1、GRE（ QUANTITATIVE）计算题模拟试卷 1及答案与解析 1 Jims Hardware store normally sells bulk nails at $1.09 a pound. There is a sale of 3 pounds of nails for $2.How much can be saved by purchasing 9 pounds of nails at the sale price? （ A） $1.89 （ B） $3.24 （ C） $4.29 （ D） $6.57 （ E） $9.90 2 In ABC, AB AC and the meas
2、ure of B is 34. What is the measure of A? （ A） 34 （ B） 56 （ C） 68 （ D） 73 （ E） 112 3 If 7y + 9 represents an odd integer, which of the following represents the next smaller odd integer? （ A） 7(y+l) （ B） 7(y-2) （ C） 7(y+3) （ D） 7(y+2) （ E） 7(y-2)+ l 4 What is the largest integer value of t that satis
3、fies the inequality ? （ A） 8 （ B） 10 （ C） 18 （ D） 19 （ E） 30 5 The larger of two numbers exceeds twice the smaller number by The sum of twice the larger and 5 times the smaller number is 7If a is the smaller number, which equation below determines the correct value of a? （ A） 5(2a + 9)+ 2a=74 （ B） 5
4、(2a-9)+ 2a=74 （ C） (4a+ 9)+5a = 74 （ D） 2(2a + 9)+ 5a = 74 （ E） 2(2a-9)+ 5a = 74 6 If W = XYZ, then which of the following is an expression for Z in terms of W, X, and Y? （ A） XY/W （ B） W/XY （ C） WXY （ D） W-XY （ E） W+XY 7 What is 1/5 of 16% of $24,000? （ A） $160 （ B） $768 （ C） $3,840 （ D） $4， 032 （
5、E） $7， 500 8 Which two of the following are NOT solutions of(x-5)(x-3)(x-9)(x+9)=0? （ A） -9 （ B） -5 （ C） -3 （ D） 3 （ E） 5 9 What is the least common multiple of 3, 4a, 5b, and 6ab? （ A） 15ab （ B） 60ab （ C） 60a2b （ D） 120ab （ E） 120a2b 10 If 3x + 4y=17 and 5x+2y=23, what is the value of x-y? 11 If -7
6、 x 5 and -3 y 4, what is the greatest possible value of(y-x)(x+y)? 12 A salesperson made a profit of $50 on the sale of a bicycle that cost the salesperson $180. What is the profit expressed as a percent of the salespersons cost? Give your answer to the nearest tenth of a percent. 13 A rope 55 feet
7、long is cut into two pieces. If one piece is 23 feet longer than the other, what is the length, in feet, of the shorter piece? 14 An integer from 10 through 99, inclusive, is to be chosen at random. What is the probability that the number chosen will have 0 as at least one digit? Give your answer as
8、 a simplified fraction. 15 108_9 = 12 16 7_2 = 3.5 17 1/4 _3/8 = 5/8 18 When 5 consecutive odd integers, each greater than 34 are added, what is the smallest possible sum? 19 What is the Lowest Common Denominator of 5/8 and 3/4? 20 + 11=_ 21 3(27 + 2 - 3)=_ 22 1/3 + 3/7=_ 23 231.2-198.7=_ 24 0.25 =_
9、 25 72 =_ 26 =_ 27 Express 3 3 as a square: _ 28 72-32 =_ 29 2 2=_ 30 2 raised to the power of_= 8 GRE（ QUANTITATIVE）计算题模拟试卷 1答案与解析 1 【正确答案】 B 【试题解析】 The correct answer is B. The first step in solving this problem is to calculate the cost of 9 pounds of nails at the regular price: 9($1.09)= $9.81 Ne
10、xt, calculate the cost of 9 pounds of nails at the sale price: 3($2.19)= $6.57 Finally, subtract $6.57 from $9.81 to get a savings of $3.24. 【知识模块】 计算 2 【正确答案】 E 【试题解析】 The correct answer is E. A good way to solve this problem is to sketch triangle ABC, as shown below: You are given that AB is congr
11、uent to AC, and that the measure of angle B is 34. This means that the measure of angle C is also 34, and the measure of angle A is 180 - 34 - 34 = 112. 【知识模块】 计算 3 【正确答案】 A 【试题解析】 The correct answer is A. To answer this question, note that odd numbers are every other number: 1, 3, 5, 7, . , etc. So
12、 an odd number plus or minus 2 would create another odd number. Therefore, 7y+7 would be the next smaller odd integer. Factor out a 7 to get 7(y + 1). 【知识模块】 计算 4 【正确答案】 D 【试题解析】 The correct answer is D. One way to solve this problem is to recognize that, in order for 24/30 to be greater than t/24,
