Which of the following numbers is farthest from the number 1 on the number line?
Circling each of the answer choices in a sketch of the number line (Figure 4) shows that of the given numbers,
is the greatest distance from 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
and 1 is
and the distance between 10 and 1 is
The correct answer is Choice A,
The figure above shows the graph of the function f, defined by
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 ?
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
shown in Figure 6.
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,
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?
Scanning the answer choices indicates that you can do at least some estimation and still answer confidently. The car used
gallons of gasoline, so the cost was
dollars. You can estimate the product
a little low, 10, and estimating 2.95 a little high, 3, to get approximately
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
which rounds to 30 dollars. Thus the correct answer is Choice C, $30.
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?
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
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.