1、GRE（ QUANTITATIVE）综合模拟试卷 20及答案与解析 1 When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value of n? 2 Ellen has received the following scores on 3 exams: 82, 74, and 90. What score will Ellen need to receive on th
2、e next exam so that the average(arithmetic mean)score for the 4 exams will be 85? 3 A mixture of 12 ounces of vinegar and oil is 40 percent vinegar, where all of the measurements are by weight. How many ounces of oil must be added to the mixture to produce a new mixture that is only 25 percent vineg
3、ar? 4 In a driving competition, Jeff and Dennis drove the same course at average speeds of 51 miles per hour and 54 miles per hour, respectively. If it took Jeff 40 minutes to drive the course, how long did it take Dennis? 5 Working alone at its constant rate, machine A takes 3 hours to produce a ba
4、tch of identical computer parts. Working alone at its constant rate, machine B takes 2 hours to produce an identical batch of parts. How long will it take the two machines, working simultaneously at their respective constant rates, to produce an identical batch of parts? 6 At a fruit stand, apples c
5、an be purchased for $0.15 each and pears for $0.20 each. At these rates, a bag of apples and pears was purchased for $3.80. If the bag contained 21 pieces of fruit, how many of the pieces were pears? 7 To produce a particular radio model, it costs a manufacturer $30 per radio, and it is assumed that
6、 if 500 radios are produced, all of them will be sold. What must be the selling price per radio to ensure that the profit(revenue from the sales minus the total production cost)on the 500 radios is greater than $8,200? 8 If $10,000 is invested at a simple annual interest rate of 6 percent, what is t
7、he value of the investment after half a year? 9 If an amount P is to be invested at an annual interest rate of 3.5 percent, compounded annually, what should be the value of P so that the value of the investment is $1,000 at the end of 3 years? 10 A college student expects to earn at least $1,000 in
8、interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal? 11 Find an algebraic expression to represent each of the following. (a)The square of y is subtracted from 5, and t
9、he result is multiplied by 37. (b)Three times x is squared, and the result is divided by 7. (c)The product of(x + 4)and y is added to 18. 12 Simplify each of the following algebraic expressions.(a)3x2-6 + x + 11-x2 +5x(b)3(5x-1)-x + 4(c) , where x4(d)(2x + 5)(3x-l) 13 (a)What is the value of f(x)= 3
10、x2 -7x + 23 when x = - 2 ?(b)What is the value of h(x)= x3-2x2 + x-2 when x = 2?(c)What is the value of k(x)= x-7 when x = 0? 14 If the function g is defined for all nonzero numbers y by g(y)= , find the value of each of the following. (a)g(2)(b)g(-2)(c)g(2)- g(-2) 15 Use the rules of exponents to s
11、implify the following.(a)(n5)(n-3)(b)(s7)(t7) (e)(w5)-3(f)(50)(d3) 16 Solve each of the following equations for x. (a)5x-7 = 28 (b)12-5x = x + 30 (c)5(x + 2)= l-3x (d)(x + 6)(2x-l)= 0 (e)x2+5x-14 = 0 (f)x2-x-l = 0 17 Solve each of the following systems of equations for x and y. (a)x + y = 24 x-y = 1
12、8 (b)3x-y = -5 x + 2y = 3 (c)15x-18-2y = -3x + 7 10x + 7y + 20 = 4x + 2 18 Solve each of the following inequalities for x. (a)-3x7 + x (b)25x + 1610-x (c)16 + x8x-12 19 For a given two-digit positive integer, the tens digit is 5 more than the units digit. The sum of the digits is 11. Find the intege
13、r. 20 If the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y? 21 Kathleens weekly salary was increased by 8 percent to $237.60. What was her weekly salary before the increase? 22 A theater sells childrens tickets for half the adult ticket price. If 5 adult tickets and 8 childrens tickets co
14、st a total of $27, what is the cost of an adult ticket? 23 Pat invested a total of $3,000. Part of the money was invested in a money market account that paid 10 percent simple annual interest, and the remainder of the money was invested in a fund that paid 8 percent simple annual interest. If the in
15、terest earned at the end of the first year from these investments was $256, how much did Pat invest at 10 percent and how much at 8 percent? 24 Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart.
