1、GRE（ QUANTITATIVE）综合模拟试卷 15及答案与解析 0 Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices: (A)Quantity A is greater. (B)Quantity B is greater. (C)The two quantities are equal
2、. (D)The relationship cannot be determined from the information given. A symbol that appears more than once in a question has the same meaning throughout the question. 1 2 Lionel is younger than Maria. 3 4 5 6 7 8 9 10 If 5x + 32 = 4 - 2x, what is the value of x ? （ A） -4 （ B） -3 （ C） 4 （ D） 7 （ E）
3、12 11 Which of the following numbers is farthest from the number 1 on the number line? （ A） -10 （ B） -5 （ C） 0 （ D） 5 （ E） 10 12 The figure above shows the graph of the function/defined by f(x)= 2x + 4 for all numbers x. For which of the following functions g, defined for all numbers x, does the gra
4、ph of g intersect the graph of f? （ A） g(x)= x-2 （ B） g(x)= x + 3 （ C） g(x)= 2x-2 （ D） g(x)= 2x + 3 （ E） g(x)= 3x-2 13 A car got 33 miles per gallon using gasoline that cost $2.95 per gallon. Approximately what was the cost, in dollars, of the gasoline used in driving the car 350 miles? （ A） $10 （ B
5、） $20 （ C） $30 （ D） $40 （ E） $50 14 A certain jar contains 60 jelly beans 22 white, 18 green, 11 yellow, 5 red, and 4 purple. If a jelly bean is to be chosen at random, what is the probability that the jelly bean will be neither red nor purple? （ A） 0.09 （ B） 0.15 （ C） 0.54 （ D） 0.85 （ E） 0.91 15 Wh
6、ich two of the following numbers have a product that is between -1 and 0 ? Indicate both of the numbers. （ A） -20 （ B） -10 （ C） 2-4 （ D） 3-2 16 Which of the following integers are multiples of both 2 and 3 ? Indicate all such integers. A 8 B 9 C 12 D 18 E 21 F 36 17 Each employee of a certain compan
7、y is in either Department X or Department 7, and there are more than twice as many employees in Department X as in Department Y. The average(arithmetic mean)salary is $25,000 for the employees in Department X and $35,000 for the employees in Department Y. Which of the following amounts could be the
8、average salary for all of the employees of the company? Indicate all such amounts. A $26,000 B $28,000 C $29,000 D $30,000 E $31,000 F $32,000 G $34,000 18 Which of the following could be the units digit of 57n, where n is a positive integer? Indicate all such digits. A 0 B 1 C 2 D 3 E 4 F 5 G 6 H 7
9、 I 8 J 9 19 One pen costs $0.25 and one marker costs $0.35. At those prices, what is the total cost of 18 pens and 100 markers? $_ 20 Rectangle R has length 30 and width 10, and square S has length 5. The perimeter of S is what fraction of the perimeter of R ? 21 RESULTS OF A USED-CAR AUCTION Small
10、Cars Large Cars Number of cars offered 32 23 Number of cars sold 16 20 Projected sales total for cars offered(in thousands) $70 $150 Actual sales total(in thousands) $41 $120 Figure 7 For the large cars sold at an auction that is summarized in the table above, what was the average sale price per car
11、? $_ 22 A merchant made a profit of $5 on the sale of a sweater that cost the merchant $15. What is the profit expressed as a percent of the merchants cost? Give your answer to the nearest whole percent. _% 23 Working alone at its constant rate, machine A produces k liters of a chemical in 10 minute
12、s. Working alone at its constant rate, machine B produces k liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce k liters of the chemical? _minutes 24 ANNUAL PERCENT CHANGE IN DOLLAR AMOUNT OF SALE
13、S AT FIVE RETAIL STORES FROM 2006 TO 2008If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008? （ A） $727,200 （ B） $792,000 （ C） $800,000 （ D） $880,000 （ E） $968,000 GRE（ QUANTITATIVE）综合模拟试卷 15答案与解析 1 【正确答案】 A 【试题解析】 For the intege
14、rs greater than 24, note that 25, 26, 27, and 28 are not prime numbers, but 29 is a prime number, as are 31 and many other greater integers. Thus, 29 is the least prime number greater than 24, and Quantity A is 29. For the integers less than 28, note that 27, 26, 25, and 24 are not prime numbers, bu
15、t 23 is a prime number, as are 19 and several other lesser integers. Thus 23 is the greatest prime number less than 28, and Quantity B is 23. The correct answer is Choice A, Quantity A is greater. 2 【正确答案】 D 【试题解析】 If Lionels age is 6 years and Marias age is 10 years, then Quantity A is greater, but
16、 if Lionels age is 4 years and Marias age is 10 years, then Quantity B is greater. Thus the relationship cannot be determined. The correct answer is Choice D, the relationship cannot be determined from the information given. 3 【正确答案】 A 【试题解析】 Without doing the exact computation, you can see that 54
17、percent of 360 is greater than 1/2 of 360, which is 180, and 180 is greater than Quantity B, 150. Thus the correct answer is Choice A, Quantity A is greater. 4 【正确答案】 D 【试题解析】 From Figure 1, you know that PQR is a triangle and that point S is between points P and R, so PS y; but if x = 1, then y = 2
