1、GRE（ QUANTITATIVE）综合模拟试卷 19及答案与解析 1 Which of the following is closest to the mean of the prices of the 700 homes sold in 2012 and 2013 combined? （ A） $265,000 （ B） $270,000 （ C） $275,000 （ D） $280,000 （ E） $285,000 2 From 1930 to 1990, approximately what was the average increase per year in per capi
2、ta income? （ A） $150 （ B） $200 （ C） $250 （ D） $300 （ E） $350 3 At the rates shown in the graph, which of the following is closest to the number of hours of work time that was required to pay for 20 kilograms of sugar in 1919 ? (1 kilogram equals 2.2 pounds, rounded to the nearest 0.1 pound.) （ A） 11
3、 （ B） 14 （ C） 20 （ D） 31 （ E） 53 4 Eight hours of work time paid for approximately how many more dozen eggs in 1997 than it did in 1919 ? （ A） 50 （ B） 70 （ C） 90 （ D） 110 （ E） 130 5 By approximately what percent did the median price of homes sold in County T decrease from 2011 to 2012 ? （ A） 10% （ B
4、） 15% （ C） 25% （ D） 33% （ E） 50% 6 Based on the information given, which of the following statements about the sum of the prices of all the homes sold in a given year must be true? Indicate all such statements. （ A） The sum of the prices for 2010 was greater than the sum for 2009. （ B） The sum of th
5、e prices for 2010 was greater than the sum for 2011. （ C） The sum of the prices for 2009 was greater than the sum for 2011. 7 County T collected a tax equal to 3 percent of the price of each home sold in the county in 2009. Approximately how much did County T collect in taxes from all homes sold in
6、2009 ? （ A） $38,000 （ B） $260,000 （ C） $380,000 （ D） $2,600,000 （ E） $3,800,000 8 In 1950 the revenue per student was approximately what percent of the per capita income? （ A） 8% （ B） 11% （ C） 14% （ D） 17% （ E） 20% 9 For how many of the seven years shown was the revenue per student less than 1/5 of
7、the per capita income for the year? （ A） One （ B） Two （ C） Three （ D） Four （ E） Five 10 What percent of 150 is 12.9? 11 15 is 60% of what number? 12 An investment in a mutual fund increased by 12% in a single day. If the value of the investment before the increase was $1,300, what was the value afte
8、r the increase? 13 The monthly enrollment at a preschool decreased by 8% during one month and increased by 6% during the next month. What was the cumulative percent change for the two months? 14 Evaluate the following. (a)15-(6-4)(-2) (b)(2-17)+ 5 (c)(60+12)-(-7+ 4) (d)(3)4-(-2)3 (e)(-5)(-3)- 15 (f)
9、(-2)4(15-18)4 (g)(20 5)2(-2 + 6)3 (h)(-85)(0)-(-17)(3) 15 Evaluate the following. 16 Which of the integers 312, 98, 112, and 144 are divisible by 8 ? 17 (a)What is the prime factorization of 372?(b)What are the positive divisors of 372? 18 (a)What are the prime divisors of 100?(b)What are the prime
10、divisors of 144? 19 Which of the integers 2, 9,19, 29, 30, 37, 45, 49, 51, 83, 90, and 91 are prime numbers? 20 What is the prime factorization of 585 ? 21 Which of the following statements are true? 22 Find the following. (a)40% of 15 (b)150% of 48 (c)0.6% of 800 (d)15 is 30% of which number? (e)11
11、 is what percent of 55? 23 If a persons salary increased from $200 per week to $234 per week, what was the percent increase in the persons salary? 24 If an athletes weight decreased from 160 pounds to 152 pounds, what was the percent decrease in the athletes weight? 25 A particular stock is valued a
12、t $40 per share. If the value increases by 20 percent and then decreases by 25 percent, what will be the value of the stock per share after the decrease? 26 If the ratio of the number of men to the number of women on a committee of 20 members is 3 to 2, how many members of the committee are women? 2
13、7 The integer a is even and the integer b is odd. For each of the following integers, indicate whether the integer is even or odd. GRE（ QUANTITATIVE）综合模拟试卷 19答案与解析 1 【正确答案】 B 【试题解析】 The number of homes sold is given in the table, and the mean of the prices is given in the line graph.The mean price o
14、f the 700 homes sold in 2012 and 2013 is the weighted average of the mean price of the 410 homes sold in 2012, which is $250,000, and the mean price of the 290 homes sold in 2013, which is $300,000: Of the choices given, the closest is $270,000. The correct answer is Choice B.This explanation uses t
