So in this case, avg(3 and 99) = (3+99)/2 = 102/2 = 51 = average termStep 3: Sum = # terms * avgvalue= (# from Step 1) * (# from step 2)= 33 terms * 51 = 1683RULE: avg value of each term = average (1st term and last term)See Video ExplanationGMAT Quant: Problem Solving

Page 108Sum of SequencesSequences: Sum, Average, # of termsSum: What is sum of all even numbers from 1 to 100?Average: What is the average of all these multiples of 2?# of Terms: How many numbers are multiples of 2 between 1 and 100?Step 1: Find # of terms:2 is the 1stterm100 is the 50thtermso there are 50 termsStep 2: The easiest way to find the sum is to multiply the # of terms by the average value of each term. So we need to find the average value!RULE: avg value of each term = average (1st term and last term)So in this case, avg(2 and 100) = (2+100)/2 = 102/2 = 51 = average termStep 3: Sum = # terms * avgvalue= (# from Step 1) * (# from step 2)= 50 terms * 51 = 2550See Video ExplanationGMAT Quant: Problem Solving

Page 109AnglesLinesYou should know…x=yp=q(x+q)=(q+y)=(p+x)=(p+y)=180(y+w+k)=(m+k)=180m=y+w(This one is common!)xoyopoqowomokoSee Video ExplanationGMAT Quant: Problem Solving

Page 110Combinations/Permutations (n Choose r)Strategy #1: Count themHow many triplets (teams of 3) can you make in a group of 5 people?Strategy #2: Use FormulaQ1) How many triplets (teams of 3) can you make in a group of 5 people?n=total # (5)r=size of selected group (3)Q2) How many pairs (teams of 2) can you form with 6 people?n=6r=21526*5)4*3*2*1)(2*1(6*5*4*3*2*1!4!2!6!1)26(!2!6)!(!!rnrn1025*4)2*1)(3*2*1(5*4*3*2*1!2!3!5!1)35(!3!5)!(!!rnrn1 2 3 4 510 possible tripletsSee Video ExplanationGMAT Quant: Problem Solving

Page 111Exponent OperationsSubtraction: 24– 22= 16-12 =12Multiplication: 24(22) = 26[Keep the base, add the exponents!]Addition: 24+ 22= 16 + 4 = 20Division: 24/22= 24-2= 22 [Keep the base, subtract the exponents!]Math Equations/RelationshipsFactorials0! = 14! = 4*3*2*1 =244! = 4* 3! = 245! = 120Averages (you should already know this)Arithmetic Mean = add them all up, divide by the # of itemsMedian = the middle number of a set of numbersIn a set of 5 (odd #) ascending numbers, the median is the 3rdnumber.In a set of 6 (even #) ascending numbers, the median is the average of 3rdand 4thterms{3, 4, 7, 9}: mean = (3+4+7+9)/4 = 23/4median = (4+7)/2 = 5.5Ratios•a:c= b:d•Cross products are equivalent•a*d = b*c1313463142331123)21(convertthen 2,ofinstead1/2basein arechoicesanswer theallIf22)2()2()2(?)161()81()21(dcbaSee Video ExplanationGMAT Quant: Problem Solving

Page 112#8: Geometry FormulasGiven diagonal is 13, what is the circumference of the rectangle?Do you have enough info?Generally, no. You need to at least know the ratio of the width/length OR be told that the width and length MUST be integers.Note: Diagrams on GMAT are NEVER drawn to scale!!