Aptitude Test Formulas on Tests of Divisibilty, Algebra, Arithmetic Progression, Geometric Progression, H.C.F and L.C.M, Percentages.

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Aptitude Test Formulas :

Tests of Divisibility :

•  A number is divisible by 2 if it is n even number.
•  A number is divisible by 3 if the sum of the digits is divisible by 3.
•  A number is divisible by 4 if the number formed by the last two digits i divisible by 4.
•  A number is divisible by 5 if the units digit is either 5 or 0.
•  A number is divisible by 6 if the number is divisible by both 2 and 3.
•  A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
•  A number is divisible by 9 if the sum of the digits is divisible by 9.
•  A number is divisible by 10 if the units digit is 0.
•  A number is divisible by 11 if the difference of the sum of its digits at odd places and sum of its digits at even places, is divisible by 11.

Algebra :

• Sum of the first n natural numbers = n(n+1)/2
• Sum of the squares of first n natural numbers =  (n(n+1)(2n+1))/6
• Sum of the cubes of first n natural numbers is = (n^2(n+1)^2)/4
• average = (sum of items)/Number of items.

Arithmetic Progression ( A.P ) :

 An A.P. is of the form a, a+d, a+2d, a+3d, ...

where a is called the ' first term ' and d is called the ' common difference '

• nth term of an A.P. Tn = a+(n-1)d.
• sum of the first n terms of an A.P. Sn = n/2(2a+(n-1)d)   or  Sn=n/2(first term+ last term).

Geometrical Progression ( G.P. ) :

 A G.P. is of the form a, ar^2, ar^3, ...

where a is called the ' first term' and r is called the ' common ratio '.

• nth term of a G.P. Tn = ar^n-1.
• Sum of the first n terms in a G.P. Sn = a|1-r^n|/|1-r|.

H.C.F and L.C.M :

H.C.F stands for Highest Common Factor. The other names for H.C.F are Greatest Common Divisor ( G.C.D ) and Greatest Common Measure (G.C.M ).

The H.C.F of two or more numbers is the greatest number that divides each one of them exactly.

The least number which is exactly divisible by each one of the given number is called their L.C.M.

Two numbers are said to be co-prime if their H.C.F is 1.

H.C.F of fractions = H.C.F of numerators/L.C.M of denominators.

L.C.M of fractions = H.C.F of numerators/H.C.F of denominators.

Product of two numbers = Product of their H.C.F and L.C.M.

Percentages :

• If A is R% more than B, then B is less than A by R/(R+100) *100
• If A is R%  less than B, then B is more than A by R/(100-R) *100
• If the Price of a commodity increases by R%, then reduction in consumption, not to increase the expenditure is : R/(R+100)*100.
• If the Price of a commodity decreases by R%, then increase in consumption, not to decrease the expenditure is : R/(R+100)*100.