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Top Reasoning Formulas

Logical reasoning and aptitude shortcuts.

1
Number Series: Constant Difference
Next Term = Current Term + Common Difference

Identify arithmetic number patterns.

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2
Arithmetic Progression: nth Term
aₙ = a + (n - 1)d

Find any term of an arithmetic progression.

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3
Probability
P(E) = Favourable Outcomes / Total Equally Likely Outcomes

Calculate the probability of an event.

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4
Combination
ⁿCᵣ = n! / [r!(n-r)!]

Count selections where order does not matter.

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5
Clock Angle
Angle = |30H - 5.5M| degrees

Calculate the smaller angle between clock hands.

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6
Handshakes
Number of Handshakes = n(n - 1) / 2

Calculate pairwise handshakes when each pair meets once.

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7
Number of Matches in Tournament
Number of Matches = n(n - 1)/2

Find total matches when each team plays every other team once.

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8
Seating Arrangement Linear
n! for n distinct people in a row

Count ways to seat n people in a straight line.

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9
Probability of Independent Events
P(A and B) = P(A) × P(B)

Find probability of two independent events occurring together.

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10
Average Speed Equal Time
Average Speed = (u + v)/2

Calculate average speed when time intervals are equal.

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11
Clock Hands Coincide
Hands coincide every 65 5/11 minutes

Find when hour and minute hands overlap.

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12
Permutation of Repeated Objects
n! / (p! q! r! …)

Arrange n objects where some are identical.

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13
Circular Arrangement
Distinct Circular Arrangements = (n - 1)!

Count arrangements of distinct people around a circle.

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14
Geometric Progression nth Term
aₙ = arⁿ⁻¹

Find a term in a geometric progression.

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15
Calendar Odd Days
Odd Days = Total Days mod 7

Find the remainder of days after complete weeks.

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16
Average Speed for Equal Distances
Average Speed = 2uv / (u + v)

Calculate average speed over two equal distances.

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17
Simple Interest Shortcut
SI = PRT / 100

Calculate simple interest quickly in aptitude problems.

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18
Percentage Change Shortcut
Percentage Change = (New - Original) / Original × 100

Calculate the relative change between two values.

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19
Calendar Leap Year Rule
Leap Year: divisible by 400, or divisible by 4 but not by 100

Determine whether a Gregorian calendar year is a leap year.

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20
Probability of Mutually Exclusive Events
P(A or B) = P(A) + P(B)

Find probability of either of two mutually exclusive events.

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21
Calendar Day of Week
Odd days determine the day of the week

Find the day of the week after a given number of days.

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