1、GRE（ QUANTITATIVE）计算题模拟试卷 3及答案与解析 1 What are the common factors of 7 and 42? 2 What is the Greatest Common Factor of 48 and 72? 3 What is the Least Common Multiple of 30 and 40? 4 What is the greatest positive integer x such that 2x is a factor of 1210? 5 3x- 17 = 4Solve for x. 6 x/4 = -Solve for x.
2、 7 If x= 15, then 4x-_= 42 8 Two trains running on parallel tracks are 600 miles apart. One train is moving east at a speed of 90 mph, while the other is moving west at 75 mph. How long will it take for the two trains to pass each other? 9 3(x - 4)= 5x -Solve for x. 10 For x = 4, 3x2 - 5x + 9 =_ 11
3、(5X3 + 3x - 12)-(2x3 - 6x + 17)=_ 12 (4x2 + 2x)(x - 6)=_ 13 What are the solution sets for x2 + 2x - 48? 14 (x - 4)and(2x + 3)are the solution sets for what equation? 15 x- 2y = 14 x- 4y = -8 16 4x - 2y = 6 -6x + 5y= 7 17 3x-y = 18 4x = 24 - 6y 18 8(y + x)= 12 4x - 3y = -22 19 4x - y = 63 3y + x = 6
4、 20 For -5 x 4x + 5? 22 If x = 7, then is 3x + 7 greater than or less than 5x - 6? 23 For which values of x is 2x - 5 4x + 6y = 24 22x = 132 x =6 Now choose one of the original equations, substitute 6 in for x, and solve fory: 3(6)-y= 18 18 -y= 18 -y=0 y=0 【知识模块】 计算 18 【正确答案】 x=-5/2 y=4 【试题解析】 First
5、, distribute the 8 to get 8y + 8x = 12. You can then multiply the second equation by -2 to isolate one of the variables, and rearrange the equations to line up the like terms:8x + 8y = 12 -8x + 6y= 44Add the equations together(note that the x terms cancel out):14y = 56 y = 4Now choose one of the ori
6、ginal equations, substitute 4 for y, and solve for x.8x + 8(4)= 12 8x + 32 = 128x = -20x= x= 【知识模块】 计算 19 【正确答案】 x=15 y=-3 【试题解析】 Line up the like terms in both equations: 4x - y = 63 x + 3y = 6 Multiply the top equation by 3 and add the equations: 12x - 3y = 189 x + 3y = 6 Note that the y terms can
7、cel out: 13x = 195 x = 15 Now substitute 15 for x in one of the equations. x + 3y = 6 15 + 3y= 6 3y= -9 y=-3 【知识模块】 计算 20 【正确答案】 x could be any number between and including -5 and 15. 【试题解析】 The inequality states that -5 is less than or equal to x AND x must be less than 15( means “less than or equa
8、l to“ and 4 【试题解析】 Solve this problem algebraically, as follows: 6x- 4x 5 -(-3) 2x 8 x 4 x must be greater than 4 for this inequality to be true. 【知识模块】 计算 22 【正确答案】 x 【试题解析】 The first step in solving this problem is to isolate the variable on one side of the inequality: -5 - 20 x It is important to
9、 remember that when dealing with inequalities, multiplying or dividing by a negative number involves reversing the sign. In this case, both sides were divided by -5, so the sign changes from . 【知识模块】 计算 24 【 正确答案】 x is greater than or equal to -7, and it is less than 15 【试题解析】 To solve this problem,
10、 subtract the 3 from both sides of the inequality:-4-3 x x 15x is greater than or equal to -7, and it is less than 15. 【知识模块】 计算 25 【正确答案】 20 【试题解析】 To solve, substitute 6 for x in the function: f(6)= 62 - 4(6)+ 8 f(6)= 36-24 + 8 f(6)= 20 【知识模块】 计算 26 【正确答案】 x2 + 2x + 1 【试题解析】 To solve, substitute(x
11、 + 1)for x in the function: f(x + 1)=(x + 1)2 (x + l)(x + 1) x2 + x + x + 1 x2 + 2x + 1 【知识模块】 计算 27 【 正确答案】 3x + 6 【试题解析】 The problem gives g(x)= 3x and f(x)= x + 2 and asks for g(f(x). The function g(f(x)means that all of the x values in g(x)are replaced with f(x), as follows: g(f(x)= 3(f(x) g(f(x
12、)= 3(x + 2) g(f(x)= 3x + 6 【知识模块】 计算 28 【正确答案 】 5 【试题解析】 To solve, substitute 2 for x in the function:f(2)= f(2)= f(2)=10/2 f(2)= 5 【知识模块】 计算 29 【正确答案】 20 【试题解析】 To solve, substitute -5 for x in the function: f(-5)=(-5)2 +(-5) f(-5)= 25-5 f(-5)= 20 【知识模块】 计算 30 【正确答案】 3 【试题解析】 First, rearrange the equation into the slope-intercept form by isolating y on the left side; divide both sides by 2: y = 2x + 3 You know that in the slope intercept formula, y = mx + b, b is the y-intercept. Because b = 3, the correct answer is 3. 【知识模块】 计算
