DSTA Entrance Examination cheat sheet

Analogies: classify the relationship (part-whole, cause-effect, degree, function, category) before choosing; the pair must share the same relationship and the same direction.

Odd-one-out: find the shared property of all but one item; the outlier may differ by category, function, material, or grammatical class rather than meaning alone.

True/False/Cannot Say: answer Cannot Say only when the passage neither confirms nor contradicts the statement; real-world plausibility is irrelevant.

Word-in-context: substitute each option into the sentence and keep only the option that preserves the sentence's logic, not the option that merely sounds formal.

Passage inference: a valid inference must follow necessarily from stated facts; a plausible but unstated assumption is not supported.

Antonym and synonym items: check for degree and connotation, since near-synonyms can differ in intensity (warm/hot/scorching) or tone (thrifty/frugal/stingy).

Sentence completion: use the connector (although, therefore, moreover) to fix the logical direction, then test options against it before reading for style.

Vocabulary in context: keep standard technical terms in English; do not translate a term whose meaning would shift.

Percentage change = (new - old) / old x 100; an increase of 20% then a decrease of 20% nets to 0.96 of the original, i.e. a 4% fall.

Successive percentage changes multiply: a 10% rise followed by a 25% rise equals x1.10 x1.25 = x1.375, a 37.5% increase.

Reverse percentage: if a price after a 15% discount is 85, the original is 85 / 0.85 = 100, not 85 x 1.15.

Ratios: to split an amount in ratio a:b:c, divide by (a+b+c) to get the unit share, then multiply by each term.

Averages: total = average x count; when one value is added, the new average = (old total + new value) / (old count + 1).

Weighted average = sum of (value x weight) / sum of weights; equal weights reduce to the simple arithmetic mean.

Simple interest = P x r x t; compound interest = P(1 + r)^t - P, where r is the rate per period and t the number of periods.

Speed, distance, time: d = s x t; for a round trip at speeds a and b the average speed is 2ab/(a+b), not (a+b)/2.

Work rates add: if A finishes in a days and B in b days, together they finish in ab/(a+b) days.

Series rules to test in order: constant step, increasing step, alternating operations, multiplication, and two interleaved sequences (odd and even positions).

Letter series: convert letters to positions (A=1 ... Z=26) and check the numeric gap between consecutive letters before assuming alphabetical cycling.

Number series with mixed rules: check whether each term is generated from the previous term (difference) or from its position (square, cube, prime).

Matrix and grid puzzles: look for a row rule and a column rule separately; a consistent rule must hold for every complete row and column.

Syllogisms: 'All A are B' and 'All B are C' imply 'All A are C'; 'Some A are B' does not imply 'Some B are not A'.

Contrapositive is valid: 'All A are B' is equivalent to 'All non-B are non-A'; the converse 'All B are A' is not valid.

Negation of 'all' is 'at least one is not'; the negation of 'some' is 'none'.

Ordering and seating puzzles: draw a line or a circle and place the most constrained item first, then apply each remaining clue as a filter.

If-then rules: 'P implies Q' is false only when P is true and Q is false; it says nothing about Q being true without P.

Lever: moment = force x distance from the pivot; a balanced lever satisfies F1 x d1 = F2 x d2.

Mechanical advantage of a lever = effort arm / load arm; a longer effort arm reduces the force needed.

Pulleys: a single fixed pulley changes direction only (MA = 1); a movable pulley sharing n supporting rope segments gives MA = n.

Gears: meshed gears turn in opposite directions; the gear ratio equals teeth count ratio, so a 20-tooth gear drives a 40-tooth gear at half speed.

Belt drives: an open belt makes both pulleys turn the same way; a crossed belt reverses the driven pulley.

Pressure = force / area; the same force on a smaller area produces greater pressure, which is why a sharp edge cuts.

Density = mass / volume; an object floats when its density is less than the fluid's density.

Spatial folding: track one face and its neighbours; on a cube, opposite faces never share an edge, so adjacent faces on the net stay adjacent when folded.

Mirror and rotation items: a mirror reverses left-right relative to the mirror plane; a 90-degree rotation preserves shape and size but changes orientation.

Read the axis units and scale first; a chart starting at a non-zero baseline exaggerates visual differences between bars.

Percentage of total: part / whole x 100; check whether the question asks for a share of the total or a change over time.

Rate questions: output per unit time = total output / total time; to compare rates, convert to a common unit before comparing.

Tables with mixed units: convert every figure to one unit (e.g. thousands to millions) before adding or ranking.

Ratios in data: a ratio of 3:2 means 3 parts to 2 parts, so the larger group is 3/5 of the total, not 3/2 of it.

Estimation shortcut: round to two significant figures to eliminate options, then compute exactly only if two options remain close.

Break-even and cost problems: total cost = fixed cost + (variable cost x units); break-even units = fixed cost / (price - variable cost).

Scheduling and constraint puzzles: list fixed constraints, then test each option against all constraints; the first option that violates any constraint is eliminated.

Rank responses by effectiveness: acting on the issue within your role and escalating when out of scope usually ranks above ignoring it or acting beyond authority.

Conflicting priorities: a safety, legal, or patient/client risk outranks a deadline or a colleague's convenience.

When a colleague's error affects output, the effective response is to raise it directly and privately first, then escalate if unresolved.

Insufficient information: the effective response is to ask the relevant person or check the source, not to guess or to proceed silently.

Teamwork items: sharing information and offering help rank above working alone to protect credit; credit-sharing is not a cost.

Communication with a superior: report facts and impact concisely, propose an option, and avoid blame language.

Work-style self-description items: answer consistently and honestly; contradictory answers across similar items are flagged, so consistency matters more than picking the 'ideal' trait.

Ethical items: a small rule breach to save time is ranked low even when the outcome is good, because the standard is the process, not only the result.