GRE(QUANTITATIVE)综合模拟试卷19(题后含答案及解析)

GRE（QUANTITATIVE）综合模拟试卷19(题后含答案及解析) 题型有：1. 2. 计算题
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．$280,000E．$285,000
正确答案：B
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 of 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 the following strategies.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation Strategy 9: Estimate
2．From 1930 to 1990, approximately what was the average increase per year in per capita income?
A．$150
B．$200
C．$250
D．$300E．$350
正确答案：D
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 approximately, 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．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
B．14
C．20
D．31E．53
正确答案：A
解析：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 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 Strategy 9: Estimate
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．110E．130
正确答案：C
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 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 Algebraic Representation Strategy 5: Simplify an Arithmetic or Algebraic Representation Strategy 9: Estimate
5．By approximately what percent did the median price of homes sold in County T decrease from 2011 to 2012 ?
A．10%
B．15%
C．25%
D．33%E．50%
正确答案：C
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 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．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 the 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.
正确答案：B，C
解析：For each year, the sum of the prices is equal to the number of homes sold times the mean price 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 statement 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．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 2009 ?
A．$38,000
B．$260,000
C．$380,000
D．$2,600,000E．$3,800,000
正确答案：E
解析：The total price 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 million. 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 Strategy 9: Estimate
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%
正确答案：C
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 following strategies.Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation Strategy 9: Estimate
9．For how many of the seven years shown was the revenue per student less than 1/5 of the per capita income for the year?
A．One
B．Two
C．Three
D．FourE．Five
正确答案：E
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, and 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.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 a Figure to an Arithmetic or Algebraic Representation Strategy 9: Estimate
10．What percent of 150 is 12.9?
正确答案：8.6%
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 proportion to find the part.
11．15 is 60% of what number?
正确答案：25
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 such thatHence, 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 of a percent is greater than the base, the percent is greater than 100%. For example, 15 is 300% of 5,
sinceand 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 teacher 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 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 percent 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. When computing a percent decrease, the base is the larger number. In either case, the base is the initial number, before the change.
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 after the increase?
正确答案：$1,456
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)($1,300)= $156. Thus, the value of the investment after the change is$1,300+ $156 = $1,456Because 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 multiply the value of the investment by the decimal equivalent of 112%, which is 1.12:($1,300)(1.12)= $1,456A quantity may have several successive percent changes. The base of each successive percent change is the result of the preceding percent change.
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?
正确答案：2.48%
解析：If E is the enrollment before 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 0.92:0.92EThe enrollment as a result of the second percent change—the 6% increase—can be found by multiplying the new base 0.92E by the decimal equivalent of 100% + 6% = 106%, which is 1.06:(1.06)(0.92)E = 0.9752EThe 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．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)(-2)4(15-18)4(g)(20 ÷5)2(-2 + 6)3(h)(-85)(0)-(-17)(3)
正确答案：(a)19(b)-3(c)8(d)89(e)0(f)1,296(g)1,024(h)51
15．Evaluate the following.
正确答案：
16．Which of the integers 312, 98, 112, and 144 are divisible by 8 ?
正确答案：312, 112, and 144
17．(a)What is the prime factorization of 372?(b)What are the positive divisors of 372?
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．(a)What are the prime divisors of 100?(b)What are the prime divisors of 144?
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．Which of the integers 2, 9,19, 29, 30, 37, 45, 49, 51, 83, 90, and 91 are prime numbers?
正确答案：2,19, 29, 37, and 83
20．What is the prime factorization of 585 ?
正确答案：585 =(32)(5)(13)
21．Which of the following statements are true?
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．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 is what percent of 55?
正确答案：(a)6(b)72(c)4.8(d)50(e)20%
23．If a persons salary increased from $200 per week to $234 per week, what was the percent increase in the person’s salary?
正确答案：17%
24．If an athletes weight decreased from 160 pounds to 152 pounds, what was the percent decrease in the athletes weight?
正确答案：5%
25．A particular stock is valued at $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?
正确答案：$36 per share
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?
正确答案：8 women
27．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.
正确答案：。