CogAT cheat sheet

Verbal Classification: all answer choices must belong to the same category as the three stem words; reject any option that fits only two of the three stem words.

Verbal Analogy format is A : B :: C : ?; the relationship must hold in the same direction (A→B as C→D), so a reversed relationship (B→A) is a distractor.

Common analogy bridges: part-to-whole, cause-to-effect, worker-to-tool, object-to-function, degree (warm : hot :: cool : cold), and category-to-member.

Sentence Completion: choose the word that fits both the sentence logic and the grammar; a connector like 'although' or 'but' signals a contrast, so the blank opposes the stated idea.

Passage-based items ask for main idea, inference, or author's purpose; the correct answer is supported by the passage text, not by outside knowledge.

Verbatim repetition of passage wording is often a trap; the correct inference restates the idea in different words without adding new claims.

Antonym and synonym items hinge on precise word meaning; a word with a secondary meaning (e.g., 'bank') must be read in the context given.

Word-part clues: prefixes (un-, dis-, pre-, re-) and suffixes (-less, -ful, -tion) narrow meaning when the whole word is unfamiliar.

Number Series: compute consecutive differences first; if differences are constant it is arithmetic, if the ratio is constant it is geometric, and if differences grow it is often a second-order or square/cube pattern.

Number Analogy format is A : B :: C : ?; identify the operation from A to B (e.g., ×3 + 1) and apply the identical operation to C.

Number Puzzle: the missing value is determined by a rule relating the surrounding numbers, such as sum of outer numbers equals the center, or a constant row/column total.

Order of operations: parentheses, then exponents, then multiplication/division left to right, then addition/subtraction left to right; this order decides many answer choices.

Percent change = (new − old) ÷ old × 100; a percent increase then an equal percent decrease does not return to the original value.

Average (mean) = sum of values ÷ number of values; if the mean of n numbers is m, the total is n × m.

Ratio problems: set up a proportion a/b = c/d and cross-multiply (a × d = b × c); keep units aligned on each side.

Divisibility shortcuts: a number is divisible by 3 if its digit sum is divisible by 3, by 9 if the digit sum is divisible by 9, and by 4 if its last two digits form a multiple of 4.

Figure Classification: find the invariant feature shared by the three stem figures (number of sides, symmetry, number of enclosed regions, or shading) and pick the option that shares it.

Figure Analogy format is A : B :: C : ?; describe the transformation from A to B (rotate, reflect, resize, add/remove a part) and apply exactly that transformation to C.

Figure Analysis (paper folding): each fold creates a mirror line; unfold by reflecting the hole pattern across each fold line in reverse order of folding.

Figure Analysis answer choices differ by hole count, position, and symmetry; the number of holes equals the number of punches times 2 raised to the number of folds that cover the punched area.

Paper-folding holes on a fold line produce merged, not doubled, holes; check whether the punch lands on the crease before counting.

Figure Matrices: read the rule across rows and down columns; the missing cell must satisfy both the row rule and the column rule.

Common transformations to test: rotation by 90° or 180°, horizontal or vertical reflection, size scaling, color/shading inversion, and part addition or removal.

Symmetry rules are frequent: a figure symmetric about a vertical axis stays symmetric if reflected horizontally, while a 90° rotation changes the axis orientation.