or definition (a phrase that restates the blank). Locate the signal before weighing vocabulary; the words are the last step, not the first.

Method

Read the whole sentence ignoring the blanks and predict a plain word of your own for each. Then match your prediction to the choices. For two- and three-blank items, no choice is correct until every blank produces a coherent sentence - a word can be perfect in blank (i) and impossible in blank (iii).

Traps

Neighbor-word attraction: a choice that echoes a nearby word often lacks any logical fit.
One-blank-at-a-time thinking: the tempting pair frequently collapses on the remaining blank.
Tone mismatch: grammatically fine but wrong register - praise where the sentence describes criticism.
Ignoring the second sentence: it often supplies the definition the first blank needs.

Rule of thumb

Start with the blank carrying the most constraints (the one with a definition or a strong signal). Eliminate there, then verify the surviving combination by rereading the full sentence.

Worked example

“Although the committee's report was ______, its recommendations were adopted almost unchanged.” The although demands a negative word in contrast with acceptance: reviled or derided fits. A choice such as conciliatory or lauded reverses the logic, and a word that merely echoes “report” (e.g., documentary) has no evaluative force at all. Predict first, match second.

Sentence Equivalence: Finding the Coherent Pair

Two answers, one meaning

The paired-completion method compares two words that produce coherent sentences of equivalent meaning; this practice page uses its own four-option interface and does not duplicate an official interaction. They need not be synonyms; they must produce two sentences that mean the same thing, and both must be independently defensible. Treat the item as a single-blank Text Completion that happens to have six options.

Method

Read the sentence and name its logic signal (contrast, cause, restatement).
Predict a word in your own vocabulary.
Scan for the pair nearest your prediction, then reread the sentence with each word substituted in full.

If two choices are near-synonyms but only one fits the logic, neither is correct - both members of the pair must fit.

Traps

The synonym decoy pair: two attractive synonyms that together violate the sentence's contrast.
The lone correct word: one excellent choice whose partner is wrong; both members must support the intended paired reading.
Intensity mismatch: words close in meaning but far apart in strength (unhelpful vs. catastrophic).
Skipping the second clause: it frequently defines or reverses the blank.

Rule of thumb

Substitute each candidate into the whole sentence and ask whether the two resulting sentences say the same thing. If you cannot state the sentence's logic in one clause - “the writer concedes X but argues Y” - you are guessing, not solving.

Worked example

“Far from being ______, the proposal drew immediate praise from every faction.” The far from signals the blank is the opposite of what praise implies. Contentious and divisive produce the same sentence and both fit. Novel and innovative are a tidy synonym pair, but they are coherent with nothing in the sentence - the classic decoy.

Analyze an Issue: Building a Nuanced, Well-Supported Position

An issue essay develops a reasoned position on a stated claim, explains evidence and examines relevant complexity. This independent chapter teaches argument construction rather than predicting an official score or supplying current timing and scoring policy.

Read the instruction, not just the prompt

Each Issue prompt is followed by a specific instruction, such as discussing the extent to which you agree or disagree, the circumstances in which a recommendation would be advantageous, or the consequences of adopting a claim. These instructions vary across the pool; answering a different question fails to address the assigned task. Underline the verb and the scope words-'extent', 'specific circumstances', 'consequences'-and make your thesis answer that exact question.

Build a position with visible complexity

High-scoring responses do not simply agree or disagree; they define the claim's scope. Identify the key qualifier-'only', 'primary', 'must', 'most important'-and test it. Concede the strongest opposing point, then explain why your position still holds. Organize reasons as paragraphs, each with a claim, explanation, and a concrete example from history, science, current events, or lived experience. Avoid invented statistics.

Worked example

Prompt: 'Governments should fund the arts only when all other public needs have been met.' Instruction: discuss the extent to which you agree or disagree, considering ways the statement might or might not hold true.

Reasoning: the word 'only' makes arts funding residual. Taken literally, it would almost never apply, because public needs are never fully satisfied. Concede that emergency needs-pandemic hospital capacity, fire response-should outrank museums. Then argue that a blanket residual rule is poor policy: arts funding supports tourism, education, and community cohesion, and the resource trade-off should be examined explicitly rather than ignored. Address the counterargument that arts subsidies can favor elite institutions; the remedy is accountability, not elimination. Thesis: urgent needs should take precedence, but 'only when' is too absolute; governments should maintain a modest, accountable baseline.

Traps that cost marks

Ignoring the instruction line and writing a generic agree/disagree essay.
A false dichotomy: 'I completely agree' followed by no acknowledgment of exceptions.
Vague examples ('studies show') or invented facts instead of explainable cases.
Listing examples without explaining how they support the claim.
No counterargument, so the position looks unexamined.

Evidence, sufficiency and quantitative comparison

Information is sufficient when it determines the answer to the question being asked, within the stated domain. A statement need not identify an exact value to answer a yes-or-no question consistently. Conversely, finding one example that gives a yes does not establish that every permitted example does. First rewrite the target question precisely; then test each supplied statement independently before combining them.

For example, if x is a real number and x²=49, its value could be 7 or-7. This is insufficient to determine x uniquely, but it is sufficient to answer whether x is nonzero. Adding x>0 determines x=7. The question matters as much as the numerical equation. Do not import a second statement when checking the first alone, and do not assume positivity, integrality or distinctness unless it is actually given.

Tables and charts introduce source discipline. Read the label, unit, date or period, denominator and any note before comparing values. A total in thousands is not directly comparable to a single-unit count without conversion. A percentage based on all responses can differ from the percentage based on respondents to one item. A share of a total, a percent increase from a baseline and a percentage-point difference answer different questions. State which one the problem requests.

In a multi-source model, assign each fact to its source and time. An original estimate and a revised estimate are not necessarily contradictory: they may answer different versions of the same planning question. If three people cost 120 per hour and two cost 90 per hour, the combined hourly rate is 540. At 200 hours the modeled labor cost is 108000; at 250 hours it is 135000. A budget note cannot silently replace the requested original duration. These are fictional calculations, not labor-market facts.

Finally, distinguish consistency from proof. A rule may fit every supplied term of a finite sequence without being the only mathematical continuation possible. Such exercises ordinarily ask for the intended simple pattern represented by the available choices. Explain that rule and test it on all supplied pairs. In an argument question, similarly identify the premise, proposed conclusion and any missing assumption. A plausible conclusion is not automatically entailed. A counterexample can disprove a universal claim, while several supporting examples alone do not establish one.