Quantitative Reasoning 2

35 Minutes 20 Questions

Directions

For each question, indicate the best answer, using the directions given.

You may use a calculator for all the questions in this section.

If a question has answer choices with ovals, then the correct answer is a single choice. If a question has answer choices with squares, then the correct answer consists of one or more answer choices. Read each question carefully.

Important Facts:

All numbers used are real numbers.

All figures lie in a plane unless otherwise noted.

Geometric figures, such as lines, circles, triangles, and quadrilaterals, may or may not be drawn to scale. That is, you should not assume that quantities such as lengths and angle measures are as they appear in a drawing. But you can assume that lines shown as straight are indeed straight, points on a line are in the order shown, and all geometric objects are in the relative positions shown. For questions involving drawn figures, base your answers on geometric reasoning, rather than on estimation, measurement, or comparison by sight.

Coordinate systems, such as xy-planes and number lines, are drawn to scale. Therefore, you may read, estimate, and compare quantities in these figures by sight or by measurement.

Graphical data presentations, such as bar graphs, line graphs, and pie charts, are drawn to scale. Therefore, you may read, estimate, and compare data values by sight or by measurement.

  2. The perimeter of isosceles ΔABC is 40, and the length of side BC is 12.

    Quantity A Quantity B
    The length of side AB 14
    1. Quantity A is greater.
    2. Quantity B is greater.
    3. The two quantities are equal.
    4. The relationship cannot be determined from the information given.

  3. f(x) = (x + 3)2

    Quantity A Quantity B
    f(0.5) 9
    1. Quantity A is greater.
    2. Quantity B is greater.
    3. The two quantities are equal.
    4. The relationship cannot be determined from the information given.
  4. Quantity A Quantity B
    The number of miles traveled by a car that traveled for four hours at an average speed of 40 miles per hour The number of miles traveled by a train that traveled for two and a half hours at an average speed of 70 miles per hour
    1. Quantity A is greater.
    2. Quantity B is greater.
    3. The two quantities are equal.
    4. The relationship cannot be determined from the information given.

  5. A single cookie weighs between 5 and 15 grams.
    A single grape weighs exactly 1 gram.

    Quantity A Quantity B
    The number of cookies in a bag that weighs 300 grams and contains only cookies The number of grapes in a bag that weighs 50 grams and contains only grapes
    1. Quantity A is greater.
    2. Quantity B is greater.
    3. The two quantities are equal.
    4. The relationship cannot be determined from the information given.
  6. Triangle ABC, with angle A equal to 60 degrees and an exterior angle from angle C is equal to 120 degrees.
  7. Quantity A Quantity B
    The length of side AB The length of side BC
    1. Quantity A is greater.
    2. Quantity B is greater.
    3. The two quantities are equal.
    4. The relationship cannot be determined from the information given
  8. Line segment PQ is composed of three colinear points. The measure from the first point, P, to the second point is a, and the measure from second point to the last point, Q, is b.
  9. Quantity A Quantity B
    The length of segment PQ 2
    1. Quantity A is greater.
    2. Quantity B is greater.
    3. The two quantities are equal.
    4. The relationship cannot be determined from the information given.

  10. x < y

    Quantity A Quantity B
    y − x x − y
    1. Quantity A is greater.
    2. Quantity B is greater.
    3. The two quantities are equal.
    4. The relationship cannot be determined from the information given.
  11. Equilateral triangle ABE is divided by two line segments drawn from vertex A, AD and AC, forming three triangles: ADE, ACD, and ABC.
  12. Quantity A Quantity B
    The length of side AD The length of side AC
    1. Quantity A is greater.
    2. Quantity B is greater.
    3. The two quantities are equal.
    4. The relationship cannot be determined from the information given.
  13. Two circles, with centers A and B, inscribed inside rectangle PQRS. The two circles intersect one another at exactly one point.

  14. The two circles with centers A and B have the same radius, r. If r = 3, what is the perimeter of rectangle PQRS?

    1. 12
    2. 18
    3. 24
    4. 36
    5. 48

  15. What is the least integer value of x for which is greater than 0?

    1. −2
    2. −1
    3. 0
    4. 1
    5. 2

  16. If then

    3. 1
  17. Points (-2.0,0.4), (-0.5,0.4), and (-0.5,1.6) on a coordinate plane, forming a triangle.

  18. What is the area of the shaded region in the figure above?

      square units

  19. Which of the following is 850% greater than 8 × 103?

    1. 8.5 × 103
    2. 6.4 × 104
    3. 6.8 × 104
    4. 7.6 × 104
    5. 1.6 × 105

  20. Which of the following are divisible by exactly 4 distinct, positive integers?

    Indicate all possible numbers.

    1. 4
    2. 6
    3. 8
    4. 12
    5. 14
  21. Triangle ABC with side AC equal to 100 meters, BC equal to 160 meters, and AB equal to 100 meters.

  22. The figure above represents a triangular field. What is the minimum distance, in meters, that a person would have to walk to go from point A to a point on side BC?

      meters

  23. If the average of two numbers is 3y and one of the numbers is y − z, what is the other number, in terms of y and z?

    1. y + z
    2. 3y + z
    3. 4y − z
    4. 5y − z
    5. 5y + z

  24. Which points lie on the graph of

    Indicate all possible choices.

    1. (−3, −5)
    2. (−2, −4)
    3. (−1, −3)

  25. Questions 18–20 refer to the charts below.

  26. Two charts, one a bar graph and one a pie graph.

    2. Which of the following physician specialties had the lowest ratio of males to females in 1986?

      1. family practice
      2. general surgery
      3. obstetrics/gynecology
      4. pediatrics
      5. psychiatry

    3. If the number of female general surgery physicians in the under-35 category represented 3.5 percent of all the general surgery physicians, approximately how many male general surgery physicians were under 35 years?

      1. 9,200
      2. 9,800
      3. 10,750
      4. 11,260
      5. 11,980

    4. Approximately what percent of all general practice physicians in 1986 were male?

      1. 23%
      2. 50%
      3. 75%
      4. 82%
      5. 90%

Your Practice Test is now complete.