area of a parallelogram, the resulting area should be A = b · h = 3 · 5 = 15 square feet.
Substitute the values into the answer choices, and the only equation that is true is the one
given in (D).
50 . K You can solve this question by choosing values for the dimensions of each hat. Make sure to
obey the relationships given in the question. Since Hat Y is the smaller hat, choose the radius
and height for Hat Y first. For Hat Y, let rY = 3 and hY = 2. Using the given formula for volume
of a cone, VY = π(3)^2 · 2 = π · 9 · 2 = 6π. The problem states that the base of Hat X is 6
times the radius of the base of Hat Y, so rX = 18. The problem then states that the height of
Hat X is 3 times the height of Hat Y, so hX = 6. With these values, VY = π(18)^2 ·6 =
π·324·6 = 648π. To compare VX to VY, divide the two volumes: = 108. Choice (F) is
the total of the two numbers given in the question, and (G) is their product. If you picked (J),
you may have squared the height instead of the radius.
51 . B You can use the answer choices and your calculator to help you find the value of x. When
using your calculator, remember to use parentheses correctly! Start in the middle with (C).
Substitute x = into the equation to find = . You’ll notice that this gives a huge
number on the left side of the equation, so let’s eliminate (C), (D), and (E), and try something
smaller. In (B), if x = , then the equation will read . Calculate these values
to find that the two sides are equal, and the correct answer is (B).
53 . A Find values for x and y that work in the given equation. Let the answers help if you’re not
sure where to start. If x = 0 and y = 0, the equation works: (0 − 0)^2 = −2(0)(0) and 0 = 0.
Because these two values work, we can keep (A) and eliminate (B), (C), and (E). Test (D)
by plugging in a few values, and you’ll find that no other values can work. Only (A) gives the
values that must be true.
