1、GRE（ QUANTITATIVE）综合模拟试卷 17及答案与解析 1 The integers x and y are greater than 1. If(4x)(7y)= 756, what is the value of x + y? x + y =_ 2 1,-3,4,1,-3,4,1,-3,4,. In the sequence above, the first 3 terms repeat without end. What is the sum of the terms of the sequence from the 150th term to the 154th term?
2、 3 A manufacturing company has plants in three locations: Indonesia, Mexico, and Pakistan. The company has 6,000 employees, and each of the employees works at only one of the plants. If 3/8 of the employees work at the plant in Indonesia and if twice as many employees work at the plant in Mexico as
3、work at the plant in Pakistan, how many employees work at the plant in Mexico? _employees 4 If xy2= 12 and xy = 4, then x = （ A） 1 （ B） 2 （ C） （ D） 2/3 （ E） 4/3 5 The total cost of 8 bagels at a bakery is x dollars. At this cost per bagel, which of the following represents the total cost, in dollars
4、, of y bagels? （ A） 8/xy （ B） 8x/y （ C） 8y/x （ D） xy/8 （ E） x/8y 6 Which of the following is equal to for all integers x and y? （ A） 4-x （ B） 4-y （ C） 2xy （ D） 4x （ E） 4y 7 How many integers are in the solution set of the inequality x2 -10 60. So Choice E is not in region R.Thus the correct answer c
5、onsists of Choices B and D.This explanation uses the following strategies.Strategy 3: Translate from an Algebraic to a Graphical Representation Strategy 8: Search for a Mathematical Relationship 11 【正确答案】 A， B 【试题解析】 The capacity of the cars tank was x gallons of gasoline. Before the trip, the tank
6、was half full and therefore contained x/2 gallons of gasoline. During the trip, 30 percent of the gasoline in the tank was used, so the number of gallons left was 70 percent of x/2, or . After Diana added 8 gallons of gasoline to the tank, the total number of gallons in the tank was . Thus one corre
7、ct choice is Choice B, .However, the question asks you to find all of the answer choices that represent the number of gallons of gasoline in the tank at the end of the trip. So you need to determine whether any of the other choices are equivalent to . Of the answer choices, only Choices A and C have
8、 the same constant term as Choice B: 8. So these are the only choices that need to be checked. Choice A, , can be simplified as follows. So Choice A is equivalent to . Choice C, , is clearly not equivalent to . Thus the correct answer consists of Choices A and B.This explanation uses the following s
9、trategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 5: Simplify an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship 12 【正确答案】 7.2 【试题解析】 Translating the given information into an algebraic expression, you see that
10、machine A produces x/12 pounds of peanut butter in 1 minute, and machine B produces x/18 pounds of peanut butter in 1 minute. Therefore, working simultaneously, machine A and machine B produce pounds of peanut butter in 1 minute.Letting t be the number of minutes it takes machines A and B, working s
11、imultaneously, to produce x pounds of peanut butter, you can set up the following equation. Solving for t, you get The correct answer is 7.2.This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathemati
12、cal Relationship 13 【正确答案】 17 【试题解析】 The property that f(x)=f(x+ 1)for all numbers x implies that f(4)=f(5), f(5)=f(6), f(6)=f(7), and f(7)=f(8). Therefore, since f(4)= 17, it Mows that f(8)= 17. Thus the correct answer is 17. This explanation uses the following strategy. Strategy 7: Find a Pattern
13、14 【正确答案】 A 【试题解析】 To compare x with -2, you should first solve the equation = 0 for x.To solve the equation, recall that a fraction a/b is equal to 0 only if a = 0 and b 0.So the fraction is equal to 0 only if x(x - 2)is equal to 0 and (x + 3)(x - 4)2 is not equal to 0. Note that the only values of
14、 x for which x(x - 2)= 0 are x = 0 and x = 2, and for these two values,(x + 3)(x-4)2 is not equal to 0. Therefore the only values of x for which the fraction is equal to 0 are x = 0 and x = 2. Since both 0 and 2 are greater than Quantity B, -2, the correct answer is Choice A.This explanation uses th
15、e following strategy.Strategy 8: Search for a Mathematical Relationship 15 【正确答案】 B 【试题解析】 Note that Quantity B, , can be expressed as , which can be simplified to . Note that Quantity A is 1/x, and for all nonzero values of x, 0. It follows that ; that is, Quantity B is greater than Quantity A. Thu
16、s the correct answer is Choice B.This explanation uses the following strategy.Strategy 8: Search for a Mathematical Relationship 16 【正确答案】 D 【试题解析】 To compare |m + 25| with 25 - m, first note that because the absolute value of any quantity is greater than or equal to 0, it must be true that |m + 25|
17、0 for all values of m. But you know that 25 - m is less than 0 when m is greater than 25. So Quantity A is greater than Quantity B when m 25. On the other hand, both |m + 25| and 25 - m are equal to 25 when m = 0. So in one case Quantity A is greater than Quantity B, and in the other case the two qu
18、antities are equal. Thus the correct answer is Choice D. This explanation uses the following strategies. Strategy 11: Divide into Cases Strategy 13: Determine Whether a Conclusion Follows from the Information Given 17 【正确答案】 A 【试题解析】 You are given that the relationship between the pressure and volum
