A number is divisible by 2, if its unit’s place digit is 0, 2, 4, or 82.
A number is divisible by 3, if the sum of its digits is divisible by 33.
A number is divisible by 4, if the number formed by its last two digits is divisible by 44.
A number is divisible by 8, if the number formed by its last three digits is divisible by 85.
A number is divisible by 9, if the sum of its digits is divisible by 96.
A number is divisible by 11, if, starting from the RHS,(Sum of its digits at the odd place) – (Sum of its digits at even place) is equal to 0 or 11x7.
Results on Division:Dividend = Quotient × Divisor + Remainder
An Arithmetic Progression (A. P.) with first term ‘a’ and Common Difference ‘d’ is givenby:[a], [(a + d)], [(a + 2d)], … … …, [a + (n – 1)d] nth term, Tn = a + (n – 1)d Sum of first ‘n’ terms, Sn= n/2 (First Term + Last Term)16.
A Geometric Progression (G. P.) with first term ‘a’ and Common Ratio ‘r’ is given by:a, ar, ar
1] Bracket 2] Order 3] Division 4] Multiplication 5] Addition 6] Subtraction
Allegations & Mixture.
Surds and Indices
Pipes and Cistern
X = Pipe fill the tank (X1, X2, X3 ….etc.)
Y = Pipe empty the tank (Y1, Y2, Y3 ….etc.)
Time required to fill tank in 1 hr. is = 1/x1 + 1/x2
Boats and Streams
Simple and Compound Interests
Time and Work
Volume and Surface Area
Stocks and Shares
True Discount and Banker’s Discount
Games of Skill
Permutations and Combination
Odd Man Out
Heights and Distances
Graphs, Bar, Pie and Line Graphs.