15、he following strategies.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation Strategy 9: Estimate 2 【正确答案】 D 【试题解析】 For the 60-year period from 1930 to 1990, the per capita income increased by $24,230 - $6,610, or $17,620. The average annual increase is , which is approxi
16、mately , or $300.(Since the choices are quite far apart, there is no need for an accurate calculation.)The correct answer is Choice D.This explanation uses the following strategies.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation Strategy 9: Estimate 3 【正确答案】 A 【试题解析】
17、 If 1 kilogram equals 2.2 pounds, then 20 kilograms equals 44 pounds. According to the graph, in 1919 the work time required to pay for 5 pounds of sugar was approximately 72 minutes, so the work time required to pay for 44 pounds of sugar was(72/5)(44), or 633.6 minutes, which is approximately 10.6
18、 hours. Of the given choices, the one closest to this number is 11 hours. The correct answer is Choice A. This explanation uses the following strategies. Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation Strategy 5: Simplify an Arithmetic or Algebraic Representation St
19、rategy 9: Estimate 4 【正确答案】 C 【试题解析】 Since the work times are given in minutes, first convert 8 hours to 480 minutes. In 1919, the work time that paid for 1 dozen eggs was approximately 80 minutes, so 480 minutes paid for 480/80, or 6 dozen eggs. In 1997, the work time that paid for 1 dozen eggs was
20、 approximately 5 minutes, so 480 minutes paid for 480/5, or 96 dozen eggs. Thus 8 hours of work time paid for 90 dozen more eggs in 1997 than it paid for in 1919. The correct answer is Choice C. This explanation uses the following strategies. Strategy 4: Translate from a Figure to an Arithmetic or A
21、lgebraic Representation Strategy 5: Simplify an Arithmetic or Algebraic Representation Strategy 9: Estimate 5 【正确答案】 C 【试题解析】 The median prices are given in the line graph. The median price decreased from $200,000 in 2011 to $150,000 in 2012, which is a decrease of $50,000. As a percent of the 2011
22、price, this is (100%), or 25%. The correct answer is Choice C.This explanation uses the following strategy.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation 6 【正确答案】 B， C 【试题解析】 For each year, the sum of the prices is equal to the number of homes sold times the mean pr
23、ice of the homes sold. For 2010, the sum is equal to(351)($275,000), or $96,525,000. For 2009, the sum is(503)($250,000), or $125,750,000, which is greater than the sum for 2010. So statement A is false. For 2011, the sum is(390)($175,000), or $68,250,000, which is less than the sum for 2010. So sta
24、tement B is true. Since the sum for 2009 is greater than the sum for 2011, statement C is true. The correct answer consists of Choices B and C. This explanation uses the following strategy. Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation 7 【正确答案】 E 【试题解析】 The total p
25、rice of all the homes sold in 2009 is equal to the number of homes sold times the mean price of the homes sold. The tax is 3% of this amount. Since the choices given are far apart, there is no need for accurate computations. Using estimation, you get a total price of about(500)($250,000), or $125 mi
26、llion. The tax of 3% is(0.03)($125 million), or approximately $3.75 million. Of the choices given, $3,800,000 is closest to this amount. The correct answer is Choice E. This explanation uses the following strategies. Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation St
27、rategy 9: Estimate 8 【正确答案】 C 【试题解析】 The table shows that in 1950 the revenue per student was $1,330. As a percent of the per capita income of $9,540, this is (100%), which is approximately 13.9%.Of the given choices, the closest is 14%. The correct answer is Choice C.This explanation uses the follo
28、wing strategies.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation Strategy 9: Estimate 9 【正确答案】 E 【试题解析】 For most of the years, a rough estimate of - of the per capita income is sufficient for the comparison to the revenue per student. For the years 1930, 1940, 1950, a
29、nd 1960, you might estimate - of the per capita incomes as $1,300, $1,400, $2,000, and $2,500, respectively, which are clearly greater than the corresponding revenues per student.For 1980 and 1990, your estimates might be $4,000 and $5,000, which are less than the corresponding revenues per student.
