GRE Algebra

Algebraic Expressions

100

Quantity A: x^3−6

Quantity B: x+1

For when x≤2

Quantity B is greater

200

Jason can run 3s miles in 2r hours. How many miles will Jason run in 80 minutes?

2s/r

300

xy^2z>0

xyz^2<0

Quantity A: y

Quantity B: z

The relationship cannot be determined.

400

If the sum of two consecutive even integers is 94 and the difference of their squares is 188, what is the smaller integer?

46

500

When the integer s is increased by 2, the result is 7 less than 3 times the integer b. What is s−3b ?

-9

Rules of Exponents

100

Simplify: (x^3 * 2x^4 * 5y + 4y^2 + 3y^2)/y

10x^7 + 7y

200

If (32⋅35)3=3x, what is the value of x?

21

300

a>0, and a is odd.

b>1

Quantity A: (1−b)^a

Quantity B: (−b)^a

Quantity A is greater

400

The speed of light is approximately 3.00⋅10^8 meters/sec.  

In scientific notation how many kilometers per hour is the speed of light?

1.08 x 10^9

500

Simplify the following:

Linear & Quadratic Equations

100

Solve the systems of equations.

8x+2y=4

4x+2y=8

(-1,6)

200

Find the value of x and y that satisfy the equations:

 x−y=5 

and

x+y=7.

x=6 and y=1

300

Perform the following operation.

Find the inverse of the function.

 g(x)=x+3 / 2x−4

g^-1 (x)= 4x+3 / 2x-1

400

Solve for x: (x2 – x) / (x – 1) = 1

No solution

500

The difference between a number and its square is 72. What is the number?

9

Linear Inequalities

100

Solve the inequality 2(x−1)>3(2x+3).

x< -11/4

200

Let x be an integer such that |x|<1.

Quantity A: x^2          

Quantity B: 0

Quantity A and Quantity B are equal

300

The value(s) for which the following function is undefined:

Quantity A: f(x)=√5x-135

Quantity B: 27

Quantity B is larger

400

Solve for x

3x+7≥−2x+4

x≥−3/5

500

The cost, in cents, of manufacturing  pencils is , where 1200 is the number of cents required to run the factory regardless of the number of pencils made, and 20 represents the per-unit cost, in cents, of making each pencil. The pencils sell for 50 cents each. What number of pencils would need to be sold so that the revenue received is at least equal to the manufacturing cost?

40

Coordinate Geometry

100

What is the slope of the line:

1/2

200

What is the y-intercept of the equation y=−2x+7?

7

300

What is the equation of the line (in slope-intercept form) that goes through the points: (2,4) and (7,8)?

y= 4/5x + 12/5

400

A line has a slope of m=−1/4, and goes through point (0,8).  What is the equation of the line in slope-intercept form?

y= -1/4 + 8

500

What is the slope (m) and the y-intercept (b) of the equation

y=1/6x−1/2

 m=1/6  b=-1/2