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Test
Math
Domain
Advanced Math
Skill
Nonlinear equations in one variable and systems of equations in two variables
Difficulty
Hard
ID: fbb96bb1
Modded SAT Question Bank by Abdullah Mallik

x-29=x-ax-29

Which of the following are solutions to the given equation, where a is a constant and a>30?

  1. a
  2. a+1
  3. 29
  1. I and II only

  2. I and III only

  3. II and III only

  4. I, II, and III


Tip: Press CTRL/Command to toggle answer
Correct Answer: C
Rationale

Choice C is correct. Subtracting the expression x-29 from both sides of the given equation yields 0=x-ax-29-x-29, which can be rewritten as 0=x-ax-29+-1x-29. Since the two terms on the right-hand side of this equation have a common factor of x-29, it can be rewritten as 0=x-29x-a+-1, or 0=x-29x-a-1. Since x-a-1 is equivalent to x-a+1, the equation 0=x-29x-a-1 can be rewritten as 0=x-29x-a+1. By the zero product property, it follows that x-29=0 or x-a+1=0. Adding 29 to both sides of the equation x-29=0 yields x=29. Adding a+1 to both sides of the equation x-a+1=0 yields x=a+1. Therefore, the two solutions to the given equation are 29 and a+1. Thus, only a+1 and 29, not a, are solutions to the given equation.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question Difficulty: Hard
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