Math-Book-GMAT-Club

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Median The median of a triangle is a line from a vertex to the midpoint of the opposite side.• The three medians intersect at a single point, called the centroid of the triangle.• Each median divides the triangle into two smaller triangles which have the same area.• Because there are three vertices, there are of course three possible medians.• No matter what shape the triangle, all three always intersect at a single point. This point is calledthe centroid of the triangle.• The three medians divide the triangle into six smaller triangles of equal area.• The centroid (point where they meet) is the center of gravity of the triangle• Two‐thirds of the length of each median is between the vertex and the centroid, while one‐third is betweenthe centroid and the midpoint of the opposite side.• , where , and are the sides of the triangle and is the side of the trianglewhose midpoint is the extreme point of median .Area The number of square units it takes to exactly fill the interior of a triangle.Usually called "half of base times height", the area of a triangle is given by the formula below.•Other formula:••Where is the length of the base, and the other sides; is the length of the corresponding altitude; isthe Radius of circumscribed circle; is the radius of inscribed circle; P is the perimeter• Heron's or Hero's Formula for calculating the area where are the threesides of the triangle andwhich is the semi perimeter of the triangle.‐ 57 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
Perimeter The distance around the triangle. The sum of its sides.• For a given perimeter equilateral triangle has the largest area.• For a given area equilateral triangle has the smallest perimeter.Relationship of the Sides of a Triangle• The length of any side of a triangle must be larger than the positive difference of the other two sides, butsmaller than the sum of the other two sides.Interior angles The three angles on the inside of the triangle at each vertex.• The interior angles of a triangle always add up to 180°• Because the interior angles always add to 180°, every angle must be less than 180°• The bisectors of the three interior angles meet at a point, called the incenter, which is the center of theincircle of the triangle.Exterior angles The angle between a side of a triangle and the extension of an adjacent side.• An exterior angle of a triangle is equal to the sum of the opposite interior angles.• If the equivalent angle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for anyconvex polygon, not just triangles.Midsegment of a Triangle A line segment joining the midpoints of two sides of a triangle• A triangle has 3 possible midsegments.‐ 58 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
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For the latest version of the GMAT
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Number TheoryDefinitionNumber Theor
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• 1 (and ‐1) are divisors of ev
Page 8 and 9: other digits: 21‐(9+8+6+9)=‐11,
Page 10 and 11: Sum of n first positive integers:Su
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 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
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Therefore, the probability of getti
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2) Reversal combinatorial approach:
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Combinations & PermutationsDefiniti
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1. The total number of arrangements
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is the first termDefining Propertie
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Solution(1) a1=8, does not tell us
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CuboidA cube is the 3‐D generaliz
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ConeA cone is a 3‐D object obtain
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Volume =Surface Area w/o base =Surf
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(2) : Sum of sides = . Not sufficie
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Math-Book-GMAT-Club

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