sin 53° = 11 sin 88°, then divide by sin 53°: XZ = .
54 . K Plug in a value for the radius of the circle, r 1 = 3, then pick a value for p: p = 2. Since the
radius of the first circle is p feet shorter than the radius of the second circle, r 2 = 3 + 2 = 5.
The circumference of the first circle is C 1 = 2πr = 2π(3) = 6π, and the circumference of the
second circle is C 2 = 2πr = 2π(5) = 10π. To find the difference in circumference, subtract Ci
from C 2 : 10π −6π = 4π. Plug p = 2 into the answer choices to find the one that gives you the
correct difference of 4π, which is (K).
55 . C Plug in some values for y to solve this problem. If y = −4, then |y + 3| = |−4 + 3| = 1. Plug y =
−4. Plug y = −4 into the answer choices to see which ones match. Choice (A) can be
eliminated because it gives you −4 − 3 = −7. When you plug in for (B), you get −4 + 3 = −1;
eliminate this choice. Plugging in for (C), you find that –(−4) −3 = 1; keep this choice.
Choice (D) can be eliminated because –(−4) + 3 = 7. Eliminate (E) because 0 does not match
the target. Therefore, the correct answer is (C).
56 . H The first piece of information given is the countries that have fewer than 20 cities. Since
these cities do not have 20, 21, or 22 cities, subtract them from the total: 18 − 7 = 11. The
next piece of information, the countries that have more than 21 cities, doesn’t affect the total
because some of those will have 22 cities. The third piece of information, countries that have
more than 22 cities, does need to be subtracted from the new total, 11 − 2 = 9, which gives
the number of countries with 20, 21, or 22 cities.
57 . C Plug the information given into the identity given in the note: . Apply
the exponent to get , then multiply both sides by 2 to get = 1 −cos 2x.
Subtract 1 from both sides, −1 = = −cos2x, then divide both sides by −1 to get − = cos
2 x.
58 . H The point (−2,8) gives the x and y values for the functions given, so that 8 − f(g(−2)).
Substitute x^3 for f(x) to get f(g(−2)) = [g(−2)]^3 . Solve for g(−2) by taking the cube root of
both sides: g(−2) = 2. Then substitute −k for g(x) and −2 for x to get g(−2)= − k = 2, or
−1 − k = 2. Add 1 to both sides, −k = 3, then divide both sides by −1 to get k = −3. Choice
(K) solves for k using only g(x).
