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Test
Math
Domain
Algebra
Skill
Linear inequalities in one or two variables
Difficulty
Hard
ID: 830120b0
Modded SAT Question Bank by Abdullah Mallik
 
 y is greater than 2 x minus 1, and, 2 x is greater than 5
 

Which of the following consists of the y-coordinates of all the points that satisfy the system of inequalities above?

  1. y is greater than 6

  2. y is greater than 4

  3. y is greater than five-halves

  4. y is greater than three-halves


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Correct Answer: B
Rationale

Choice B is correct. Subtracting the same number from each side of an inequality gives an equivalent inequality. Hence, subtracting 1 from each side of the inequality 2 x is greater than 5 gives 2 x minus 1, is greater than 4. So the given system of inequalities is equivalent to the system of inequalities y is greater than, 2 x minus 1 and 2 x minus 1, is greater than 4, which can be rewritten as y is greater than, 2 x minus 1, which is greater than 4. Using the transitive property of inequalities, it follows that y is greater than 4.

Choice A is incorrect because there are points with a y-coordinate less than 6 that satisfy the given system of inequalities. For example, the point with coordinates 3 comma 5 point 5 satisfies both inequalities. Choice C is incorrect. This may result from solving the inequality 2 x is greater than 5 for x, then replacing x with y. Choice D is incorrect because this inequality allows y-values that are not the y-coordinate of any point that satisfies both inequalities. For example, y equals 2 is contained in the set y is greater than three halves; however, if 2 is substituted into the first inequality for y, the result is x is less than three halves. This cannot be true because the second inequality gives x is greater than five halves.

 

Question Difficulty: Hard
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