Verbal & Non-Verbal Reasoning Core Concepts

Comprehensive practice flashcards defining core vocabulary, mathematical formulas, and analytical reasoning principles from the Verbal & Non-Verbal Reasoning textbook.

Triangular Number Pattern

A number series pattern of the form $a, a + (a + 1), a + (a + 1) + (a + 2), \dots$, where the $n^{\text{th}}$ term is calculated using the formula $\left[\frac{n(n + 1)}{2}\right]$.

EJOTY Rule

A mnemonic device in alphabet series reasoning used to recall the numerical positions of English letters at intervals of five: $E = 5$, $J = 10$, $O = 15$, $T = 20$, and $Y = 25$.

Direct Information (Matrix Arrangement)

Information in matrix arrangement problems that explicitly connects an individual object or person directly to one of its specific properties or attributes.

Indirect Information (Matrix Arrangement)

Information in matrix arrangement problems that defines a relationship between two or more properties of an object rather than stating an explicit match.

Circular Arrangement

A reasoning puzzle format where persons or objects are positioned along a closed circular perimeter, with relative directions (left or right) determined by whether individuals face towards the centre or outward.

Relative Speed of Clock Hands

The relative rate at which the minute hand gains on the hour hand, calculated as $6^\circ/\text{min} - \frac{1}{2}^\circ/\text{min} = \frac{11}{2}^\circ/\text{min}$.

Clock Angle Formula

The mathematical formula used to determine the angle between the hour hand and the minute hand at $P$ hours and $Q$ minutes: $\left|\frac{11}{2}Q - 30P\right|$.

Clock Hands Coincidence Interval

The exact time interval between consecutive moments when both hands of a clock coincide, equal to $\frac{360^\circ}{\frac{11}{2}^\circ/\text{min}} = \frac{720}{11}\text{ minutes}$, or $65\frac{5}{11}\text{ minutes}$.

Euler's Formula for a Cube

The geometric formula relating the number of faces ($F = 6$), vertices ($V = 8$), and edges ($E = 12$) of a cube: $F + V = E + 2$.

Cube Cuts to Pieces Formula

The principle stating that if $a$, $b$, and $c$ cuts are made along three mutually perpendicular planes of a cube, the total number of resulting pieces is $(a + 1)(b + 1)(c + 1)$.

Formula for Painted Cubes with Two Faces

The formula $12(n - 2)$, which gives the number of smaller cubes with exactly two painted faces when a larger painted cube is cut into $n^3$ smaller cubes, located along the $12$ edges excluding the corners.

Formula for Painted Cubes with One Face

The formula $6(n - 2)^2$, which gives the number of smaller cubes with exactly one painted face when a larger painted cube is sliced into $n^3$ smaller cubes, located on the interiors of the $6$ faces.

Formula for Unpainted Cubes

The formula $(n - 2)^3$, which determines the number of inner cubes with zero painted faces when a larger painted cube is sliced into $n^3$ identical smaller cubes.

Gregorian Century Leap Year Rule

The calendar rule establishing that a century year is considered a leap year only if its numerical value is evenly divisible by $400$ (e.g., $1600$ and $2000$ are leap years, whereas $1900$ and $2100$ are ordinary years).

Zeller's Rule

A formula used to compute the day of the week for any given calendar date: $f = k + \left[\frac{13m - 1}{5}\right] + D + \left[\frac{D}{4}\right] + \left[\frac{C}{4}\right] - 2C$, where $k$ is the day of the month, $m$ is the month number (March = $1$ through February = $12$), $D$ is the last two digits of the year, and $C$ represents the century.

Odd Days

The extra days remaining after dividing the total number of days in a given period by $7$; an ordinary year contains $1$ odd day ($365 \div 7 = 52\text{ weeks} + 1\text{ day}$) and a leap year contains $2$ odd days.

Upset (Tournament)

An outcome in a seeded knockout tournament where a lower-ranked (lower-seeded) participant defeats a higher-ranked (higher-seeded) participant.

Round Robin Tournament

A tournament structure in which every competitor or team plays against each of the other participating teams or players exactly once, requiring a total of $\binom{n}{2}$ matches for $n$ teams.

Logical Connective "If X then Y"

A conditional statement establishing that the occurrence of event $X$ guarantees the occurrence of event $Y$ ($X \to Y$), and the non-occurrence of $Y$ guarantees the non-occurrence of $X$ ($\sim Y \to \sim X$).

Logical Connective "Unless X, Y"

A logical formulation meaning that if event $X$ does not occur, then event $Y$ must occur ($\sim X \to Y$), and if event $Y$ does not occur, then event $X$ must occur ($\sim Y \to X$).

Middle Term (Syllogism)

The term common to both premises in a categorical syllogism that serves to link the subject and predicate but must never appear in the derived conclusion.

Universal Affirmative Proposition

A categorical statement beginning with qualifiers like "All," "Every," or "Each," characterized by distributing its subject term while leaving its predicate term undistributed.

Course of Action

An administrative measure, practical step, or decision taken to resolve, improve, or follow up on a problem or policy situation described in a statement.

Assumption

An unstated premise that is taken for granted, presupposed, or accepted as true by the speaker when making a statement.

Strong Argument

An argument that is both significant and directly relevant to the central question or policy issue, supported by sound reasoning rather than trivial points.

Water Image

The optical reflection of an object across a horizontal plane, resulting in a vertical upside-down inversion while the lateral left and right positions remain unchanged.

Mirror Image

The optical reflection of an object across a vertical plane, resulting in a lateral inversion where the left and right sides interchange while the top and bottom remain unchanged.

Pythagoras Theorem (Direction Sense)

The mathematical relationship $a^2 + b^2 = c^2$ used in distance and direction reasoning to find the shortest straight-line distance ($c$) between an initial point and a final point.

Conditions for No-Relationship (Inequality)

Sequences of conflicting inequality signs between two variables (such as $> <$, $\ge \le$, $< >$, or $\le \ge$) that prevent the deduction of any definite relationship between those variables.

Analogy

A reasoning question type based on correspondence, where a defined relationship between an initial pair of terms must be identified and replicated for another term using the given options.