Quantitative Aptitude — Quick Reference

Percentage-to-fraction conversions (memorize these cold)

%	Fraction	%	Fraction

|---|---|---|---|

50%	1/2	20%	1/5
33.33%	1/3	16.67%	1/6
25%	1/4	14.28%	1/7
12.5%	1/8	11.11%	1/9
10%	1/10	6.25%	1/16

Core formulas

Profit % = (Profit / Cost Price) × 100
Loss % = (Loss / Cost Price) × 100

Simple Interest = (P × R × T) / 100
Compound Interest: A = P × (1 + R/100)^T
2-year CI − SI shortcut = P × (R/100)²

Speed = Distance / Time
Relative speed (opposite directions) = sum of speeds
Relative speed (same direction) = difference of speeds

Downstream speed = Boat speed + Stream speed
Upstream speed = Boat speed − Stream speed
Boat speed = (Downstream + Upstream) / 2
Stream speed = (Downstream − Upstream) / 2

Work rate = 1 / (days to complete alone)
Combined rate = sum of individual rates

Alligation rule (mixtures)

Cheaper : Dearer = (Dearer value − Mean) : (Mean − Cheaper value)

Number series — systematic check order

1.Constant difference (arithmetic)

2.Constant ratio (geometric)

3.Difference-of-differences (second-order pattern)

4.Alternating/interleaved pattern

5.Position-based (squares, cubes, index relationship)

Divisibility rules

Divisor	Rule

|---|---|

2	Last digit even
3	Digit sum divisible by 3
4	Last two digits divisible by 4
5	Last digit 0 or 5
9	Digit sum divisible by 9
11	Alternating digit sum divisible by 11

Squares and cubes worth memorizing

•Squares: 1² through 30² memorized cold

•Cubes: 1³ through 15³ memorized cold

Compounding frequency adjustment

Frequency	Rate used	Period used

|---|---|---|

Annual	R	T
Half-yearly	R/2	2T
Quarterly	R/4	4T