## Simple Interest Principal: The money borrowed or lent out for a certain period is called the principal or the sum.

Interest: Extra money paid for using other’s money is called interest.

At what rate percent per annum will a sum of money double.

Quantitative Aptitude: Useful for SSC,CGL, CPO, CPMF, CHSL, UPSC, CDS, NDA, GATE, Railways RRB, PO, Clerk, Bank, Army, Force, Sub-Inspector, Teacher, Constable, Police, Lekhpal, UPSSC, State govt, Jobs and Entrance Examination

## Percentage % video- for Competitive Exam Concept of Percentage
To express % as a fraction & decimal
Commodity price increases & decrease
Population of a city after or before few years
Depreciation of Machinery or Plant
If A is R% more than B, then B is less than A by

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## “BODMAS” Rule – Quantitative Aptitude B   –    Brackets first –   in the order(), {} and [].

O  – Orders (i.e. Powers and Square Roots, etc.)

DM – Division and Multiplication (left-to-right)

Useful for : SSC,CGL, CHSL, CPO, CPMF, UPSC, CDS, NDA, GATE, Railways RRB, PO, Clerk, Bank, Army, Force, Sub-Inspector, Teacher, Constable, Police, Lekhpal, UPSSC, State govt, Jobs and Entrance Exam

Mathematics Quantitative Aptitude “BODMAS” Rule

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## Least Common Multiple (L.C.M.) Factorization Method & Division Method- Quantitative Aptitude Quantitative aptitude – Least Common Multiple (L.C.M.)
Factorization Method & Division Method (Short cut method)
Product of two numbers =Product of their H.C.F. and L.C.M.,
Co-primes, H.C.F. & LCM of Fractions:
Useful for : SSC,CGL, CPO, CPMF, UPSC, CDS, NDA, GATE, Railways RRB, PO, Clerk, Bank, Army, Force, Sub-Inspector, Teacher, Constable, Police, Lekhpal, UPSSC, State govt, Jobs and Entrance Exam

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## Quantitative Aptitude: Numbers – Progression or Sequence Useful for
SSC,CGL, CPO, CPMF, UPSC, CDS, NDA, GATE, Railways RRB, PO, Clerk, Bank, Army, Force, Sub-Inspector, Teacher, Constable, Police, Lekhpal, UPSSC, State govt, Jobs and Entrance Examination

PROGRESSION  or Sequence:  A succession of numbers formed and arranged in a definite order according to certain definite rule, is called a progression.

1. Arithmetic Progression (A.P.) or Sequence : If each term of a progression differs from its preceding term by a constant, then such a progression is called an arithmetical progression. This constant difference is called the common difference of the A.P. An A.P. with first term a and common difference d is given by a, (a + d), (a + 2d),(a + 3d),…..

The nth term of this A.P. is given by Tn =a + (n – 1) d.

The sum of n terms of this A.P.  Sn = n/2 [2a + (n – 1) d] = n/2 [a + a + (n – 1) d]

= n/2   (first term + last term).

Some important results : ü(1 + 2 + 3 +…. + n) =n(n+1)/2 ü(l2 + 22 + 32 + … + n2) = n (n+1)(2n+1)/6 ü(13 + 23 + 33 + … + n3) =n2(n+1)2 /4

2.Geometrical Progression (G.P.) also known as Geometric Sequence :                   A progression of numbers in which every term bears a constant ratio with its preceding term, is called a geometrical progression. The constant ratio is called the common ratio of the G.P.

A G.P. with first term a and common ratio r is :

G.P.   –     a, ar, ar2, ar3 …..

In this G.P. Tn = arn-1

sum of the n terms,      Sn=   a(1-rn)

(1-r)

Ex.      2,6,18,54…..

2, 2*3, 2*3²,2*33…… ,       Fist term a=2, common ratio r =3

If n= 5, than T5 = arn-1   = 2*35-1   = 2* 34 = 162

Sn=   a(1-rn)   =   2(1-35)  / (1-3) = 2(1-243)/-2 = 242

(1-r)

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## Quantitative Aptitude Part -2 TESTS OF DIVISIBILITY for SSC, bank, RRB, Police, Teacher TESTS OF DIVISIBILITY Divisibility By 2 : A number is divisible by 2, if its unit’s digit is any of 0, 2, 4, 6, 8. Ex. 61752 is divisible by 2,

Divisibility By 3 : A number is divisible by 3, if the sum of its digits is divisible by 3. Ex.592482 is divisible by 3, since sum of its digits = (5 + 9 + 2 + 4 + 8 + 2) = 30, which is divisible by 3.

Divisibility By 4 : A number is divisible by 4, if the number formed by the last two digits is divisible by 4. Ex. 892648 is divisible by 4, since the number formed by the last two digits is 48, which is divisible by 4. Divisibility By 5 : A number is divisible by 5, if its unit’s digit is either 0 or 5. Thus, 20820 and 50345 are divisible by 5,

Divisibility By 6 : A number is divisible by 6, if it is divisible by both 2 and 3. Ex. The number 35256 is clearly divisible by 2. Sum of its digits = (3 + 5 + 2 + 5 + 6) = 21, which is divisible by 3. Thus, 35256 is divisible by 2 as well as 3. Hence, 35256 is divisible by 6.

Divisibility By 8 : A number is divisible by 8, if the number formed by the last three digits of the given number is divisible by 8. ,Ex. 953360 is divisible by 8, since the number formed by last three digits is 360, which is divisible by 8.

Divisibility By 9 : A number is divisible by 9, if the sum of its digits is divisible by 9. Ex. 60732 is divisible by 9, since sum of digits * (6 + 0 + 7 + 3 + 2) = 18, which is divisible by 9.

Divisibility By 10 : A number is divisible by 10, if it ends with 0. Ex. 96410, 10480 are divisible by 10, Divisibility By 11 : A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11. Ex. The number 4832718 is divisible by 11, since : (sum of digits at odd places) – (sum of digits at even places) (8 + 7 + 3 + 4) – (1 + 2 + 8) = 11, which is divisible by 11.

Divisibility By 12 ; A number is divisible by 12, if it is divisible by both 4 and 3. Ex. Consider the number 34632. The number formed by last two digits is 32, which is divisible by 4, Sum of digits = (3 + 4 + 6 + 3 + 2) = 18, which is divisible by 3. Thus, 34632 is divisible by 4 as well as 3. Hence, 34632 is divisible by 12.

Divisibility By 14 : A number is divisible by 14, if it is divisible by 2 as well as 7.

Divisibility By 15 : A number is divisible by 15, if it is divisible by both 3 and 5.

Divisibility By 16 : A number is divisible by 16, if the number formed by the last4 digits is divisible by 16. Ex.7957536 is divisible by 16, since the number formed by the last four digits is 7536, which is divisible by 16.

Divisibility By 24 : A given number is divisible by 24, if it is divisible by both3 and 8.

Divisibility By 40 : A given number is divisible by 40, if it is divisible by both 5 and 8.

Divisibility By 80 : A given number is divisible by 80, if it is divisible by both 5 and 16.

Note : If a number is divisible by p as well as q, where p and q are co-primes, then the given number is divisible by pq.

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