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    Formulas , Tips and Tricks

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    Abhishek

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    Formulas , Tips and Tricks

    Post  Abhishek on Mon Apr 18, 2011 12:16 am

    Pour all your formulas here and let this thread be only for formulas to make things easier for us :

    Area, Surface area and Volume



    Rectangle:


    Area =
    lw
    Perimeter = 2l + 2w

    Parallelogram:


    Area = bh

    Triangle


    Area = 1/2 of the base X the height =
    1/2 bh
    Perimeter = a + b + c

    Trapezoid



    Perimeter = P = a + b1 + b2 + c

    Circle:


    The distance around the circle is a circumference. The distance across the circle is the diameter (d). The radius (r) is the distance from the center to a point on the circle. (Pi = 3.14)
    d = 2r
    c =
    pd = 2 pr
    A =
    pr2
    (p=3.14)


    Rectangular Solid


    Volume = lwh
    Surface = 2lw + 2lh + 2wh


    Prisms


    Volume = Base area X Height
    Surface = 2b + Ph (b is the area of the base P is the perimeter of the base)

    Cylinder



    Volume = pr2 h
    Surface =
    2prh


    Pyramid


    V = 1/3 bh
    b is the area of the base
    Surface Area: Add the area of the base to the sum of the areas of all of the triangular faces. The areas of the triangular faces will have different formulas for different shaped bases.

    Cones


    Volume = 1/3 pr2 x height = 1/3 pr2h
    Surface =
    pr2 + prs = pr2 + pr

    Sphere


    Volume = 4/3 pr^3
    Surface area = 4pr^2

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    Abhishek

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    Re: Formulas , Tips and Tricks

    Post  Abhishek on Mon Apr 18, 2011 12:23 am


    Simple And Compound Interest


    <BLOCKQUOTE style="PADDING-BOTTOM: 0px; MARGIN: 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; WORD-WRAP: break-word; PADDING-TOP: 0px" class="postcontent restore ">1. Simple Interest = PNR/100

    where, P --> Principal amount
    N --> time in years
    R --> rate of interest for one year

    2. Compound interest (abbreviated C.I.) = A -P =

    where A is the final amount, P is the principal, r is the rate of interest compounded yearly and n is the number of years

    3. When the interest rates for the successive fixed periods are r1 %, r2 %, r3 %, ..., then the final amount A is given by A =


    4. S.I. (simple interest) and C.I. are equal for the first year (or the first term of the interest period) on the same sum and at the same rate.

    5.
    C.I. of 2nd year (or the second term of the interest period) is more than the C.I. of Ist year (or the first term of the interest period), and C.I. of 2nd year -C.I. of Ist year = S.I. on the interest of the first year.</BLOCKQUOTE>

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    Abhishek

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    Comparing Fractions Useful for DI and Percentage and Ratio Calculation

    Post  Abhishek on Mon Apr 18, 2011 12:35 am


    Comparing Fractions



    This topic is of extremely important for Data Interpretation and other areas of Quants Paper. It is highly recommended for aspirants of various exams to internalize the concepts .


    Type 1 : When the numerators are same

    When the numerators are same and denominators are different , the fraction with the highest denominator is the smallest.

    Example : 3/5 , 3/7 , 3/13 , 3/8

    Here the smallest fraction is 3/13 and the largest fraction is 3/5

    Type 2 : When the numerators are different but the denominators are all same

    The fraction with the largest denominator is the largest.

    Example : 7/5 , 9/5 , 4/5 , 11/5

    Here the smallest fraction is 4/5 and the largest fraction is 11/5

    Type 3 :Fraction with the largest denominator and smallest numerator is the largest
    Example : 19/16 , 24/11 , 17/13 , 21/14 , 23 /15

    Here 24/11 is the largest fraction.

    Type 4 :When the difference between the numerator and the denominator is same ( When the value of the fraction is less than 1)


    When the difference between the numerator and the denominator is same the fraction with the largest value of numerator and denominator is the largest.


    Example : 31/37 , 23/29 , 17/23 , 35/41 , 13/19

    Here 35/41 is the largest fraction and 13/19 is the smallest fraction.



    Type 5 :When the difference between the numerator and the denominator is same ( When the value of fraction is more than 1)

    When the difference between the numerator and the denominator is same the fraction with the smallest value of numerator and denominator is the largest.

    Example :31/27 , 43/39 , 57/53 , 27/23 , 29/25

    Here the largest fraction is 27/23


    These fraction comparisons are extremely useful for quick DI calculations .

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    Divisibility Rules

    Post  Abhishek on Mon Apr 18, 2011 12:37 am

    I hope everyone is aware of the division rules , still I am posting them here some of the divisibility rules:


    Divisibility by 2: If its units digit is any of 0,2,4,6,8.