18、(12)+ 7(1)-3 = 6, so in that case, y x. Thus the correct answer is Choice D, the relationship cannot be determined from the information given. This explanation uses the following strategies. Strategy 10: Trial and Error Strategy 13: Determine Whether a Conclusion Follows from the Information Given N
19、ote that plugging numbers into expressions may not be conclusive. It is conclusive, however, if you get different results after plugging in different numbers: the conclusion is that the relationship cannot be determined from the information given. It is also conclusive if there are only a small numb
20、er of possible numbers to plug in and all of them yield the same result, say, that Quantity B is greater. Now suppose that there are an infinite number of possible numbers to plug in. If you plug many of them in and each time the result is, for example, that Quantity A is greater, you still cannot c
21、onclude that Quantity A is greater for every possible number that could be plugged in. Further analysis would be necessary and should focus on whether Quantity A is greater for all possible numbers or whether there are numbers for which Quantity A is not greater. 6 【正确答案】 B 【试题解析】 Set up the initial
22、 comparison:However, the problem asks for a comparison between Quantity A and Quantity B, not a comparison between 1 and y. To go from the comparison between 1 and y to a comparison between Quantities A and B, start with the last comparison, 1 -1 and the resulting relationship is greater than(). In
23、reverse order, each simplification step implies the inequality greater than()in the preceding comparison. Therefore Quantity A is greater than Quantity B.The correct answer is Choice A, Quantity A is greater.This explanation uses the following strategies.Strategy 5: Simplify an Arithmetic or Algebra
24、ic Representation Strategy 8: Search for a Mathematical Relationship 9 【正确答案】 D 【试题解析】 Set up the initial comparison: The comparison cannot be simplified any further. Although you are given that wl, you still dont know how w compares to 9/5, or 1.8. For example, if w= 1.5, then w 1.8. In other words
25、, the relationship between w and 9/5 cannot be determined.Note that each of these simplification steps is reversible, so in reverse order, each simplification step implies that the relationship cannot be determined in the preceding comparison. Thus the relationship between Quantities A and B cannot
26、be determined.The correct answer is Choice D, the relationship cannot be determined from the information given.This explanation uses the following strategies.Strategy 5: Simplify an Arithmetic or Algebraic RepresentationStrategy 13: Determine Whether a Conclusion Follows from the Information GivenTh
27、e strategy of simplifying the comparison works most efficiently when you note that a simplification step is reversible while actually taking the step. Here are some common steps that are always reversible: Adding any number or expression to both sides of a comparison Subtracting any number or expres
28、sion from both sides Multiplying both sides by any nonzero number or expression Dividing both sides by any nonzero number or expressionRemember that if the relationship is an inequality, multiplying or dividing both sides by any negative number or expression will yield the opposite inequality. Be aw
29、are that some common operations like squaring both sides are generally not reversible and may require further analysis using other information given in the question in order to justify reversing such steps. 10 【正确答案】 A 【试题解析】 Solving the equation for x, you get 7x = -28, and so x = -4. The correct a
30、nswer is Choice A, -4. This explanation uses the following strategy. Strategy 5: Simplify an Arithmetic or Algebraic Representation 11 【正确答案】 A 【试题解析】 Circling each of the answer choices in a sketch of the number line(Figure 4)shows that of the given numbers, -10 is the greatest distance from 1.Anot
31、her way to answer the question is to remember that the distance between two numbers on the number line is equal to the absolute value of the difference of the two numbers. For example, the distance between -10 and 1 is |-10-l| = 11, and the distance between 10 and 1 is |10 - 1| = |9| = 9.The correct
32、 answer is Choice A, -10.This explanation uses the following strategy.Strategy 2: Translate from Words to a Figure or Diagram 12 【正确答案】 E 【试题解析】 You can see that all five choices are linear functions whose graphs are lines with various slopes and y-intercepts. The graph of Choice A is a line with sl
33、ope 1 and y-intercept -2, shown in Figure 6. It is clear that this line will not intersect the graph of f to the left of the y-axis. To the right of the y-axis, the graph of f is a line with slope 2, which is greater than slope 1. Consequently, as the value of x increases, the value of y increases f