19、e of the gas throughout the experiment was PV= C, where C is a positive constant. Quantity A is the volume of the gas when the pressure was 40 psi. At this pressure, the equation PV= C becomes 40 V= C. Solving this equation for V, you get V = C/40 = 0.025C; that is, the volume of the gas was 0.025C
20、cubic inches. Quantity B is 1.2 times the volume of the gas when the pressure was 50 psi. At this pressure, the equation PV=C becomes 50V = C, or V =C/50= 0.02C. Therefore (1.2)V =(1.2)(0.02C)= 0.024C; that is, Quantity B is 0.024C cubic inches. Thus the correct answer is Choice A. This explanation
21、uses the following strategies. Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship 18 【正确答案】 C 【试题解析】 Note that Quantity A can be expressed algebraically as(x/100)(100x). Simplifying this algebraic expression gives x2, whic
22、h is Quantity B. The correct answer is therefore Choice C. This explanation uses the following strategy. Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation 19 【正确答案】 B 【试题解析】 The given equation(4x - 2y)(6x + 3y)= 18 can be simplified as follows. Step 1: Note that(4x - 2y)=
23、 2(2x- y)and(6x + 3y)= 3(2x + y), so the given equation can be rewritten as(2)(2x - y)(3)(2x+y)= 18. Step 2: Dividing both sides of the rewritten equation by 6 gives(2x - y)(2x + y)= 3. Step 3: Multiplying out the left side of the equation in Step 2 gives 4x2-y2= 3. Since Quantity A is 4x2 -y2, it f
24、ollows that Quantity A is equal to 3. Since Quantity B is 6, the correct answer is Choice B. This explanation uses the following strategy. Strategy 8: Search for a Mathematical Relationship 20 【正确答案】 A 【试题解析】 The line in the xy-plane passes through the origin and the point with coordinates(6, 6), so
25、 the equation of the line is y = x. Since the point with coordinates(c, d)is above the line, it follows that d c, and since the point with coordinates(w, z)is below the line, it follows that w z. From the fact that d c and w z, you get w + d c + z; that is, Quantity A is greater than Quantity B. Thu
26、s the correct answer is Choice A. This explanation uses the following strategy. Strategy 8: Search for a Mathematical Relationship 21 【正确答案】 C 【试题解析】 Since the point(2, 2)is a vertex of square S and the point(6, 6)is the midpoint of the diagonals, it follows that the point(10,10)is also a vertex of
27、the square. Using this information you can sketch square S in the xy-plane, labeling the points(2, 2),(6, 6), and(10,10)as shown in the figure below. From the figure, you can see that S has sides of length 8. Therefore the area of S is 82= 64. Hence Quantity A is equal to Quantity B, and the correct
28、 answer is Choice C.This explanation uses the following strategies.Strategy 2: Translate from Words to a Figure or DiagramStrategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation 22 【正确答案】 C 【试题解析】 A regular pentagon has 5 sides of equal length, so the length of a side of a r
29、egular pentagon is 1/5 of its perimeter. Thus Quantity A is , or 2.5. A regular hexagon has 6 sides of equal length, so the length of a side of a regular hexagon is 1/6 of its perimeter.Thus Quantity B is 15/6, or 2.5. So Quantity A and Quantity B are both equal to 2.5, and the correct answer is Cho
30、ice C.This explanation uses the following strategy.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation 23 【 正确答案】 A 【试题解析】 You can begin by sketching the line in the xy-plane and labeling the points(5, 4)and(2, -1)on the line, as shown below. From the figure, you can see th
31、at the line through the two points slants upward and to the right. So the slope of the line is greater than 0; that is, Quantity A is greater than Quantity B. The correct answer is Choice A.(Note that it is not necessary to calculate the slope of the line.)This explanation uses the following strateg
32、y.Strategy 2: Translate from Words to a Figure or Diagram 24 【正确答案】 D 【试题解析】 The figure looks like a right triangle with legs of length 5 + y and 12 - y and hypotenuse of length 13. If y = 0, then the sides of the triangle have lengths 5, 12, and 13. This triangle is in fact a right triangle because
33、 52 + 122 = 132. So the angle labeled x is a right angle; that is, x = 90. In this case, Quantity A is equal to Quantity B. Now consider another value of y, say y=1, to see if the triangle is still a right triangle in this case. If y = 1, then the sides of the triangle have lengths 6, 11, and 13. Th
34、is triangle is not a right triangle because 62 + 112132. So the angle labeled x is not a right angle; that is, x90. In this case, Quantity A is not equal to Quantity B. Because Quantity A is equal to Quantity B in one case and Quantity A is not equal to Quantity B in another case, the correct answer
35、 is Choice D. This explanation uses the following strategies. Strategy 10: Trial and Error Strategy 13: Determine Whether a Conclusion Follows from the Information Given 25 【正确答案】 B 【试题解析】 Since the area of the circle is 25, it follows that the radius of the circle is 5 and the diameter is 10. Line
36、segment RT is a diameter of the circle if and only if angle RST is a right angle. Since you are given that the measure of angle RST is greater than 90, it follows that angle RST is not a right angle and that line segment RT is a chord but not a diameter. Therefore the length of line segment RT is less than 10, and the correct answer is Choice B. This explanation uses the following strategy. Strategy 8: Search for a Mathematical Relationship
