GAT General cheat sheet

Synonym questions: the correct option matches the stem word's meaning in its given context; when a word has several senses, the sense implied by the sentence controls the answer.

Antonym questions: the answer must be opposite in the same part of speech; options that are merely unrelated to the stem are wrong even though they are not similar.

Analogy items are solved by building a short bridge sentence for the stem pair (for example, 'a chisel is a tool used to cut') and applying that exact sentence to each option.

Standard analogy relations to test in order: species-to-genus, part-to-whole, object-to-function, cause-to-effect, worker-to-tool, degree of intensity, and antonymy.

Sentence completion: contrast signals (although, despite, however, rather, yet) force the blank to oppose an idea in the sentence, while cause signals (because, therefore, since) force agreement.

Two-blank items: solve the more predictable blank first, eliminate every option that fails it, then check the second blank for grammar and logic.

Reading comprehension main-idea options must cover the whole passage; an option that mentions only one paragraph is a detail, not the main idea.

Inference items require an answer that must be true given the passage; statements that are merely plausible or are true only from outside knowledge do not qualify.

Answer-choice scope rule: a correct option may be narrower than the passage but never broader, so any option introducing a topic the passage never discusses is eliminated.

Average = sum of values / number of values; equivalently sum = average × count, which answers problems that supply either the average or the total.

Percent change = (new value − old value) / old value × 100; the denominator is always the original amount, not the new one.

Successive percent changes of a and b combine multiplicatively: net change = (1 + a/100)(1 + b/100) − 1, so a 20% rise then a 20% fall leaves a 4% net fall.

Splitting a total T in the ratio a : b gives parts aT/(a+b) and bT/(a+b); add the ratio terms first to find the number of equal parts.

Two workers who alone need a and b hours work at rates 1/a and 1/b, so together they finish in ab/(a+b) hours.

Average speed = total distance / total time; for equal distances covered at speeds x and y it equals 2xy/(x+y), never (x+y)/2.

Simple interest = P × R × T / 100; compound amount = P(1 + R/100)^T and compound interest = that amount − P.

Circle: area = πr², circumference = 2πr = πd; triangle: area = ½ × base × height; quadrilateral area sums follow from splitting into triangles.

Memorise Pythagorean triples 3-4-5, 5-12-13, 8-15-17, 7-24-25 and their multiples; interior angles total 180° in a triangle and 360° in a quadrilateral.

'If A then B' licenses B whenever A holds, and also licenses the contrapositive 'if not B then not A'; it never licenses 'if B then A'.

'A only if B' translates to A → B (B is necessary for A); 'A if B' translates to B → A; reversing either is the most common puzzle error.

The number of different linear orders of n distinct items is n! (n factorial); for five items that is 120.

The number of distinct circular seating orders of n distinct people is (n − 1)!, because rotating the entire arrangement changes nothing.

Solve by fixing the most constrained element first: the item with the fewest legal positions, or the one touched by the most rules, forces the rest of the layout.

Adjacency rule: when two items must sit together, treat them as one block while counting, then multiply by 2 if their internal order is free.

Syllogism chain: 'All A are B' plus 'All B are C' yields 'All A are C'; a premise using 'some' supports only a swapped 'some' conclusion, never 'all' or 'none'.

Distinct pairs in a group of n (handshakes, matches, head-to-head comparisons) equal n(n − 1)/2, the division by 2 removing double counting.

'Either A or B' in most puzzles means at least one is selected; test whether the rules also forbid both before assuming exactly one.