34、aster for /than for g, and therefore the graphs do not intersect to the right of the y-axis. Choice B is similarly ruled out. Note that if the y-intercept of either of the lines in Choices A and B were greater than or equal to 4 instead of less than 4, they would intersect the graph of f.Choices C a
35、nd D are lines with slope 2 and y-intercepts less than 4. Hence, they are parallel to the graph of f(to the right of the y-axis)and therefore will not intersect it. Any line with a slope greater than 2 and a y-intercept less than 4, like the line in Choice E, will intersect the graph of f(to the rig
36、ht of the y-axis).The correct answer is Choice E, g(x)= 3x- 2.This explanation uses the following strategies.Strategy 3: Translate from an Algebraic to a Graphical RepresentationStrategy 6: Add to a Geometric FigureStrategy 8: Search for a Mathematical Relationship 13 【正确答案】 C 【试题解析】 Scanning the an
37、swer choices indicates that you can do at least some estimation and still answer confidently. The car used 350/33 gallons of gasoline, so the cost was (350/33)(2.95)dollars. You can estimate the product(350/33)(2.95)by estimating 350/33 a little low, 10, and estimating 2.95 a little high, 3, to get
38、approximately(10)(3)= 30 dollars. You can also use the calculator to compute a more exact answer and then round the answer to the nearest 10 dollars, as suggested by the answer choices. The calculator yields the decimal 31.287., which rounds to 30 dollars. Thus the correct answer is Choice C, $30. T
39、his explanation uses the following strategies. Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 9: Estimate 14 【正确答案】 D 【试题解析】 Since there are 5 red and 4 purple jelly beans in the jar, there are 51 that are neither red nor purple, and the probability of selecti
40、ng one of these is 51/60. Since all of the answer choices are decimals, you must convert the fraction to its decimal equivalent, 0.85. Thus the correct answer is Choice D, 0.85. This explanation uses the following strategies. Strategy 1: Translate from Words to an Arithmetic or Algebraic Representat
41、ion Strategy 5: Simplify an Arithmetic or Algebraic Representation 15 【正确答案】 B， C 【试题解析】 For this question, you must select a pair of answer choices. The product of the pair must be negative, so the possible products are(-20)(2-4),(-20)(3-2),(-10)(2-4), and( 10)(3-2). The product must also be greate
42、r than -1. The first product is -1, so you can stop there.The correct answer consists of Choices B(-10)and C(2-4).This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 10: Trial and Error 16 【正确答案】 C， D， F 【试题解析】 You can
43、 first identify the multiples of 2, which are 8, 12,18, and 36, and then among the multiples of 2 identify the multiples of 3, which are 12, 18, and 36. Alternatively, if you realize that every number that is a multiple of 2 and 3 is also a multiple of 6, you can identify the choices that are multip
44、les of 6. The correct answer consists of Choices C(12), D(18), and F(36). This explanation uses the following strategies. Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 11: Divide into Cases 17 【正确答案】 A， B 【试题解析】 One strategy for answering this kind of questio
45、n is to find the least and/or greatest possible value. Clearly the average salary is between $25,000 and $35,000, and all of the answer choices are in this interval. Since you are told that there are more employees with the lower average salary, the average salary of all employees must be less than
46、the average of $25,000 and $35,000, which is $30,000. If there were exactly twice as many employees in Department X as in Department Y, then the average salary for all employees would be, to the nearest dollar, the following weighted mean, 28,333 dollarswhere the weight for $25,000 is 2 and the weig
47、ht for $35,000 is 1. Since there are more than twice as many employees in Department X as in Department Y, the actual average salary must be even closer to $25,000 because the weight for $25,000 is greater than 2. This means that $28,333 is the greatest possible average. Among the choices given, the
48、 possible values of the average are therefore $26,000 and $28,000.Thus the correct answer consists of Choices A($26,000)and B($28,000).Intuitively, you might expect that any amount between $25,000 and $28,333 is a possible value of the average salary. To see that $26,000 is possible, in the weighted
49、 mean above, use the respective weights 9 and 1 instead of 2 and 1. To see that $28,000 is possible, use the respective weights 7 and 3.This explanation uses the following strategies.Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation Strategy 8: Search for a Mathematical Relationship Strategy 12: Adapt Solutions to Related Problems 18 【正确答案】 B,D,H,J 【试题解析】 The units digit of 57n is the same as the units digit of 7n for all positive integers n. To see why this is true
