Multiple-choice Questions — Select One Answer Choice Sample Questions

Directions: Select a single answer choice.

  1. If 5x plus 32 equals 4 minus 2x what is the value of x ?

    (A) Negative 4
    (B) Negative 3
    (C) 4
    (D) 7
    (E) 12

    Explanation

    Solving the equation for x, you get 7x equals negative 28 and so x equals negative 4 The correct answer is Choice A, Negative 4

  2. Which of the following numbers is farthest from the number 1 on the number line?

    (A) Negative 10
    (B) Negative 5
    (C) 0
    (D) 5
    (E) 10

    Explanation

    Circling each of the answer choices in a sketch of the number line (Figure 4) shows that of the given numbers, Negative 10 is the greatest distance from 1.

    Figure 4

    The figure is a number line with 23 equally spaced tick marks labeled with the integers from negative 11 through positive 11. Going from left to right, the 5 evenly spaced integers negative 10, negative 5, 0, 5 and 10 are circled. The integer 1 is 1 tick mark to the right of 0. There is an arrow pointing to the integer 1.

    Another way to answer the question is to remember that the distance between two numbers on the number line is equal to the absolute value of the difference of the two numbers. For example, the distance between Negative 10 and 1 is The absolute value of negative 10 minus one, which equals 11 and the distance between 10 and 1 is The absolute value of negative 10 minus one, which equals 11 The correct answer is Choice A, Negative 10


  3. Figure 5

    The shows the graph in the x y plane of the function f of x equals the absolute value of 2x, end absolute value, + 4. There are equally spaced tick marks along the x axis and along the y axis. The first tick mark to the right of the origin, and the first tick mark above the origin, are both labeled 1. The graph of the function f is in the shape of the letter V. It is above the x axis and is symmetric with respect to the y axis. The lowest point on the graph of f is the point 0 comma 4, which is located on y axis at the fourth tick mark above the origin. Going leftward from the point 0 comma 4, the graph of f is a line that slants upward, passing through the point negative 2 comma 8. Going rightward from the point 0 comma 4, the graph of f is a line that slants upward, passing through the point 2 comma 8.

    The figure above shows the graph of the function f, defined by f of x = the absolute value of 2x, end absolute value, + 4 for all numbers x. For which of the following functions g, defined for all numbers x, does the graph of g intersect the graph of f ?

    (A) g of x = x minus 2
    (B) g of x = x + 3
    (C) g of x = 2x minus 2
    (D) g of x = 2x + 3
    (E) g of x = 3x minus 2

    Explanation

    You can see that all five choices are linear functions whose graphs are lines with various slopes and y-intercepts. The graph of Choice A is a line with slope 1 and y-intercept Negative 2 shown in Figure 6.

    Figure 6

    Figure 6 is the same as figure 5 except that the graph of the line with slope 1 and y intercept negative 2 has been added. The line slants upward as you go from left to right and intersects the x axis at 2. The line is below the graph of y equals f of x.

    It is clear that this line will not intersect the graph of f to the left of the y-axis. To the right of the y-axis, the graph of f is a line with slope 2, which is greater than slope 1. Consequently, as the value of x increases, the value of y increases faster for f than for g, and therefore the graphs do not intersect to the right of the y-axis. Choice B is similarly ruled out. Note that if the y-intercept of either of the lines in choices A and B were greater than or equal to 4 instead of less than 4, they would intersect the graph of f.

    Choices C and D are lines with slope 2 and y-intercepts less than 4. Hence, they are parallel to the graph of f (to the right of the y-axis) and therefore will not intersect it. Any line with a slope greater than 2 and a y-intercept less than 4, like the line in Choice E, will intersect the graph of f (to the right of the y-axis). The correct answer is Choice E, g of x = 3x minus 2

  4. A car got 33 miles per gallon using gasoline that cost $2.95 per gallon. Approximately what was the cost, in dollars, of the gasoline used in driving the car 350 miles?

    (A) $10
    (B) $20
    (C) $30
    (D) $40
    (E) $50

    Explanation

    Scanning the answer choices indicates that you can do at least some estimation and still answer confidently. The car used 350 over 33 gallons of gasoline, so the cost was Open parenthesis, 350 over 33, close parenthesis, times 2.95 dollars. You can estimate the product Open parenthesis, 350 over 33, close parenthesis, times 2.95 by estimating 350 over 33 a little low, 10, and estimating 2.95 a little high, 3, to get approximately 10 times 3 = 30 dollars. You can also use the calculator to compute a more exact answer and then round the answer to the nearest 10 dollars, as suggested by the answer choices. The calculator yields the decimal 31 point two, eight, seven, dot, dot, dot. which rounds to 30 dollars. Thus, the correct answer is Choice C, $30.

  5. A certain jar contains 60 jelly beans — 22 white, 18 green, 11 yellow, 5 red and 4 purple. If a jelly bean is to be chosen at random, what is the probability that the jelly bean will be neither red nor purple?

    (A) 0.09
    (B) 0.15
    (C) 0.54
    (D) 0.85
    (E) 0.91

    Explanation

    Since there are 5 red and 4 purple jelly beans in the jar, there are 51 that are neither red nor purple and the probability of selecting one of these is 51 over 60 Since all of the answer choices are decimals, you must convert the fraction to its decimal equivalent, 0.85. Thus, the correct answer is Choice D, 0.85.

 

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