16、If one car traveled, on average, 8 miles per hour faster than the other car, what was the average speed of each car for the 2-hour trip? 25 A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by
17、 $12. (a)What is the fixed total cost to charter the aircraft? (b)What is the cost per person if 40 people charter the aircraft? GRE（ QUANTITATIVE）综合模拟试卷 20答案与解析 1 【正确答案】 11 2 【正确答案】 94 【试题解析】 Let x represent the score on Ellens next exam. This initial step of assigning a variable to the quantity th
18、at is sought is an important beginning to solving the problem. Then in terms of x, the average of the 4 exams is which is supposed to equal 85. Now simplify the expression and set it equal to 85: Solving the resulting linear equation for x, you get246 + x = 340 x = 94Therefore, Ellen will need to at
19、tain a score of 94 on the next exam. 3 【正确答案】 7.2 【试题解析】 Let x represent the number of ounces of oil to be added. Then the total number of ounces of the new mixture will be 12 + x, and the total number of ounces of vinegar in the new mixture will be(0.40)(12). Since the new mixture must be 25 percen
20、t vinegar, Therefore,(0.40)(12)=(12+ x)(0.25)4.8 = 3 + 0.25x 1.8 = 0.25x7.2 = xThus, 7.2 ounces of oil must be added to produce a new mixture that is 25 percent vinegar. 4 【正确答案】 37.8 minutes 【试题解析】 Let x be the time, in minutes, that it took Dennis to drive the course. The distance d, in miles, is
21、equal to the product of the rate r, in miles per hour, and the time t, in hours; that is,d=rtNote that since the rates are given in miles per hour, it is necessary to express the times in hours; for example, 40 minutes equals of an hour. Thus, the distance traveled by Jeff is the product of his spee
22、d and his time,(51)( )miles, and the distance traveled by Dennis is similarly represented by(54)( )miles. Since the distances are equal, Thus, it took Dennis approximately 37.8 minutes to drive the course. 5 【正确答案】 6/5 hours, or 1 hour 12 minutes 【试题解析】 Since machine A takes 3 hours to produce a bat
23、ch, machine A can produce 1/3 of the batch in 1 hour. Similarly, machine B can produce - of the batch in 1 hour. If we let x represent the number of hours it takes both machines, working simultaneously, to produce the batch, then the two machines will produce - of the job in 1 hour. When the two mac
24、hines work together, adding their individual production rates, 1/3 and 1/2, gives their combined production rate 1/x. Therefore, Thus, working together, the machines will take 6/5 hours, or 1 hour 12 minutes, to produce a batch of parts. 6 【正确答案】 13 【试题解析】 If a represents the number of apples purcha
25、sed and p represents the number of pears purchased, the information can be translated into the following system of equations. 0.15a+ 0.20p = 3.80(total cost) a+p = 21(total number of fruit) From the second equation, a = 21-p. Substituting 21-p into the first equation for a gives 0.15(21-p)+ 0.20p =
26、3.80 (0.15)(21)- 0.15p + 0.20p = 3.80 3.15-0.15p + 0.20p = 3.80 0.05p = 0.65 p=13 Thus, of the 21 pieces of fruit, 13 were pears. 7 【正确答案】 $46.40 【试题解析】 If y represents the selling price per radio, then the profit is 500(y - 30). Therefore, we set500(y-30) 8,200Solving the inequality, we get500y- 15
27、,000 8,200 500y 23,200y 46.4Thus, the selling price must be greater than $46.40 to ensure that the profit is greater than $8,200.Some applications involve computing interest earned on an investment during a specified time period. The interest can be computed as simple interest or compound interest.S
28、imple interest is based only on the initial deposit, which serves as the amount on which interest is computed, called the principal, for the entire time period. If the amount P is invested at a simple annual interest rate of r percent, then the value V of the investment at the end of t years is give
29、n by the formulaV = P(1+ )where P and V are in dollars.In the case of compound interest, interest is added to the principal at regular time intervals, such as annually, quarterly, and monthly. Each time interest is added to the principal, the interest is said to be compounded. After each compounding
30、, interest is earned on the new principal, which is the sum of the preceding principal and the interest just added. If the amount P is invested at an annual interest rate of r percent, compounded annually, then the value V of the investment at the end of t years is given by the formulaV = If the amo
31、unt P is invested at an annual interest rate of r percent, compounded n times per year, then the value V of the investment at the end of t years is given by the formulaV = 8 【正确答案】 $10,300 【试题解析】 According to the formula for simple interest, the value of the investment after 1/2 year is =$10,000(1.0
32、3)= $10,300 9 【正确答案】 $901.94 【试题解析】 According to the formula for 3.5 percent annual interest, compounded annually, the value of the investment after 3 years isP(1 + 0.035)3and we set it to be equal to $1,000P(l + 0.035)3 = $1,000To find the value of P, we divide both sides of the equation by(1 + 0.0
33、35)3.P = $901.94 Thus, an amount of approximately $901.94 should be invested. 10 【正确答案】 4.91 percent 【试题解析】 According to the formula for r percent annual interest, compounded quarterly, the value of the investment after 1 year is By setting this value greater than or equal to $21,000 and solving for
34、 r, we get We can use the fact that taking the positive fourth root of each side of an inequality preserves the direction of the inequality. This is also true for the positive square root or any other positive root. To compute the fourth root, we can use the fact that for x 0; that is, we can comput
35、e a fourth root by taking a square root twice: So the least annual interest rate is approximately 4.91 percent. 11 【正确答案】 (a)37(5-y2), or 185-37y2(b) (c)18 +(x + 4)(y), or 18 + xy + 4y 12 【正确答案】 (a)2x2 + 6x + 5 (b)14x+l (c)x + 4 (d)6x2+13x-5 13 【正确答案】 (a)49(b)0(c)-7 14 【正确答案】 (a)1(b)-1(c)2 15 【正确答案】
36、 (a)n2(b)(sf)7(c)r8(d) (e) (f)d3(g) (h)9x2y3 16 【正确答案】 (a)7(b)-3(c) (d)-6, 1/2(e)-7, 2(f) 17 【正确答案】 (a)x=21 y=3 (b)x=-1 y=2 (c)x=1/2 y=-3 18 【正确答案】 (c)x 19 【正确答案】 83 20 【正确答案】 15 to 8 21 【正确答案】 220 22 【正确答案】 3 23 【正确答案】 $800 at 10% and $2,200 at 8% 24 【正确答案】 48 mph and 56 mph 25 【正确答案】 (a)$4,320(b)$108
