scores each group received. To illustrate this, plug in! Let’s say that the scores of Group A
were {1, 1, 7, 7, 7}, and the scores for Group B were {1, 1, 6, 6, 6}. The scores of the
whole group would, therefore, be {1, 1, 1, 1, 6, 6, 6, 7, 7, 7}. This set has a mode of 1, so
eliminate (A), (B), and (C) and choose (D).- C First, count the number of blocks that Josh needs to drive. He needs to drive 4 blocks north
and 6 blocks east for a total of 10 blocks. You need to convert this into miles, which can bedone with the following proportion: . The drive is a total of 6 miles.Since Josh drives at 30 miles per hour, you can set up a second proportion: . Cross-multiply and solve to get that x = or of an hour. This
equals 12 minutes in (C).
D The first step is to rewrite the bottom equation so that it is in the same format as the first
equation. Move all of the variables in the bottom equation to the left side of the equation to
get 6s – t = 12. If the answer is (A) and there are infinitely many solutions to the system of
equations, then the two equations must be the same equation. To determine whether this is
the case, multiply the top equation through by 3 to get 6s – t = 30. Since it cannot be the
case that the equation 6s – t equals both 12 and 30, the correct answer is (D). There are no
solutions to the system of equations.
C Two factors are important in determining how to poll a group: the size of the sample and
how that sample is selected. Secretary Stephens’s plan has the largest sample with 250
students, but all those students belong to the senior class. Perhaps the senior class would
prefer a theme that the other three classes would not. The sample is skewed and not
necessarily representative of the entire student body, so eliminate (B). The other three plans
all poll 100 students, so the manner in which those students are selected becomes more
important. President Peterson’s plan is also skewed specifically to friends of the student
council members, whose opinions might not reflect the majority, so eliminate (A). Vice
President Vaiyda’s plan has more potential for a varied sample, but it is still not as good as
Treasurer Thompson’s plan, which guarantees that a random assortment of people will be
chosen for the poll. Eliminate (D), and choose (C).
C Since x and y are points on the circle, plug in the point (–2, –2) into the left side of the
equation. This gives you (–2 + 3)^2 + (–2 – 1)^2 , which equals 1^2 + (–3)^2 . Simplifying, you
get 10. Because 10 is greater than r^2 (which is 9), the point must be outside the circle,
which is (C).- D Whenever the question includes variables, think Plugging In. According to the question,
. Plug in 12 for x to get , or .