30、For 1970, you do have to calculate = $3,468, which is greater than $3,440.So the revenue per student was less than 1/5 of the per capita income for the five years 1930, 1940,1950,1960, and 1970. The correct answer is Choice E.This explanation uses the following strategies.Strategy 4: Translate from
31、a Figure to an Arithmetic or Algebraic Representation Strategy 9: Estimate 10 【正确答案】 8.6% 【试题解析】 Here the whole is 150 and the part is 12.9. = 0.086 = 8.6%To find the part that is a certain percent of a whole, you can either multiply the whole by the decimal equivalent of the percent or set up a pro
32、portion to find the part. 11 【正确答案】 25 【试题解析】 Use the decimal equivalent of 60%. Because 60% of some number z is 15, multiply z by the decimal equivalent of 60%, or 0.6.0.6z=15Now solve for z by dividing both sides of the equation by 0.6 as follows.z = = 25 Using a proportion, look for a number z su
33、ch that Hence, 60z =(15)(100), and therefore, z = = 25. That is, 15 is 60% of25. Although the discussion about percent so far assumes a context of a part and a whole, it is not necessary that the part be less than the whole. In general, the whole is called the base of the percent. When the numerator
34、 of a percent is greater than the base, the percent is greater than 100%. For example, 15 is 300% of 5, since and 250% of 16 is( )(16)=(2.5)(16)= 40. Note that the decimal equivalent of 250% is 2.5.It is also not necessary for the part to be related to the whole at all, as in the question, “a teache
35、r s salary is what percent of a banker s salary?“When a quantity changes from an initial positive amount to another positive amount, for example, an employees salary that is raised, you can compute the amount of change as a percent of the initial amount. This is called percent change. If a quantity
36、increases from 600 to 750, then the percent increase is found by dividing the amount of increase, 150, by the base, 600, which is the initial number given: = 0.25 = 25%We say the percent increase is 25%. Sometimes this computation is written as (100%)=25%If a quantity doubles in size, then the perce
37、nt increase is 100%. For example, if a quantity changes from 150 to 300, then the percent increase is = 100%If a quantity decreases from 500 to 400, calculate the percent decrease as follows. = 0.20 = 20%The quantity decreased by 20%.When computing a percent increase, the base is the smaller number.
38、 When computing a percent decrease, the base is the larger number. In either case, the base is the initial number, before the change. 12 【正确答案】 $1,456 【试题解析】 The percent increase is 12%. Therefore, the value of the increase is 12% of $1,300, or, using the decimal equivalent, the increase is(0.12)($1
39、,300)= $156. Thus, the value of the investment after the change is $1,300+ $156 = $1,456 Because the final result is the sum of the initial investment 100% of $1,300 and the increase 12% of $1,300 the final result is 100% + 12% = 112% of $1,300. Thus, another way to get the final result is to multip
40、ly the value of the investment by the decimal equivalent of 112%, which is 1.12: ($1,300)(1.12)= $1,456 A quantity may have several successive percent changes. The base of each successive percent change is the result of the preceding percent change. 13 【正确答案】 2.48% 【试题解析】 If E is the enrollment befo
41、re the first month, then the enrollment as a result of the 8% decrease can be found by multiplying the base E by the decimal equivalent of 100% - 8% = 92%, which is 0.92: 0.92E The enrollment as a result of the second percent change the 6% increase can be found by multiplying the new base 0.92E by t
42、he decimal equivalent of 100% + 6% = 106%, which is 1.06: (1.06)(0.92)E = 0.9752E The percent equivalent of 0.9752 is 97.52%, which is 2.48% less than 100%. Thus, the cumulative percent change in the enrollment for the two months is a 2.48% decrease. 14 【正确答案】 (a)19 (b)-3 (c)8 (d)89 (e)0 (f)1,296 (g
43、)1,024 (h)51 15 【正确答案】 16 【正确答案】 312, 112, and 144 17 【正确答案】 (a)372 =(22)(3)(31) (b)The positive divisors of 372 are 1, 2, 3, 4, 6,12, 31, 62, 93, 124,186, and 372. 18 【正确答案】 (a)100 =(22)(52), so the prime divisors are 2 and 5. (b)144 =(24)(32), so the prime divisors are 2 and 3. 19 【正确答案】 2,19, 29,
44、 37, and 83 20 【正确答案】 585 =(32)(5)(13) 21 【正确答案】 (a)True(b)True(c)False; division by 0 is undefined(d)True(e)True(f)True(g)False; = 3 0(h)True(i)False; -|-23| = -23(j)True(k)False;(59)3(59)2= 593+2= 595(l)True 22 【正确答案】 (a)6 (b)72 (c)4.8 (d)50 (e)20% 23 【正确答案】 17% 24 【正确答案】 5% 25 【正确答案】 $36 per share 26 【正确答案】 8 women 27 【正确答案】