    Divisibility by 3: If the sum of its digits is divisible by 3.


    Divisibility by 4: If the number formed by the last two digits is divisible by 4

    Divisibility by 5: If its units digit is either 0 or 5.


    Divisibility by 6: If it is divisible by both 2 & 3.



    Divisibility by 8: If the last three digits of the number are divisible by 8.


    Divisibility by 9: If the sum of its digit is divisible by 9.


    Divisibility by 10: If the digit at units place is 0 it is divisible by10.


    Divisibility by 11: If the difference of the sum of its digits at odd places and sum of its digits at even places, is either 0 or a number divisible by 11.


    Divisibility by 12: A number is divisible by 12 if it is divisible by both 4 and 3.

    Divisibility by 14: If a number is divisible by 2 as well as 7.

    Divisibility by 15: If a number is divisible by both 3 & 5.

    Divisibility by 16: If the number formed by the last 4 digits is divisible by 16.


    Divisibility by 24: If a number is divisible by both 3 & 8.

    Divisibility by 40: If it is divisible by both 5 & 8.

    Divisibility by 80: If a number is divisible by both 5 & 16.



    Number
    Method
    Example
    7
    Subtract 2 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 7, the original number is also divisible by 7Check for 945: : 94-(2*5)=84. Since 84 is divisible by 7, the original no. 945 is also divisible
    13
    Add 4 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 13, the original number is also divisible by 13Check for 3146:: 314+ (4*6) = 338:: 33+(4*8) = 65. Since 65 is divisible by 7, the original no. 3146 is also divisible
    17
    Subtract 5 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 17, the original number is also divisible by 17Check for 2278:: 227-(5*8)=187. Since 187 is divisible by 17, the original number 2278 is also divisible.
    19
    Add 2 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 19, the original number is also divisible by 19Check for 11343:: 1134+(2*3)= 1140. (Ignore the 0):: 11+(2*4) = 19. Since 19 is divisible by 19, original no. 11343 is also divisible
    23
    Add 7 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 23, the original number is also divisible by 23Check for 53935:: 5393+(7*5) = 5428 :: 542+(7*8)= 598:: 59+ (7*8)=115, which is 5 times 23. Hence 53935 is divisible by 23
    29
    Add 3 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 29, the original number is also divisible by 29Check for 12528:: 1252+(3*8)= 1276 :: 127+(3*6)= 145:: 14+ (3*5)=29, which is divisible by 29. So 12528 is divisible by 23
    31
    Subtract 3 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 31, the original number is also divisible by 31Check for 49507:: 4950-(3*7)=4929. Since 492-(3*9) is divisible by 465:: 46-(3*5)=31. Hence 49507 is divisible by 31
    37
    Subtract 11 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 37, the original number is also divisible by 37Check for 11026:: 1102 - (11*6) =1036. Since 103 - (11*6) =37 is divisible by 37. Hence 11026 is divisible by 31
    41
    Subtract 4 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 41, the original number is also divisible by 41Check for 14145:: 1414 - (4*5) =1394. Since 139 - (4*4) =123 is divisible by 41. Hence 14145 is divisible by 41
    43
    Add 13 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 43, the original number is also divisible by 43. *This process becomes difficult for most of the peoplebecause of multiplication with 13.Check for 11739:: 1173+(13*9)= 1290:: 129 is divisible by 43. 0 is ignored. So 11739 is divisible by 43
    47
    Subtract 14 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 47, the original number is also divisible by 47. This too is difficult to operate for people who are not comfortable with table of 14.Check for 45026:: 4502 - (14*6) =4418. Since 441 - (14*8) =329, which is 7 times 47. Hence 45026 is divisible by 47


    Last edited by Abhishek on Tue Apr 19, 2011 6:08 pm; edited 1 time in total
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    Abhishek

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    Re: Formulas , Tips and Tricks

    Post  Abhishek on Mon Apr 18, 2011 12:40 am

    Addition and Subtraction Concepts are easy to learn and are very helpful.Unfortunately after trying a number of times I failed to show it here due to formatting issues.

    I am hence going to provide you with a link to download the files and have a look.The tutorial files are comprehensive and easy to learn.

    http://www.ziddu.com/download/11129676/VedicMathematicsaddition.doc.html

    http://www.ziddu.com/download/11129666/VedicMathematicssubtraction.doc.html
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    Squares and Cubes

    Post  Abhishek on Mon Apr 18, 2011 12:42 am

    Reciprocal of Fractions


    1/1 1


    1/2 0.5


    1/3 0.33


    1/4 0.25


    1/5 0.20


    1/6 0.1666....


