Math-Book-GMAT-Club

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two of the courses and 1 employee has taken all three of the courses. How many of the 50 employees havetaken none of the courses?Translating:"There are 50 employees in the office of ABC Company": Total=50;"22 have taken an accounting course, 15 have taken a course in finance and 14 have taken a marketing course";A=22, B=15, and C=14;"Nine of the employees have taken exactly two of the courses": (sum of EXACTLY 2‐group overlaps)=9;"1 employee has taken all three of the courses": AnBnC=g=1;Question:: None=?Apply secondformula:‐‐> ‐‐> .Answer: 10. Discuss this question HERE.Example 8 (hard):In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of thoseasked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked allthree of the products, what percentage of the survey participants liked more than one of the three products?Translating:"85% of those surveyed liked at least one of three products: 1, 2, and 3": Total=100%. Also, since 85% of thosesurveyed liked at least one of three products then 15% liked none of three products, thus None=15%;"5% of the people in the survey liked all three of the products": AnBnC=g=5%;Question:: what percentage of the survey participants liked more than one of the three products?Apply second formula:Total = {liked product 1} + {liked product 2} + {liked product 3} ‐ {liked exactly two products} ‐ 2*{likedexactly three product} + {liked none of three products}‐‐> , so 5% liked exactly two products. More than one productliked those who liked exactly two products, (5%) plus those who liked exactly three products (5%), so 5+5=10%liked more than one product.Answer: 10%. Discuss this question HERE.Example 9 (hard):In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey andCricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of thesegiven sports, how many students play exactly two of these sports?Translating:"In a class of 50 students...": Total=50;"20 play Hockey, 15 play Cricket and 11 play Football": H=20, C=15, and F=11;"7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football": HnC=7, CnF=4, andHnF=5. Notice that "7 play both Hockey and Cricket" does not mean that out of those 7, some does not playFootball too. The same for Cricket/Football and Hockey/Football;‐ 53 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
"18 students do not play any of these given sports": Neither=18.Question:: how many students play exactly two of these sports?Apply first formula:{Total}={Hockey}+{Cricket}+{Football}‐{HC+CH+HF}+{All three}+{Neither}50=20+15+11‐(7+4+5)+{All three}+18 ‐‐> {All three}=2;Those who play ONLY Hockey and Cricket are 7‐2=5;Those who play ONLY Cricket and Football are 4‐2=2;Those who play ONLY Hockey and Football are 5‐2=3;Hence, 5+2+3=10 students play exactly two of these sports.Answer: 10. Discuss this question HERE.Example 10 (hard DS question on three overlapping sets):A student has decided to take GMAT and TOEFL examinations, for which he has allocated a certain number ofdays for preparation. On any given day, he does not prepare for both GMAT and TOEFL. How many days did heallocate for the preparation?(1) He did not prepare for GMAT on 10 days and for TOEFL on 12 days.(2) He prepared for either GMAT or TOEFL on 14 daysWe have: {Total} = {GMAT } + {TOEFL} ‐ {Both} + {Neither}. Since we are told that "on any given day, he doesnot prepare for both GMAT and TOEFL", then {Both} = 0, so {Total} = {GMAT } + {TOEFL} + {Neither}. We need tofind {Total}(1) He did not prepare for GMAT on 10 days and for TOEFL on 12 days ‐‐> {Total} ‐ {GMAT } = 10 and {Total} ‐{TOEFL} =12. Not sufficient.(2) He prepared for either GMAT or TOEFL on 14 days ‐‐> {GMAT } + {TOEFL} = 14. Not sufficient.(1)+(2) We have three linear equations ({Total} ‐ {GMAT } = 10, {Total} ‐ {TOEFL} =12 and {GMAT } + {TOEFL} =14) with three unknowns ({Total}, {GMAT }, and {TOEFL}), so we can solve for all of them. Sufficient.Just to illustrate. Solving gives:{Total} = 18 ‐ he allocate total of 18 days for the preparation;{GMAT } = 8 ‐ he prepared for the GMAT on 8 days;{TOEFL} = 6 ‐ he prepared for the TOEFL on 6 days;{Neither} = 4 ‐ he prepared for neither of them on 4 days.Answer: C. Discuss this question HERE.Example 11 (disguised three overlapping sets problem):Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 35, whatis the minimum possible range in scores of the three test‐takers?A. 17B. 28C. 35D. 45E. 80‐ 54 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
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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 52 and 53: the writing club. If 6 students sig
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
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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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