GRE Algebraic Equations and Functions 3 — Questions and Answers
Question 1: Solve the system: x + y = 10 and x - y = 4. What is x?
- 7 (Correct answer)
- 6
- 5
- 3
Correct answer: 7
Adding the equations gives 2x = 14, so x = 7.
Question 2: Factor completely: x² - 9.
- (x - 3)(x + 3) (Correct answer)
- (x - 9)(x + 1)
- (x - 3)²
- (x + 9)(x - 1)
Correct answer: (x - 3)(x + 3)
This is a difference of squares: x² - 9 = (x - 3)(x + 3).
Question 3: If f(x) = x² - 4x + 4, what are the roots?
- x = 2 (double) (Correct answer)
- x = -2, 2
- x = 0, 4
- x = 1, 4
Correct answer: x = 2 (double)
x² - 4x + 4 = (x - 2)², so x = 2 is a repeated root.
Question 4: Simplify: (2x³)(3x²).
- 6x⁵ (Correct answer)
- 5x⁵
- 6x⁶
- 5x⁶
Correct answer: 6x⁵
Multiply coefficients (2·3 = 6) and add exponents (3 + 2 = 5) to get 6x⁵.
Question 5: If 3^x = 81, what is x?
- 4 (Correct answer)
- 3
- 27
- 9
Correct answer: 4
Since 81 = 3⁴, x = 4.
Question 6: What is the y-intercept of f(x) = -2x + 7?
- 7 (Correct answer)
- -2
- 3.5
- 0
Correct answer: 7
The y-intercept occurs at x = 0, giving f(0) = 7.
Question 7: Solve for x: (x/3) + 2 = 6.
- 12 (Correct answer)
- 8
- 4
- 18
Correct answer: 12
Subtract 2 to get x/3 = 4, then multiply by 3 to get x = 12.
GRE Algebraic Equations and Functions 3
Solve the system: x + y = 10 and x - y = 4.
What is x?