1、GRE（ QUANTITATIVE）综合模拟试卷 1及答案与解析 0 7 In the figure above, what is the value of ? （ A） 2 （ B） 3 （ C） 4 （ D） 5 （ E） 6 8 A certain store sells two types of pens: one type for $2 per pen and the other type for $3 per pen. If a customer can spend up to $25 to buy pens at the store and there is no sales t
2、ax, what is the greatest number of pens the customer can buy? （ A） 9 （ B） 10 （ C） 11 （ D） 12 （ E） 20 9 If y = 3x and z = 2y, what is x + y + z in terms of x ? （ A） 10x （ B） 9x （ C） 8x （ D） 6x （ E） 5x 10 A certain shipping service charges an insurance fee of $0.75 when shipping any package with conte
3、nts worth $25.00 or less and an insurance fee of $1.00 when shipping any package with contents worth over $25.00. If Dan uses the shipping company to ship three packages with contents worth $18.25, $25.00, and $127.50, respectively, what is the total insurance fee that the company charges Dan to shi
4、p the three packages? （ A） 1.75 （ B） 2.25 （ C） 2.5 （ D） 2.75 （ E） 3 11 If 55 percent of the people who purchase a certain product are female, what is the ratio of the number of females who purchase the product to the number of males who purchase the product? （ A） 11 to 9 （ B） 10 to 9 （ C） 9 to 10 （
5、D） 9 to 11 （ E） 5 to 9 12 In the rectangular solid above, TU = 3, UV = 4, and VR = What is the area of the shaded rectangular region?_ 13 A list of numbers has a mean of 8 and a standard deviation of 2.If x is a number in the list that is 2 standard deviations above the mean, what is the value of x
6、? x=_ 14 The circle graph above shows the distribution of 200,000 physicians by specialty. Which of the following sectors of the circle graph represent more than 40,000 physicians?Indicate all such sectors. （ A） Pediatrics （ B） Internal Medicine （ C） Surgery （ D） Anesthesiology （ E） Psychiatry GRE（
7、QUANTITATIVE）综合模拟试卷 1答案与解析 1 【正确答案】 A 【试题解析】 In this question you are asked to compare the price at which Emma sold the bicycle with $140. From the information given, you can conclude that Emma spent a total of 75 + 27 = 102 dollars buying and repairing the bicycle and that she sold it for 40 percen
8、t more than the $102 she spent buying and repairing it. If you notice that 140 is 40 percent more than 100, you can conclude that 40 percent more than 102 is greater than 40 percent more than 100, and therefore, Quantity A is greater than Quantity B. The correct answer is Choice A.(If you solve the
9、problem in this way, you do not have to calculate the value of Quantity A.) Another way to solve the problem is by explicitly calculating the value of Quantity A and comparing the result with $140 directly. Since 40 percent of 102 is(0.4)(102)= 40.8, it follows that Quantity A, the price at which Em
10、ma sold the bicycle, is 102.00 + 40.80 = 142.80 dollars. Thus Quantity A, $142.80, is greater than Quantity B, $140, and the correct answer is Choice A. 2 【正确答案】 C 【试题解析】 In this question you are asked to compare the area of the shaded region with 36. You are given that both PQRV and VRST are square
11、s with sides of length 6. Therefore, you can conclude that the length of QS is 12, and the area of the shaded right triangle PQS is 1/2(12)(6), or 36. Thus Quantity A is equal to Quantity B, and the correct answer is Choice C. 3 【正确答案】 A 【试题解析】 Before making the comparison in this problem, you need
12、to analyze the information given to see what it tells you about the value of Quantity A, the property tax in 2009 on a home in Town X that had an assessed value of $160,000. One way of doing this is to determine the value of the constant p and then use that value to calculate the tax on the home tha
13、t had an assessed value of $160,000. Since it is given that a home that had an assessed value of $125,000 had a property tax of $2,500, you can conclude that p is equal to , or 2%. Once you know that the property tax is 2% of the assessed value, you can determine that tax on the home that had an ass
14、essed value of $160,000 was 2% of 160,000, or 3,200. The correct answer is Choice A. Another way to calculate the property tax on a home with an assessed value of $160,000 is by setting up a proportion. Because the tax rate is the same for each home in Town X, you can let the variable x represent th
15、e tax for the home assessed at $160,000 and solve for x as follows.The correct answer is Choice A. 4 【正确答案】 D 【试题解析】 One way to approach this question is to plug in values for one of the variables and determine the corresponding value for the other variable. One way to plug in: Plug in easy values.
