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GMAT Practice Questions - Coordinate Geometry

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You will get two to three questions from Coordinate Geometry in the GMAT quant section. Questions appear in both variants viz., problem solving and data sufficiency. The concepts tested include finding the slope, identifying the quadrants through which a line passes, finding the length of a line segment, determining the equation of a line, equations of parallel and perpendicular lines, area of triangle, and equation of circles. A collection of GMAT practice questions from coordinate geometry is given below. Attempt these questions and check whether you have got the correct answer. If you have not go to the explanatory answer or the video explanations (wherever provided) to learn how to crack the question.

  1. What is the equation of a circle of radius 6 units centered at (3, 2)?

    1. x2 + y2 + 6x - 4y = 23
    2. x2 + y2 - 6x + 4y = 23
    3. x2 + y2 + 6x + 4y = 23
    4. x2 + y2 - 6x - 4y = -23
    5. x2 + y2 - 6x - 4y = 23
    • Correct AnswerChoice (E).
      The equation of the circle is 2 + y2 - 6x - 4y = 23.
      Correct answer
    • Explanatory Answer
    • Circles : Equation
    • Easy
  2. Set S contains points whose abscissa and ordinate are both natural numbers. Point P, an element in set S has the property that the sum of the distances from point P to the point (8, 0) and the point (0, 12) is the lowest among all elements in set S. How many such points P exist in set S?

    1. 1
    2. 5
    3. 11
    4. 8
    5. 3
    • Correct AnswerChoice (E).
      3 such points exist in set S.
      Correct answer
    • Explanatory Answer
    • Properties of Lines
    • Hard
  3. Data Sufficiency : Line L is perpendicular to line K whose equation is 3y = 4x + 12; Lines L and K intersect at (p, q).
    Is p + q > 0?

    1. x intercept of Line L is less than that of Line K
    2. y intercept of Line L is less than that of Line K
    • Correct AnswerChoice (A).
      Statement 1 alone is sufficient; statement 2 is not.
      Correct answer
    • Explanatory Answer
    • Perpendicular Lines
    • Medium
  4. Data Sufficiency : Does the line x + y = 6 intersect or touch the circle C with radius 5 units?

    1. Center of the circle lies in the third quadrant.
    2. Point (-4, -4) does not lie inside the circle.
    • Correct AnswerChoice (E).
      The two statements together are NOT sufficient.
      Correct answer
    • Explanatory Answer
    • Circles, intersecting lines
    • Hard
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