Math-Book-GMAT-Club

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Converting Decimals to Fractions• To convert a terminating decimal to fraction:1. Calculate the total numbers after decimal point2. Remove the decimal point from the number3. Put 1 under the denominator and annex it with "0" as many as the total in step 14. Reduce the fraction to its lowest termsExample: Convert to a fraction.1: Total number after decimal point is 2.2 and 3: .4: Reducing it to lowest terms:• To convert a recurring decimal to fraction:1. Separate the recurring number from the decimal fraction2. Annex denominator with "9" as many times as the length of the recurring number3. Reduce the fraction to its lowest termsExample #1: Convert1: The recurring number is .to a fraction.2: , the number is of length so we have added two nines.3: Reducing it to lowest terms: .• To convert a mixed‐recurring decimal to fraction:1. Write down the number consisting with non‐repeating digits and repeating digits.2. Subtract non‐repeating number from above.3. Divide 1‐2 by the number with 9's and 0's: for every repeating digit write down a 9, and for every non‐repeatingdigit write down a zero after 9's.Example #2: Convertto a fraction.1. The number consisting with non‐repeating digits and repeating digits is 2512;2. Subtract 25 (non‐repeating number) from above: 2512‐25=2487;3. Divide 2487 by 9900 (two 9's as there are two digits in 12 and 2 zeros as there are two digits in 25):2487/9900=829/3300.RoundingRounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places,and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 orsmaller, round down (keep the same) the last digit that you keep.Example:5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5.5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5.5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5.Ratios and ProportionsGiven that , where a, b, c and d are non‐zero real numbers, we can deduce other proportions by simpleAlgebra. These results are often referred to by the names mentioned along each of the properties obtained.‐ invertendo‐ 11 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
‐ alternendo‐ componendo‐ dividendo‐ componendo & dividendoEXPONENTSExponents are a "shortcut" method of showing a number that was multiplied by itself several times. For instance,number multiplied times can be written as , where represents the base, the number that is multipliedby itself times and represents the exponent. The exponent indicates how many times to multiple thebase, , by itself.Exponents one and zero:Any nonzero number to the power of 0 is 1.For example: and• Note: the case of 0^0 is not tested on the GMAT.Powers of zero:Any number to the power 1 is itself.If the exponent is positive, the power of zero is zero: , where .If the exponent is negative, the power of zero ( , where ) is undefined, because division by zero isimplied.Powers of one:Negative powers:The integer powers of one are one.Powers of minus one:If n is an even integer, then .If n is an odd integer, then .Operations involving the same exponents:Keep the exponent, multiply or divide the basesand not‐ 12 ‐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 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 58 and 59: Median The median of a triangle is
Page 60 and 61: • 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
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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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