Math-Book-GMAT-Club

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FactorialsDefinitionThe factorial of a non‐negative integer , denoted by , is the product of all positive integers less than orequal to .For example: .Properties Factorial of a negative number is undefined. , zero factorial is defined to equal 1. , valid for .Trailing zeros:Trailing zeros are a sequence of 0's in the decimal representation of a number, after which no other digits follow.For example: 125,000 has 3 trailing zeros;The number of trailing zeros in the decimal representation of n!, the factorial of a non‐negative integerbe determined with this formula:, can, where must be chosen such thatExample:How many zeros are in the end (after which no other digits follow) of 32!?. Notice that the denominators must be less than or equal to 32 also notice that we takeinto account only the quotient of division (that isnot 6.4). Therefore, 32! has 7 trailing zeros.The formula actually counts the number of factors 5 in , but since there are at least as many factors 2, this isequivalent to the number of factors 10, each of which gives one more trailing zero.Finding the powers of a prime number p, in the n!The formula is: , where must be chosen such thatExample:What is the power of 2 in 25!?‐ 21 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
Additional Practice Resources:if‐60‐is‐written‐out‐as‐an‐integer‐with‐how‐many‐101752.htmlhow‐many‐zeros‐does‐100‐end‐with‐100599.htmlfind‐the‐number‐of‐trailing‐zeros‐in‐the‐expansion‐of‐108249.htmlfind‐the‐number‐of‐trailing‐zeros‐in‐the‐product‐of‐108248.htmlif‐n‐is‐the‐product‐of‐all‐multiples‐of‐3‐between‐1‐and‐101187.htmlif‐m‐is‐the‐product‐of‐all‐integers‐from‐1‐to‐40‐inclusive‐108971.htmlif‐p‐is‐a‐natural‐number‐and‐p‐ends‐with‐y‐trailing‐zeros‐108251.htmlif‐10‐2‐5‐2‐is‐divisible‐by‐10‐n‐what‐is‐the‐greatest‐106060.htmlp‐and‐q‐are‐integers‐if‐p‐is‐divisible‐by‐10‐q‐and‐cannot‐109038.htmlquestion‐about‐p‐prime‐in‐to‐n‐factorial‐108086.htmlif‐n‐is‐the‐product‐of‐integers‐from‐1‐to‐20‐inclusive‐106289.htmlwhat‐is‐the‐greatest‐value‐of‐m‐such‐that‐4‐m‐is‐a‐factor‐of‐105746.htmlif‐d‐is‐a‐positive‐integer‐and‐f‐is‐the‐product‐of‐the‐first‐126692.htmlif‐10‐2‐5‐2‐is‐divisible‐by‐10‐n‐what‐is‐the‐greatest‐106060.htmlhow‐many‐zeros‐are‐the‐end‐of‐142479.html.‐ 22 ‐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 18 and 19: Absolute ValueDefinitionThe absolut
Page 20 and 21: satisfied (‐15 is not within (‐
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
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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
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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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Math-Book-GMAT-Club

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