13、t must be less than 24. This is true because any fraction with a denominator larger than or equal to its numerator will always be less than a fraction whose numerator is larger than or equal to its denominator. So, t/24is only less than 24/30 when t is less than 24. Because you are asked for the lar
14、gest integer value of t and you know that t must be less than 24, the correct answer must be 19. You could also set the values equal to each other, cross-multiply and solve for t, as follows: 24/30=t/24 30t=576 r=19.2 The integer value that makes 24/30 greater than t/24, therefore, is 19. 【知识模块】 计算
15、5 【正确答案】 D 【试题解析】 The correct answer is D. To solve this problem, first convert the information given into its mathematical equivalent, as follows(use b to represent the larger number): The larger of two numbers exceeds twice the smaller number by 9: b = 2a + 9 The sum of twice the larger and five t
16、imes the smaller number is 74: 2b + 5a = 74 Now, simply substitute the value of b into the second equation in order to solve for a: 2(2a + 9)+ 5a = 74 【知识模块】 计算 6 【正确答案】 B 【试题解析】 The correct answer is B. Dont let the fact that there are no numbers in this math problem confuse you! Simply remember th
17、at W, X, Y, and Z each represent some number, and perform the correct mathematical operations to isolate Z on one side of the equation, as follows: W=XYZ W/XY=Z 【知识模块】 计算 7 【正确答案】 B 【试题解析】 The correct answer is B. To solve this problem, first calculate 16% of 24,000, as follows: 24,00016 = 3,840 Nex
18、t, calculate 1/5 of 3,840, as follows: 3,840 x1/5 = 3,840 5 = 768 【知识模块】 计算 8 【 正确答案】 B,C 【试题解析】 The correct answer is B and C. The solutions are the values of x that make the product of(x-5)(x-9)(x-3)(x+9)equal to 0. Therefore, x can equal 5, 3, 9, or -9, but x cannot equal -5 or -3. 【知识模块】 计算 9 【正
19、确答案】 B 【试题解析】 The correct answer is B. Each of the numbers in the values given must divide evenly into the least common multiple. Therefore, you can quickly eliminate answer choice A because 4 does not divide evenly into 15. Next, notice that each of the number values divides evenly into 60, which i
20、s less than 120, so eliminate answer choices D and E. Because ab is a smaller multiple than a2b, and ab divides evenly into the product of all of the given values, answer choice B is the least common multiple of the given values. 【知识模块】 计算 10 【正确答案】 3 【试题解析】 The correct answer is 3. In order to solv
21、e this system of equations, subtract the first equation from the second. The result is 2x - 2y = 6. Factor out 2 to get 2(x-y)= 6. Divide both sides by 2 to get x-y= 3. 【知识模块】 计算 11 【正确答案】 99 【试题解析】 The correct answer is 99. Because you are looking for the greatest value of(y- x)(x + y), your goal i
22、s to make x + y as big as possible and y- x as big as possible. Therefore, from the range of values given, choose x= 5 and y=4 to get x + y=9, and x= -7 and y=4 to get y-x=ll. The greatest value of(y-x)(x + y)is(9)(11)= 99. 【知识模块】 计算 12 【正确答案】 27.8 【试题解析】 The correct answer is 27.8. One way to solve
23、 this problem is to set up a proportion, as follows: $50 is to $180 as x is to 100% 50/180 =x/100 180x = 5,000 x = 27.777, which should be rounded to 27.8, as per the instructions in the question. 【知识模块】 计算 13 【正确答案】 16 【试题解析】 The correct answer is 16. To solve this problem, set up an equation to de
24、termine the length of the shorter piece, substituting x for the unknown, shorter length: x +(x+23)= 55 2x+23 = 55 2x=32 x=16 【知识模块】 计算 14 【正确答案】 1/10 【试题解析】 The correct answer is 1/10. The first step in solving this problem is to determine how many integers between 10 and 99, inclusive, will have 0
25、as at least one digit, as follows: 10, 20, 30, 40, 50, 60, 70, 80, 90 There are 9 integers that will have 0 as at least one digit. Next, because there is a total of 90 numbers in the given range, the probability of choosing one of those 9 numbers is 9/90, which simplifies to 1/10. 【知识模块】 计算 15 【正确答案
