Quantitative Reasoning Practice Set 3

Numbers

All numbers are real numbers.

Figures

The position of points, lines, angles, and so on may be assumed to be in the order shown; all lengths and angle measures may be assumed to be positive.

Lines shown as straight may be assumed to be straight.

Figures lie in the plane of the paper unless otherwise stated.

Figures that accompany questions are intended to provide useful information. However, unless a note states that a figure has been drawn to scale, you should solve the problems by using your knowledge of mathematics, not by estimation or measurement.

Directions

Each of the following questions, 1–8, consists of two quantities, Quantity A and Quantity B. You are to compare the two quantities and choose

    1. if Quantity A is greater
    2. if Quantity B is greater
    3. if the two quantities are equal
    4. if the relationship cannot be determined from the information given

Common Information

In a question, information concerning one or both of the quantities to be compared is centered above the two quantities. A symbol that appears in both quantities represents the same thing in Quantity A as it does in Quantity B.

    1. The diameter of a circle equals the diagonal of a square whose side length is 4.

      Quantity A Quantity B
      The circumference of the circle
      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.
    2. Quantity A Quantity B
      ac 0
      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. Quantity A Quantity B
      The number of distinct positive integer factors of 96 The number of distinct positive integer factors of 72
      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. x > 0
      Quantity A Quantity B
      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. 2p = 4q
      Quantity A Quantity B
      p 2q
      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. Quantity A Quantity B
      The number of seconds in 7 hours The number of hours in 52 weeks
      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.
    7. Angles measuring t² − 2t + 12 degrees and t² + 2t + 24 degrees form a straight line.
      Quantity A Quantity B
      t 12
      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. x > 2
      Quantity A Quantity B
      x3 4x
      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.

    1. If and what is the value of

       

    2. Rectangle A has a length of 12 inches and a width of 5 inches. Rectangle B has a length of 9 inches and a width of 10 inches. By what number must the area of rectangle A be multiplied in order to get the area of rectangle B?

       

    3. Right triangle ABC. The right angle is at vertex A.

      In right triangle ABC above, side AB has a length of x units, side AC has a length of 12 units, and side BC has a length of x + 8 units. What is the area of ABC in square units?

        square units

    4. If the average test score of four students is 85, which of the following scores could a fifth student receive such that the average of all five scores is greater than 84 and less than 86?

      Indicate all such scores.

      1. 88
      2. 86
      3. 85
      4. 83
      5. 80

    5. Meg is twice as old as Rolf, but three years ago, she was two years older than Rolf is now. How old is Rolf now?

        years old

    6. The cost, in cents, of manufacturing x crayons is 570 + 0.5x. The crayons sell for 10 cents each. What is the minimum number of crayons that need to be sold so that the revenue received recoups the manufacturing cost?

      1. 50
      2. 57
      3. 60
      4. 61
      5. 95

    7. If xy ≠ 0,

  3. Set J is comprised of all positive integers x such that x3 is a multiple of both 72 and 216. Which of the following integers are factors of every member of set J? 

    Indicate all such integers.

    1. 2
    2. 3
    3. 6
    4. 9
    5. 12

  4. If x > 0 and 2x2 + 6x = 8, then the average (arithmetic mean) of x + 2, 2x – 1, and x + 4 is equal to which of the following?

    1. –2
    2. 3
    3. 3.5
    4. 5
    5. 7

    1. Questions 18-20 refer to the following graphs:

    2. Bar graph of team revenues in millions of dollars in 1997, with points from 0 to 180 in multiples of 20 on the vertical axis and teams X, Y, Z, Q, and R on the horizontal axis. Each bar plotted on the graph has three components: venue revenue shaded in white, media revenue in dark grey, and other revenue in light grey. The venue revenue is $40M for team X, between $20M and $40M for team Y, and below $20M for teams Z, Q, and R. The media revenue is between $60M and $80M for team X and between $20M and $40M for teams Y, Z, and Q, and about $20M for team R. Other revenue is between $40M and $60M for team X, $60M for team Y, and between $20M and $40M for teams Z, Q, and R. The total revenue is $160M for team X, $120M for team Y, between $60M and $80M for team Z, $60M for team Q, and between $40M and $60M for team R. The pie graph presents the percentages of venue revenues for team X in 1997. 30% came from beer sales, 35% from food sales, 10% from ticket sales, 20% from merchandise, and 5% from other.

    3. For the team with the median venue revenue in 2018, media revenue represented approximately what percent of that team’s total revenue?

      1. 25%
      2. 30%
      3. 45%
      4. 70%
      5. 85%

    4. If Team Y earned total revenues of at least $150 million in 2019, then Team Y’s total revenue could have increased by what percent from 2018 to 2019?

      Indicate all such percents.

      1. 20%
      2. 25%
      3. 30%
      4. 35%
      5. 40%

    5. In 2018, the venue revenues for Team X from merchandise sales and ticket sales were approximately what percent of the venue revenues for Team X from food sales?

      1. 43%
      2. 53%
      3. 67%
      4. 71%
      5. 86%