Math-Book-GMAT-Club

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Volume =Surface Area w/o base =Surface Area with base =Some simple configurationsThese may appear in various forms on the GMAT, and are good practice to derive on one's own :1. Sphere inscribed in cube of side : Radius of sphere is2. Cube inscribed in sphere of radius : Side of cube is3. Cylinder inscribed in cube of side : Radius of cylinder is ; Height4. Cone inscribed in cube of side : Radius of cone is ; Height5. Cylinder of radius in sphere of radius ( ) : Height of cylinder isExamplesExample 1 : A certain right circular cylinder has a radius of 5 inches. There is oil filled in this cylinder to theheight of 9 inches. If the oil is poured completely into a second right cylinder, then it will fill the second cylinderto a height of 4 inches. What is the radius of the second cylinder, in inches?A. 6B. 6.5C. 7D. 7.5E. 8Solution : The volume of the liquid is constant.Initial volume =New volume =Answer is (d)Example 2 : A spherical balloon has a volume of 972cubic cm, what is the surface area of the balloon in sq.‐ 123 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
cm?A) 324B) 729C) 243D) 324E) 729Solution:Answer (d)Example 3 : A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centime cubes, how many 1cubic centimeter cubes will have exactly one of their sides painted?A. 9B. 61C. 98D. 54E. 64Solution: Notice that the new cubes will be each of side 1Cm. So on any face of the old cube there will be 5x5=25of the smaller cubes. Of these, any smaller cube on the edge of the face will have 2 faces painted (one for everyface shared with the bigger cube). The number of cubes that have exactly one face painted are all except the oneson the edges. Number on the edges are 16, so 9 per face.There are 6 faces, hence 6*9=54 smaller cubes with just one face painted.Answer is (d)Example 4 : What is the surface area of the cuboid C ?(1) The length of the diagonal of C is 5(2) The sum of the sides of C is 10Solution: Let the sides of cuboid C beWe know that the surface area is given be(1) : Diagonal = . Not sufficient to know the area‐ 124 ‐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
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• The midsegment is always parall
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Equilateral triangle all sides have
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• A right triangle where the angl
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Then the triangles ABC, CHB and CHA
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Quadrilateral A polygon with four '
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Squares A 4‐sided regular polygon
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• 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 126: (2) : Sum of sides = . Not sufficie
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Math-Book-GMAT-Club

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