Must know formulas for CSAT
Algebraic Identities
Must know formulas for CSAT
Algebraic Identities

Divisibility Rule
2  An even number or a number with an even last digit, such as 0, 2, 4, 6, and 8.
3  The number should be divisible by 3 when the sum of all its digits is considered.
4  The result of the number's last two digits must be either 00 or a multiple of 4.
5  Numbers with the digits 0 or 5 in the ones place.
6  A number that can be divided by both 2 and 3
7  Multiple of 7 is obtained by deducting twice the number's last digit from the other digits.
8  The sum of a number's last three digits must be divisible by 8 or equal to 000.
9  The number should be divisible by 9 when the sum of all its digits is considered.
10  Any number with the digit 0 in the ones position.
11  A number is divisible by 11 when the sums of its alternative digits differ from each other.
12  A number that can be divided by 3 and 4.
Profit Loss: Formulas
 Cost Price = Selling Price ( No profit No loss)
 Gain Percentage = (Gain × 100)/(C.P.)
 Loss Percentage = (Loss × 100)/(C.P.)
 Profit, P = SP – CP; SP>CP
 Loss, L = CP – SP; CP>SP
 P% = (P/CP) x 100
 L% = (L/CP) x 100
 SP = {(100 + P%)/100} x CP
 SP = {(100 – L%)/100} x CP
 CP = {100/(100 + P%)} x SP
 CP = {100/(100 – L%)} x SP
 Discount = MP – SP
 SP = MP Discount
 For false weight, profit percentage will be P% = [(True weight – false weight)/ false weight] x 100.
 When there are two successful profits, say m% and n%, then the net percentage profit equals to [m+n+(mn/100)]
 When the profit is m%, and loss is n%, then the net % profit or loss will be: [mn(mn/100)]
 If a product is sold at m% profit and then again sold at n% profit then the actual cost price of the product will be: CP = [100 x 100 x P/(100+m)(100+n)]. In case of loss, CP = [100 x 100 x L/(100m)(100n)]
 If P% and L% are equal then, P = L and %loss = P2/100
Interest Formulas for SI and CI
(Simple and Compound) 
Formula 
S.I. 
Principal × Rate × Time 
C.I. 
Principal (1 + Rate)^Time − Principal 
Arithmetic Progression
There are a few key terms we'll encounter in AP that are defined as:
 First term (a)
 Common difference (d)
 nth Term (an)
 Sum of the first n terms (Sn)
All three terms stand for the arithmetic progression property.
First Term of AP
The AP can also be written in terms of common differences, as follows;
a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d 
where “a” is the first term of the progression.
Common Difference in Arithmetic Progression
In this progression, for a given series, the terms used are the first term, the common difference and nth term. Suppose, a1, a2, a3, ……………., an is an AP, then; the common difference “ d ” can be obtained as;
d = a2 – a1 = a3 – a2 = ……. = an – an – 1 
Where “d” is a common difference. It can be positive, negative or zero.
General Form of an AP
Consider an AP to be: a1, a2, a3, ……………., an
Position of Terms 
Representation of Terms 
Values of Term 
1 
a1 
a = a + (11) d 
2 
a2 
a + d = a + (21) d 
3 
a3 
a + 2d = a + (31) d 
4 
a4 
a + 3d = a + (41) d 
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n 
an 
a + (n1)d 

a, a + d, a + 2d, a + 3d, . . . 

an = a + (n – 1) × d 

S = n/2[2a + (n − 1) × d] 

n/2(a + l) 