Math-Book-GMAT-Club

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Absolute ValueDefinitionThe absolute value (or modulus)of a real number x is x's numerical value without regard to its sign.For example, ; ;Graph:Important properties:‐ 17 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
3‐steps approach:General approach to solving equalities and inequalities with absolute value:1. Open modulus and set conditions.To solve/open a modulus, you need to consider 2 situations to find all roots:Positive (or rather non‐negative)NegativeFor example,a) Positive: if , we can rewrite the equation as:b) Negative: if , we can rewrite the equation as:We can also think about conditions like graphics. is a key point in which the expression under modulusequals zero. All points right are the first conditions and all points left are second conditions .2. Solve new equations:a) ‐‐> x=5b) ‐‐> x=‐33. Check conditions for each solution:a) has to satisfy initial condition . . It satisfies. Otherwise, we would have toreject x=5.b) has to satisfy initial condition . . It satisfies. Otherwise, we wouldhave to reject x=‐3.3‐steps approach for complex problemsLet’s consider following examples,Example #1Q.:. How many solutions does the equation have?Solution: There are 3 key points here: ‐8, ‐3, 4. So we have 4 conditions:a) . ‐‐> . We reject the solution because our condition isnot satisfied (‐1 is not less than ‐8)b) . ‐‐> . We reject the solution because ourcondition is not satisfied (‐15 is not within (‐8,‐3) interval.)c) . ‐‐> . We reject the solution because our condition is not‐ 18 ‐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 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 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 '
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Squares A 4‐sided regular polygon
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• Area ‐ The usual way to calcu
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• A circle is the shape with the
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ChordA line that links two points o
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angle.• An inscribed angle is exa
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chords.‐ This becomes the theorem
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Coordinate GeometryDefinitionCoordi
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As you can see, the distance formul
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Lines in Coordinate GeometryIn Eucl
Page 88 and 89:
The equation of a straight line tha
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Positive slopeHere, y increases as
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A horizontal line has a slope of ze
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Solution: We first find the slope o
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To answer, we must find the slope o
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Example #2Q: Find the point of inte
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ParabolaA parabola is the graph ass
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Standard DeviationDefinitionStandar
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Standard deviation of is . Decrease
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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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