26、】 【试题解析】 In order for 12 to be the result of this operation, you must divide 108 by 9. Insert the symbol in the blank. 【知识模块】 计算 16 【正确答案】 【试题解析】 To reach an answer of 3.5, you must divide 7 by 2. Insert the symbol in the blank. 【知识模块】 计算 17 【正确答案】 + 【试题解析】 One way to solve this problem is to look f
27、or the Lowest Common Denominator(LCD). The smallest number that both 4 and 8 divide evenly into is 8, so the fraction 3/8 does not need to be changed. The fraction 1/4 is equivalent to 2/8; 2/8 plus 3/8 equals 5/8, so insert the + symbol in the blank. 【知识模块】 计算 18 【正确答案】 195 【试题解析】 To find the small
28、est possible sum, take the 5 consecutive odd integers that are the closest to 34(remember, they all must be greater than 34). These numbers would be: 35, 37, 39, 41, and 43. Add them together: 35 + 37 + 39 + 41 + 43 = 195. 【知识模块】 计算 19 【正确答案】 8 【试题解析】 The Lowest Common Denominator(LCD)is the smalles
29、t number into which all of the denominators will divide evenly. For this problem, you must find the smallest number into which 8 and 4 will divide evenly. Since 4 will divide evenly into 8(8/4= 2), 8 is the LCD. 【知识模块】 计算 20 【正确答案】 16 【试题解析】 You must first complete the operation within the parenthes
30、es(96-21 = 75). Next, do any multiplication or division in the problem, from left to right: 75/15=5. Finally, do any addition or subtraction in the problem, from left to right: 5 + 11 = 16. 【知识模块】 计算 21 【正确答案】 78 【试题解析】 You must first do the operations within the parentheses(27 + 2 - 3 = 26). Now mu
31、ltiply the value from the parentheses by 3: 3 26 = 78. 【知识模块】 计算 22 【正确答案】 16/21 【试题解析】 You must first find the Lowest Common Denominator(LCD)for the two fractions involved. The denominators are 3 and 7. The smallest number into which both of these numbers can divide evenly is 21. Convert each denom
32、inator to 21 by multiplying 1/3 by 7/7 and 3/7 by 3/3. This gives you 7/21+9/21, which equals 16/21. 【知识模块 】 计算 23 【正确答案】 32.5 【试题解析】 This is a simple subtraction problem. To solve this without a calculator, line up the decimal points and subtract(remember to “borrow“ and “carry“), as follows: 【知识模块
33、】 计算 24 【正确答案】 1/20 【试题解析】 First convert 1/5 to its decimal equivalent, which is .2. Then multiply .25 by .2 to get .05. Another way to solve is to first convert .25 to its equivalent fraction, which is 1/4. When multiplying the two fractions, you first multiply the numerators, and then the denomina
34、tors, giving you 1/20. Because this is equivalent to .05, either answer will be correct. 【知识模块】 计算 25 【正确答案】 49 【试题解析】 72 simply means 7 times 7, which is 49. 【知识模块】 计算 26 【正确答案】 3 【试题解析】 Find the square roots before you do the division. The square root of 36 is 6, and the square root of 4 is 2. You
35、 then divide 6 by 2, which equals 3. 【知识模块】 计算 27 【正确答案】 32 【试题解析】 3 times 3 can be stated as “3 squared.“ The proper way to write this is 32. 【知识模块】 计算 28 【正确答案】 40 【试题解析】 Both numbers are raised to the power of 2(they are squared.)You must first find these squares before you do your subtraction; 7
36、 squared is 49, and 3 squared is 9. So, the answer is 49 - 9, which equals 40. 【知识模块】 计算 29 【正确答案】 32 【试题解析】 This problem requires you to find a square root of a number as well as a number squared. The square root of 64 is 8(64 is called a “perfect square“ because its square root is a whole number), and 2 squared equals 4. The answer is 8 times 4, which is 32. 【知识模块】 计算 30 【正确答案】 3 【试题解析 】 The power that a number is raised to is equivalent to the number of times you multiply that number by itself: 2 2 2 is equal to 8, so the answer is 2 raised to the power of 3(23). 【知识模块】 计算
