ABF Officer Recruit Cognify cheat sheet

Percentage change = (new − old) ÷ old × 100. A 20% rise followed by a 20% fall leaves 96% of the original value, not 100%.

Simple interest: A = P(1 + rn). Compound interest: A = P(1 + r)^n, where r is the decimal rate per period and n the number of periods.

Speed = distance ÷ time. Convert metres per second to kilometres per hour by multiplying by 3.6; divide by 3.6 for the reverse.

To split an amount N in the ratio a:b:c, the shares are N·a/(a+b+c), N·b/(a+b+c), N·c/(a+b+c).

Combined work rate = 1/a + 1/b; time working together = ab/(a+b). Two workers at 6 and 3 days finish together in 2 days.

Divisibility: by 3 if the digit sum is a multiple of 3; by 9 if the digit sum is a multiple of 9; by 4 if the last two digits form a multiple of 4.

Profit% = (SP − CP) ÷ CP × 100. Two successive discounts d1 and d2 give a net factor of (1 − d1)(1 − d2).

Average = sum ÷ count. Adding a value equal to the current mean leaves the mean unchanged; adding a larger value raises it.

Estimation rule: round operands to two significant figures to select among options that are far apart, then compute exactly only if the options are close.

All A are B plus all B are C entails all A are C. The converse, all C are A, does not follow from those premises.

In formal logic 'some' means at least one and possibly all. A conclusion asserting that some are not is not supported by a 'some' premise alone.

'A only if B' means A → B, so B is necessary for A. 'A if B' means B → A, so B is sufficient for A.

Any premise containing 'no' or 'none' supports only negative conclusions; a conclusion asserting existence is invalid.

A valid inference must be supported by the passage alone. Statements that are true in the real world but absent from the text are out of scope.

Universal words ('all', 'always', 'never', 'only') make a conclusion easier to falsify; one counter-example is enough to reject it.

For antonym items, identify the stem word's polarity (positive, negative, neutral) before comparing options; then check intensity and register.

Parallel-reasoning items require matching the logical structure of the argument, not its subject matter or wording.

For main-idea items, the correct option covers the whole passage; options that are true but cover only one paragraph are too narrow.

Rotating a point 90° clockwise about the origin maps (x, y) to (y, −x); 90° counter-clockwise maps (x, y) to (−y, x); 180° maps (x, y) to (−x, −y).

In two dimensions there are exactly four distinct orientations of an asymmetric shape under rotation: 0°, 90°, 180°, 270°.

Rotation preserves size, shape and the clockwise order of vertices. Reflection reverses handedness, so a mirror image can never be rotated into its original in the plane.

On a cube net, faces separated by exactly one face in a straight line become opposite faces; opposite faces never share an edge when folded.

Exactly eleven distinct nets of a cube exist. A valid cube net has six squares and folds without overlap.

Vertices meeting at a corner of a folded cube are three mutually adjacent faces; no two of them can be opposite.

When mentally rotating, track one asymmetric feature such as a notch, dot or coloured corner; symmetric outlines match under several rotations and produce false matches.

A shape rotated in the plane keeps the same orientation of any internal arrow or letter; if the letter reads reversed, the transformation was a reflection, not a rotation.

Feature search (target defined by one distinctive attribute such as colour) is fast and nearly independent of display size; conjunction search (two or more combined attributes) is slower and effortful.

A unique colour, orientation or size 'pops out' pre-attentively, so search time stays roughly flat as distractors increase.

Vigilance decrement: detection accuracy falls after roughly 10–20 minutes of monotonous monitoring, with errors of omission rising faster than errors of commission.

Inattentional blindness: an unexpected object is missed when attention is fully engaged on a demanding primary task, even if the object is central.

Change blindness: changes go undetected when they occur during a saccade, blink or brief mask, or when they are introduced gradually.

Systematic scanning in fixed grid cells (left to right, top to bottom) detects more targets than free scanning, which revisits areas and skips others.

In string comparison the most frequently missed errors are transpositions of adjacent letters ('ie' versus 'ei') and doubled letters; compare character by character, not by word shape.

Working-memory capacity is about four chunks, plus or minus one, under modern estimates; the classic 7 ± 2 figure reflects rehearsal-supported immediate serial recall.

Chunking - grouping items into meaningful units such as dates or acronyms - increases the amount of information held within a fixed capacity.

The phonological loop holds verbal material for roughly two seconds without rehearsal; articulatory rehearsal refreshes it.

Serial position effect: first (primacy) and last (recency) items are recalled best, middle items worst; a filled delay removes the recency advantage.

Proactive interference: older learned material disrupts recall of newer similar material. Retroactive interference: newer material disrupts older.

Maintenance rehearsal repeats items rote; elaborative rehearsal links items to existing knowledge and produces stronger long-term retention.

Dual-task interference is smaller when the two tasks use different codes (verbal versus spatial) than when both compete for the same modality.

Recognition is generally more accurate than free recall because the target is presented among cues and only a match decision is required.

Check first differences: constant first differences mean an arithmetic rule; constant second differences mean a quadratic rule such as n².

Constant ratios (×2, ×3) indicate a geometric sequence; alternating ratios often signal two interleaved series.

Fibonacci-type rule: each term equals the sum of the two preceding terms (2, 3, 5, 8, 13); the ratio of successive terms approaches 1.618.

When consecutive terms look unrelated, split the series into odd-positioned and even-positioned subsequences and find a rule in each.

Know the key number sets: squares 1, 4, 9, 16, 25, 36; cubes 1, 8, 27, 64, 125; primes 2, 3, 5, 7, 11, 13.

Letter values run A = 1 to Z = 26; Atbash mirrors the alphabet (A↔Z), so the mirror of a letter is 27 minus its position.

In matrix puzzles, test each row and column separately for addition, multiplication, rotation or movement of elements before assuming a single global rule.

Odd-one-out items: identify the attribute shared by all but one option - number of sides, symmetry axes, enclosed regions or open versus closed lines.

Analogy form A : B :: C : ? - name the relation in the first pair (part–whole, function, cause–effect, degree, category) and apply it to C.

Expected value = Σ (probability × outcome). A 30% chance of 100 with 70% chance of 0 has an expected value of 30.

Sunk costs are unrecoverable past expenditures and must be excluded; only future costs and benefits are relevant to the choice.

Base-rate neglect: combine the prior probability with the strength of new evidence rather than relying on the evidence alone.

Availability heuristic: events that are vivid, recent or heavily publicised are judged more probable than base rates justify.

Confirmation bias: actively seek evidence that could falsify the current hypothesis instead of evidence that supports it.

Framing effect: logically identical outcomes described as gains or as losses produce different choices; restate options in absolute numbers before deciding.

Elimination rule: discard every option that violates a stated constraint first, then compare only the survivors.

Speed–accuracy trade-off: when there is no time bonus, an extra few seconds of checking beats a fast but wrong answer, because a wrong answer scores zero.