Math-Book-GMAT-Club

Recommendations

Info

Sum of n first positive integers:Sum of n first positive odd numbers: , where is thelast, term and given by: . Given first odd positive integers, then their sum equalsto .Sum of n first positive even numbers: , where is thelast, term and given by: . Given first positive even integers, then their sum equalsto .• If the evenly spaced set contains odd number of elements, the mean is the middle term, so the sum is middleterm multiplied by number of terms. There are five terms in the set {1, 7, 13, 19, 25}, middle term is 13, so thesum is 13*5 =65.FRACTIONSDefinitionFractional numbers are ratios (divisions) of integers. In other words, a fraction is formed by dividing one integer byanother integer. Set of Fraction is a subset of the set of Rational Numbers.Fraction can be expressed in two forms fractional representation and decimal representation .Fractional representationFractional representation is a way to express numbers that fall in between integers (note that integers can also beexpressed in fractional form). A fraction expresses a part‐to‐whole relationship in terms of a numerator (the part)and a denominator (the whole).• The number on top of the fraction is called numerator or nominator. The number on bottom of the fraction iscalled denominator. In the fraction,, 9 is the numerator and 7 is denominator.• Fractions that have a value between 0 and 1 are called proper fraction. The numerator is always smaller thanthe denominator.is a proper fraction.• Fractions that are greater than 1 are called improper fraction. Improper fraction can also be written as a mixednumber.is improper fraction.• An integer combined with a proper fraction is called mixed number.is a mixed number. This can also bewritten as an improper fraction:Converting Improper Fractions• Converting Improper Fractions to Mixed Fractions:1. Divide the numerator by the denominator2. Write down the whole number answer3. Then write down any remainder above the denominatorExample #1: Convertto a mixed fraction.‐ 9 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
Solution: Divide with a remainder of . Write down the and then write down the remainder abovethe denominator, like this:• Converting Mixed Fractions to Improper Fractions:1. Multiply the whole number part by the fraction's denominator2. Add that to the numerator3. Then write the result on top of the denominatorExample #2: Convert to an improper fraction.Solution: Multiply the whole number by the denominator:. Add the numerator to that:. Then write that down above the denominator, like this:ReciprocalReciprocal for a number , denoted by or , is a number which when multiplied by yields . Thereciprocal of a fraction is . To get the reciprocal of a number, divide 1 by the number. For example reciprocalof is , reciprocal of is .Operation on Fractions• Adding/Subtracting fractions:To add/subtract fractions with the same denominator, add the numerators and place that sum over the commondenominator.To add/subtract fractions with the different denominator, find the Least Common Denominator (LCD) of thefractions, rename the fractions to have the LCD and add/subtract the numerators of the fractions• Multiplying fractions: To multiply fractions just place the product of the numerators over the product of thedenominators.• Dividing fractions: Change the divisor into its reciprocal and then multiply.Example #1:Example #2: Given , take the reciprocal of . The reciprocal is . Now multiply: .Decimal RepresentationThe decimals has ten as its base. Decimals can be terminating (ending) (such as 0.78, 0.2) or repeating (recurring)decimals (such as 0.333333....).Reduced fraction (meaning that fraction is already reduced to its lowest term) can be expressed as terminatingdecimal if and only (denominator) is of the form , where and are non‐negative integers. Forexample: is a terminating decimal , as (denominator) equals to . Fraction is also aterminating decimal, as and denominator .‐ 10 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
Page 2 and 3: For the latest version of the GMAT
Page 4 and 5: Number TheoryDefinitionNumber Theor
Page 6 and 7: • 1 (and ‐1) are divisors of ev
Page 8 and 9: other digits: 21‐(9+8+6+9)=‐11,
Page 12 and 13: Converting Decimals to Fractions•
Page 14 and 15: Operations involving the same bases
Page 16 and 17: PERCENTDefinitionA percentage is a
Page 18 and 19: Absolute ValueDefinitionThe absolut
Page 20 and 21: satisfied (‐15 is not within (‐
Page 22 and 23: FactorialsDefinitionThe factorial o
Page 24 and 25: AlgebraScopeManipulation of various
Page 26 and 27: There is a common misconception tha
Page 28 and 29: RemaindersDefinitionIf and are posi
Page 30 and 31: A. 2B. 4C. 8D. 20E. 45divided by yi
Page 32 and 33: Example #10 (hard)When positive int
Page 34 and 35: Word Problems OverviewThe Following
Page 36 and 37: Key words: less than (implies subtr
Page 38 and 39: Distance/Speed/Time Word ProblemsWh
Page 40 and 41: In the next section we will learn h
Page 42 and 43: Time(3) = Time(1) + Time(2) ‐‐
Page 44 and 45: 3*x = 5*(x ‐ 20) ‐‐> x = 50 m
Page 46 and 47: Work Word ProblemsWhat is a ‘Work
Page 48 and 49: Example 3:Working together, printer
Page 50 and 51: Advanced Overlapping Sets ProblemsS
Page 52 and 53: the writing club. If 6 students sig
Page 54 and 55: two of the courses and 1 employee h
Page 56 and 57: Consider this problem to be an over
Page 58 and 59: Median The median of a triangle is
Page 60 and 61:
• The midsegment is always parall
Page 62 and 63:
Equilateral triangle all sides have
Page 64 and 65:
• A right triangle where the angl
Page 66 and 67:
Then the triangles ABC, CHB and CHA
Page 68 and 69:
Quadrilateral A polygon with four '
Page 70 and 71:
Squares A 4‐sided regular polygon
Page 72 and 73:
• Area ‐ The usual way to calcu
Page 74 and 75:
• A circle is the shape with the
Page 76 and 77:
ChordA line that links two points o
Page 78 and 79:
angle.• An inscribed angle is exa
Page 80 and 81:
chords.‐ This becomes the theorem
Page 82 and 83:
Coordinate GeometryDefinitionCoordi
Page 84 and 85:
As you can see, the distance formul
Page 86 and 87:
Lines in Coordinate GeometryIn Eucl
Page 88 and 89:
The equation of a straight line tha
Page 90 and 91:
Positive slopeHere, y increases as
Page 92 and 93:
A horizontal line has a slope of ze
Page 94 and 95:
Solution: We first find the slope o
Page 96 and 97:
To answer, we must find the slope o
Page 98 and 99:
Example #2Q: Find the point of inte
Page 100 and 101:
ParabolaA parabola is the graph ass
Page 102 and 103:
Standard DeviationDefinitionStandar
Page 104 and 105:
Standard deviation of is . Decrease
Page 106 and 107:
ProbabilityDefinitionA number expre
Page 108 and 109:
Therefore, the probability of getti
Page 110 and 111:
2) Reversal combinatorial approach:
Page 112 and 113:
Combinations & PermutationsDefiniti
Page 114 and 115:
1. The total number of arrangements
Page 116 and 117:
is the first termDefining Propertie
Page 118 and 119:
Solution(1) a1=8, does not tell us
Page 120 and 121:
CuboidA cube is the 3‐D generaliz
Page 122 and 123:
ConeA cone is a 3‐D object obtain
Page 124 and 125:
Volume =Surface Area w/o base =Surf
Page 126:
(2) : Sum of sides = . Not sufficie
show all

Math-Book-GMAT-Club

Create successful ePaper yourself

Delete template?

Save as template?