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1、GRE Quantitative Reasoning (Step 2) Bo Wang University of Virginia Aug 2015 Bo Wang (UVA)GRE MathAug 20151 / 106 Overview 1Arithmetic 2Algebra 3Geometry 4Data Analysis 5Problem-solving Techniques Bo Wang (UVA)GRE MathAug 20152 / 106 0 SN “!%cG #GRE%“:8B K.KE|!o( SK “ !GRE!rz#!) uGRE!%kr#I!) K8%$!) #
2、!O 5“%“:KE|!o( KSKJ%(”u$puGRE!pJ) Bo Wang (UVA)GRE MathAug 20153 / 106 1 O“)P$P%SN!“: 2 veZuSKS 3 U!OwindowsgO%O 4 Xk7O5 o. 5 3(O Bo Wang (UVA)GRE MathAug 201514 / 106 1 K8w+AKn)!c 2 “:# 3 “KkKvw%M%(! 4 %! Bo Wang (UVA)GRE MathAug 201515 / 106 Arithmetic 1 Integers 2 Factors and multiples 3 quotient
3、s and reminders 4 odd and even number 5 prime and composite number 6 fractions 7 exponents and roots 8 decimals 9 real number 10 ratio 11 percent Bo Wang (UVA)GRE MathAug 201516 / 106 Integers) Integers)Positive Integers)Negative IntegersK) %“:+=*=KKK+KKK=KKKKKK*KKK= Example 1 a,b,c are all integers
4、, suppose a3b4c5is negative then which of the following CANNOT be true? A a + b 0 B b + c 0 C a + c 0 D ac 0 E abc 0 Bo Wang (UVA)GRE MathAug 201517 / 106 Factors and Multiplesf0 factors (divisors)f, multiple 0, least common multiple)0, greatest common divisor% %“:)%)000 Example 2 Let S be the set o
5、f all positive integers n such that n2is a multiple of both 24 and 108. Which of the following integers are divisor of every integer n in S? Indicate all such integers A 12 B 24 C 36 D 72 Bo Wang (UVA)GRE MathAug 201518 / 106 Quotients and Remainders) a divided by b is q remainder r , a=bq+r where (
6、0 r 0Kk”!) ? = b2? 4ac = 0Kk) ? = b2? 4ac /“k!/“ sides3:vertices trianglen2/quadrilateralo/pentagon /,hexagon8 /,octagonl/ n!/S2180(n ? 2)o /regular polygon, perimeter(, area%“:SSS222 Example 20 What is the maximum possible number of interior angles that are right angles of a decagon (10-side polygo
7、n)? Bo Wang (UVA)GRE MathAug 201552 / 106 polygons/ Example 21 What is a + b + c + d + e + f + g? Bo Wang (UVA)GRE MathAug 201553 / 106 trianglesn2/ n2/S2180o n2/equilateral triangle,+n2/isosceles triangle 2n2/right triangle2legs.hypotenuse ./*nPythagorean theorem.x.d*n Bo Wang (UVA)GRE MathAug 2015
8、54 / 106 A!n2/ n1 : 1 : p2 n1 : p3 : 2 Bo Wang (UVA)GRE MathAug 201555 / 106 n2/! Bo Wang (UVA)GRE MathAug 201556 / 106 “n2/qn2/ “n2/“/G)!“,!n2/ qn2/“/G,6)*,!n2/ XABCDEF“qn2/!(AB CD = BC EF = AC DF %“:kkk Bo Wang (UVA)GRE MathAug 201557 / 106 n2/ Example 22 In the fi gure above, what is the area of
9、triangle BDE and ABE given that the area of triangle ACE is 4, the area of triangle CDE is 3? Bo Wang (UVA)GRE MathAug 201558 / 106 n2/ Example 23 suppose 2 + ? 100 then which of the following could be the value of ? Indicates all possible values A) 60B) 89C) 80D) 45E) 50F) 51 Bo Wang (UVA)GRE MathA
10、ug 201559 / 106 n2/ Example 24 What is the perimeter of ABCDE if both and ? are 150o, A,B are right angles and AC=AB=BD=1? Bo Wang (UVA)GRE MathAug 201560 / 106 quadrilateralso/ (/rectangle,/square,$1o/parallelogram,F/trapezoid $1o/.*p F/.+e.*p/2 Bo Wang (UVA)GRE MathAug 201561 / 106 circles, circle
11、,center,%,radius,diameter chordu,arcl,circumference(C = 2r areaA = r2,sector/,concentric circles”%, tangent line, :point of tangency, ,S4/inscribed polygon, ,(4/circumscribed polygon Bo Wang (UVA)GRE MathAug 201562 / 106 , Example 25 suppose A(o) is the origin and the radius of the circle is 2. supp
12、ose CE=3, DEFG is a rectangle. Quantity AQuantity B area of DEFG7 Bo Wang (UVA)GRE MathAug 201563 / 106 , Example 26 Quantity AQuantity B area of ABCarea of region CD Bo Wang (UVA)GRE MathAug 201564 / 106 three-dimensional fi guresN/ rectangular solid(N cubeN,faces edges,vertex3: volumeNV = lwh surf
13、ace areaL A = 2(lw + lh + wh) circular cylinder, axis/(PQ) volumeNV = r2h surface areaLA = 2r2+ 2pirh Bo Wang (UVA)GRE MathAug 201565 / 106 three-dimensional fi guresN/ %“: LLL%NNN Example 27 An ice cube is 1cm long, if we slice it into two pieces. Quantity AQuantity B Resulting surface area of all
14、the slices8 cm2 Bo Wang (UVA)GRE MathAug 201566 / 106 Exercise13 AC=40, BC=25, EF=10, and AD is parallel to EC. Quantity AQuantity B area of ABD90 Bo Wang (UVA)GRE MathAug 201567 / 106 Exercise14 triangle CDE is equilateral. Column AColumn B area of CDEtotal area of the other parts of the circle Bo
15、Wang (UVA)GRE MathAug 201568 / 106 Exercise15 In the fi gure above AB AC = AC BC What is AB BC? Bo Wang (UVA)GRE MathAug 201569 / 106 Exercise16 AB=3, AC=6 Column AColumn B area of ABC8 Bo Wang (UVA)GRE MathAug 201570 / 106 Exercise17 In the above circle CG = 10, FG = 8, CF = 9 and DG = 12. What is the length of DE? A) 10B) 11.5C) 12D) 13.5E) 15 Bo Wang (UVA
