Math-Book-GMAT-Club

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2) Reversal combinatorial approach: In this example reversal approach is a bit shorter and faster.‐ we choose 1 couple out of 5 couples.‐ we chose one person out of remaining 8 people.‐ the total number of combinations to choose 3 people out of 10 people.3) probability approach:1st person: ‐ we choose any person out of 10.2nd person:3rd person:‐ we choose any person out of 8=10‐2(one couple from previous choice)‐ we choose any person out of 6=10‐4(two couples from previous choices).Probability treeSometimes, at 700+ level you may see complex probability problems that include conditions or restrictions. Forsuch problems it could be helpful to draw a probability tree that include all possible outcomes and theirprobabilities.Example #1Q: Julia and Brian play a game in which Julia takes a ball and if it is green, she wins. If the first ball is not green,she takes the second ball (without replacing first) and she wins if the two balls are white or if the first ball is grayand the second ball is white. What is the probability of Julia winning if the jar contains 1 gray, 2 white and 4 greenballs?Solution: Let's draw all possible outcomes and calculate all probabilities.Now, It is pretty obvious that the probability of Julia's win is:‐ 109 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
Tips and Tricks: SymmetrySymmetry sometimes lets you solve seemingly complex probability problem in a few seconds. Let's consider anexample:Example #1Q: There are 5 chairs. Bob and Rachel want to sit such that Bob is always left to Rachel. How many ways it can bedone?Solution: Because of symmetry, the number of ways that Bob is left to Rachel is exactly 1/2 of all possible ways:Practice from the GMAT Official Guide:The Official Guide, 12th Edition: DT #4; DT #7; PS #12; PS #67; PS #105; PS #158; PS #174; PS #214; DS #3; DS#107;The Official Guide, Quantitative 2th Edition: PS #79; PS #160;The Official Guide, 11th Edition: DT #4; DT #7; PS #10; PS #64; PS #173; PS #217; PS #231; DS #82; DS #114;Generated from [GMAT ToolKit]ResourcesProbability DS problems: [search]Probability PS problems: [search]Walker's post with Combinatorics/probability problems: [Combinatorics/probability Problems]Bullet's post with probability problems: [Combined Probability Questions]‐ 110 ‐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
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other digits: 21‐(9+8+6+9)=‐11,
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Sum of n first positive integers:Su
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Converting Decimals to Fractions•
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Operations involving the same bases
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PERCENTDefinitionA percentage is a
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Absolute ValueDefinitionThe absolut
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satisfied (‐15 is not within (‐
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FactorialsDefinitionThe factorial o
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AlgebraScopeManipulation of various
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There is a common misconception tha
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RemaindersDefinitionIf and are posi
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A. 2B. 4C. 8D. 20E. 45divided by yi
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Example #10 (hard)When positive int
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Word Problems OverviewThe Following
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Key words: less than (implies subtr
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Distance/Speed/Time Word ProblemsWh
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In the next section we will learn h
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Time(3) = Time(1) + Time(2) ‐‐
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3*x = 5*(x ‐ 20) ‐‐> x = 50 m
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Work Word ProblemsWhat is a ‘Work
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Example 3:Working together, printer
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Advanced Overlapping Sets ProblemsS
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the writing club. If 6 students sig
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two of the courses and 1 employee h
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Consider this problem to be an over
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Median The median of a triangle is
Page 60 and 61: • The midsegment is always parall
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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 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
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Math-Book-GMAT-Club

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