Math-Book-GMAT-Club

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the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?Translating:"Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum ofthree academic clubs": Total=59, Neither=0 (as members are required to sign up for a minimum of one);"22 students sign up for the poetry club": P=22;"27 students for the history club": H=27;"28 students for the writing club": W=28;"6 students sign up for exactly two clubs": (sum of EXACTLY 2‐group overlaps)=6, so the sum of sections d, e,and f is given to be 6, (among these 6 students there are no one who is a member of ALL 3 clubs)Question:: "How many students sign up for all three clubs?" ‐‐>Apply secondformula:‐‐> ‐‐> .Answer: 6. Discuss this question HERE.Example 3:Of 20 Adults, 5 belong to A, 7 belong to B, and 9 belong to C. If 2 belong to all three organizations and 3belong to exactly 2 organizations, how many belong to none of these organizations?Translating:"20 Adults": Total=20;"5 belong to A, 7 belong to B, and 9 belong to C": A=5, B=7, and C=9;"2 belong to all three organizations": AnBnC=g=2;"3 belong to exactly 2 organizations": (sum of EXACTLY 2‐group overlaps)=3, so the sum of sections d, e, and f isgiven to be 3, (among these 3 adults there are no one who is a member of ALL 3 clubs)Question:: Neither=?Apply secondformula:‐‐> ‐‐> .Answer: 6. Discuss this question HERE.Example 4:This semester, each of the 90 students in a certain class took at least one course from A, B, and C. If 60students took A, 40 students took B, 20 students took C, and 5 students took all the three, how many studentstook exactly two courses?Translating:"90 students": Total=90;"of the 90 students in a certain class took at least one course from A, B, and C": Neither=0;"60 students took A, 40 students took B, 20 students took C": A=60, B=40, and C=20;"5 students took all the three courses": AnBnC=g=5;‐ 51 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
Question:: (sum of EXACTLY 2‐group overlaps)=?Apply secondformula:‐‐> ‐‐> .Answer: 20. Discuss this question HERE.Example 5:In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?Translating:"60 people own cats, dogs, or rabbits": Total=60; and Neither=0;"30 people owned cats, 40 owned dogs, 10 owned rabbits": A=30, B=40, and C=10;"12 owned exactly two of the three types of pet": (sum of EXACTLY 2‐group overlaps)=12;Question:: AnBnC=g=?Apply secondformula:‐‐> ‐‐> .Answer: 4. Discuss this question HERE.Example 6:When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economicsclass (E) had 26 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S)had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and Mand S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes arecombined with no student's name listed more than once, how many names will be on the combined roster?Translating:"E had 26 names, M had 28, and S had 18": E=26, M=28, and S=18;"E and M had 9 names in common, E and S had 7, and M and S had 10": EnM=19, EnS=7, and MnS=10;"4 names were on all 3 rosters": EnMnS=g=4;Question:: Total=?Apply firstformula: ‐‐> ‐‐> .Answer: 50. Discuss this question HERE.Example 7:There are 50 employees in the office of ABC Company. Of these, 22 have taken an accounting course, 15 havetaken a course in finance and 14 have taken a marketing course. Nine of the employees have taken exactly‐ 52 ‐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 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 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
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 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 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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