16、For example, you can plug in x = 0 and find that the corresponding value of y is -1; then you can plug in y = 0 and find that the corresponding value of x is -1. Since in the first case x is greater than y and in the second case y is greater than x, the correct answer is Choice D, the relationship c
17、annot be determined from the information given. A second way to plug in: If you prefer to always plug in values of x to determine corresponding values of y, you can begin by writing the equation x +y = -1 asy = -x - 1. Writing it in this form makes it easier to find the corresponding values of y. Yo
18、u can start by plugging in the value x = 0. For this value of x, the corresponding value of y is y = -1, and therefore, x is greater than y. If you continue plugging in a variety of values of x, some negative and some positive, you will see that sometimes x is greater than y and sometimes y is great
19、er than x. If you inspect the equation y = x - 1, you can conclude that since there is a negative sign in front of the x but not in front of the y, for each value of x that is greater than 0, the corresponding value of y is less than 0; therefore, for each x 0, x is greater than y. What about negati
20、ve values of x? A quick inspection of the equation y = x - 1 allows you to conclude that if x 0, so y is greater than x. So for some values of x and y that satisfy the equation, x is greater than y; and for other values, y is greater than x. Therefore, the relationship between the two quantities x a
21、nd y cannot be determined from the information given, and the correct answer is Choice D. 5 【正确答案】 B 【试题解析】 You are given that three numbers, r, s, and t, are consecutive odd integers and that r In the last step of the simplification, you can easily see that 3 5. If you follow the simplification ste
22、ps in reverse, you can see that the placeholder in each step remains unchanged, so you can conclude that Quantity B is greater than Quantity A, and the correct answer is Choice B. Simplification 2: Since the number s appears in both quantities, you can begin the simplification by subtracting 5 from
23、both sides of the relationship and then express t in terms of r. The steps in this simplification can be done as follows. In the last step of the simplification, you can easily see that 1 3. If you follow the simplification steps in reverse, you can see that the placeholder in each step remains unch
24、anged, so you can conclude that Quantity B is greater than Quantity A, and the correct answer is Choice B. Note that in this solution, the fact that r is odd is not used; what is used is the fact that the consecutive odd integers differ by 2. 6 【正确答案】 A 【试题解析】 Note that the slope of each of the line
25、s is positive, since each line rises as it goes to the right. Since the slopes of both lines are positive and line k rises faster(or is steeper)than line t, line k has the greater slope, and the correct answer is Choice A. You can also use the definition of the slope to arrive at the correct answer.
26、 Slope can be defined as the ratio of “rise“ to “run“ between any two points on a line, where the rise is the vertical distance between the points and the run is the horizontal distance, and the slope is respectively positive or negative depending on whether the line rises or falls when viewed from
27、left to right. Because both lines pass through point P on the y-axis, they have the same rise from P to the x-axis. However, line t intersects the X-axis at a greater value than line k. Thus, the run of line l from the y-axis to the x-intercept is greater than the run of line k. When the slope is ex
28、pressed as a ratio, both lines have the same numerator(rise), but line l has a greater denominator(run). The greater denominator results in a lesser fraction and a lesser slope for line l. Therefore, the correct answer is Choice A. 7 【正确答案】 C 【试题解析】 The sum of the measures, in degrees, of the three
29、interior angles of any triangle is 180. As shown in the figure, the three angles of the triangle have measures of x, y, and z, so x + y + z = 180. Therefore, = 4, and the correct answer is Choice C. 8 【正确答案】 D 【试题解析】 It is fairly clear that the greatest number of pens that can be bought for $25 will
30、 consist mostly, if not entirely, of $2 pens. In fact, it is reasonable to begin by looking at how many of the $2 pens the customer can buy if the customer does not buy any $3 pens. It is easy to see that the customer could buy 12 of the $2 pens, with $1 left over. If the customer bought 11 of the $
31、2 pens, there would be $3 left over with which to buy a $3 pen. In this case, the customer could still buy 12 pens. If the customer bought 10 of the $2 pens, there would be $5 left over. Only 1 of the $3 pens could be bought with the $5, so in this case, the customer could buy only 11 pens. As the n
32、umber of $2 pens decreases, the total number of pens that the customer can buy with $25 decreases as well. Thus the greatest number of pens the customer can buy with $25 is 12. The correct answer is Choice D. 9 【正确答案】 A 【试题解析】 It is not necessary to find the individual values of x, y, and z to answe
33、r the question. You are asked to rewrite the expression x + y + z as an equivalent expression in terms of x. This means that you need to use the information provided about y and z to express them in terms of the variable x. The variable y is already given in terms of x; that is, y = 3x; and because
34、z = 2y, it follows that z =(2)(3x)= 6x. Using substitution, you can rewrite the expression as follows. x + y + z=x +(3x)+(6x) =(1 +3 + 6)x =10x The correct answer is Choice A. 10 【正确答案】 C 【试 题解析】 Note that two of the packages being shipped have contents that are worth $25.00 or less. Therefore, each
35、 of them has an insurance fee of $0.75, for a total of $1.50. The third package has contents worth over $25.00, and it has an insurance fee of $1.00. Therefore, the total insurance fee for the three packages is $1.50 + $1.00 = $2.50, and the correct answer is Choice C. 11 【正确答案】 A 【试题解析】 Note that b
36、ecause 55 percent of the people who purchase the product are females, it follows that 45 percent of the people who purchase the product are males. Therefore, the ratio of the number of females who purchase the product to the number of males who purchase the product is 55 to 45, or 11 to 9, and the c
37、orrect answer is Choice A. 12 【正确答案】 10 【试题解析】 To find the area of the shaded rectangular region, you need to multiply the length of the rectangular region by its width. In this question you are given the lengths of three edges: TU = 3, UV = 4, and VR = 2. Note that VR is the length of the shaded re
38、ctangle. To find the width of the shaded rectangle, you need to find either RS or VT. Note that VT lies on the front face of the rectangular solid. It is the hypotenuse of right triangle VUT. You know that UV = 4 and TU = 3, so by the Pythagorean theorem you can conclude that VT = = 5. Therefore, th
39、e area of the shaded rectangular region is(5)(2)= 10. The correct answer is 10. 13 【正确答案】 13 【试题解析】 You are given that x is 2 standard deviations above the mean, 8. Because the standard deviation of the numbers in the list is 2.5, it follows that x is(2)(2.5), or 5 units above the mean 8. Therefore,
40、 x = 8 + 5 = 13, and the correct answer is 13. 14 【正确答案】 A,B,C 【试题解析】 One approach to solve this problem is to find out what percent of 200,000 is 40,000 and then compare this percent with the percents given in the circle graph. Because = 0.2, it follows that 40,000 is 20% of 200,000, and any specialty that has more than 20% of the distribution has more than 40,000 physicians. This is true for the specialties of pediatrics, internal medicine, and surgery. The correct answer consists of Choices A, B, and C.