    1/7 0.142857..........


    1/8 0.125



    1/9 0.11111.........


    1/10 0.10


    1/11 0.0909.....


    1/12 0.8333........


    1/13 0.076293


    1/14 0.0714285.......


    1/15 0.066.......


    1/16 0.0625



    1/17 0.058823


    1/18 0.055...........


    1/19 0.052631



    1/20 0.05





    With a little practice, it's not hard to recall
    the decimal equivalents of fractions up to 10/11!


    First, there are 3 you should know already:

    1/2 = .5
    1/3 = .333...
    1/4 = .25


    Starting with the thirds, of which you already know one:

    1/3 = .333...
    2/3 = .666...


    You also know 2 of the 4ths, as well, so there's only one new one to learn:

    1/4 = .25
    2/4 = 1/2 = .5
    3/4 = .75


    Fifths are very easy. Take the numerator (the number on top),
    double it, and stick a decimal in front of it.


    1/5 = .2
    2/5 = .4
    3/5 = .6
    4/5 = .8


    There are only two new decimal equivalents to learn with the 6ths:

    1/6 = .1666...
    2/6 = 1/3 = .333...
    3/6 = 1/2 = .5
    4/6 = 2/3 = .666...
    5/6 = .8333...


    What about 7ths? We'll come back to them
    at the end. They're very unique.


    8ths aren't that hard to learn, as they're just
    smaller steps than 4ths. If you have trouble
    with any of the 8ths, find the nearest 4th,
    and add .125 if needed:


    1/8 = .125
    2/8 = 1/4 = .25
    3/8 = .375
    4/8 = 1/2 = .5
    5/8 = .625
    6/8 = 3/4 = .75
    7/8 = .875


    9ths are almost too easy:

    1/9 = .111...
    2/9 = .222...
    3/9 = .333...
    4/9 = .444...
    5/9 = .555...
    6/9 = .666...
    7/9 = .777...
    8/9 = .888...


    10ths are very easy, as well.
    Just put a decimal in front of the numerator:


    1/10 = .1
    2/10 = .2
    3/10 = .3
    4/10 = .4
    5/10 = .5
    6/10 = .6
    7/10 = .7
    8/10 = .8
    9/10 = .9


    Remember how easy 9ths were? 11th are easy in a similar way,
    assuming you know your multiples of 9:


    1/11 = .090909...
    2/11 = .181818...
    3/11 = .272727...
    4/11 = .363636...
    5/11 = .454545...
    6/11 = .545454...
    7/11 = .636363...
    8/11 = .727272...
    9/11 = .818181...
    10/11 = .909090...


    As long as you can remember the pattern for each fraction, it is
    quite simple to work out the decimal place as far as you want
    or need to go!


    Oh, I almost forgot! We haven't done 7ths yet, have we?

    One-seventh is an interesting number:

    1/7 = .142857142857142857...

    For now, just think of one-seventh as: .142857

    See if you notice any pattern in the 7ths:

    1/7 = .142857...
    2/7 = .285714...
    3/7 = .428571...
    4/7 = .571428...
    5/7 = .714285...
    6/7 = .857142...


    Notice that the 6 digits in the 7ths ALWAYS stay in the same
    order and the starting digit is the only thing that changes!


    If you know your multiples of 14 up to 6, it isn't difficult to,
    work out where to begin the decimal number. Look at this:


    For 1/7, think "1 * 14", giving us .14 as the starting point.
    For 2/7, think "2 * 14", giving us .28 as the starting point.
    For 3/7, think "3 * 14", giving us .42 as the starting point.


    For 4/14, 5/14 and 6/14, you'll have to adjust upward by 1:

    For 4/7, think "(4 * 14) + 1", giving us .57 as the starting point.
    For 5/7, think "(5 * 14) + 1", giving us .71 as the starting point.
    For 6/7, think "(6 * 14) + 1", giving us .85 as the starting point.


    Practice these, and you'll have the decimal equivalents of
    everything from 1/2 to 10/11 at your finger tips!


    If you want to demonstrate this skill to other people, and you know
    your multiplication tables up to the hundreds for each number 1-9, then give them a
    calculator and ask for a 2-digit number (3-digit number, if you're up to it!) to be
    divided by a 1-digit number.


    If they give you 96 divided by 7, for example, you can think,
    "Hmm... the closest multiple of 7 is 91, which is 13 * 7, with 5 left over.
    So the answer is 13 and 5/7, or: 13.7142857



    The reciprocal charts should be memorized by heart . For quick calculation of Percentages , Data Interpretation Questions and other questions requiring quick conversion.

    Subsequent posts will show you the practical application of these forms.

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    Re: Formulas , Tips and Tricks

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