chickens, but yields different total numbers of each animal. Choice (A) subtracts the number
of 1-animal groups from the number of 10-animal groups of rabbits.
36 . G Find the total number of chickens by multiplying the number of groups of each kind by the
number of animals in the group and adding them together: (0)(1) + (20)(5) + (30)(10) = 400.
Find of the total: (400) = 80. To find the price per chicken, divide the total price by the
number of chickens purchased: $1,200 ÷ 80 = $15.
37 . E There are 22 goats in 1-animal groups. To find the number of 5-animal groups that could be
created, divide 22 by 5: 22 ÷ 5 = 4.4, or 4 with a remainder of 2, so 4 complete groups can
be created. Choice (D) incorrectly rounds 4.4 up to 5. Choice (B) adds the correct answer, 4,
to the existing number of 5-animal groups of goats, 10. Choice (A) gives the number of goats.
38 . G Since point F is on the x-axis, the y-coordinate must be 0, which means that (F), (J), and (K)
can be eliminated. You know triangle DEF is isoceles, so DE must be equal to EF since
DEF is obtuse. Point E then comes halfway between points D and F, meaning the x-
coordinate of point F is twice the x-coordinate of point E, or 2c.
39 . E EDF and EFD add up to 180° − 135° = 45°. Since triangle DEF is isoceles, each angle is
45° ÷ 2 = 22.5. To find the measure of the angle formed by DE and the y-axis, subtract EDF
from 90°: 90° − 22.5° = 67.5°. Choice (A) gives the measure of DE and the x-axis. Choice
(C) gives the measure of EDF and EFD together.
40 . J When the triangle is rotated 180°, point E will lie in Quadrant III. In Quadrant III, both
coordinates will be negative, which means (F), (G), and (K) can be eliminated. Point E will
be the same distance from the origin on both the x- and y-axes, but in the opposite direction,
so both coordinates should be the opposite of the original values, or (−c, −d) as in (J).
41 . A The total volume of the pyramid is 2 gallons, or 2 × 231 = 462 in^3 . Plug the values you know
into the given equation to get 462 = b(15). To solve for b, multiply both sides by 3, 1,386 =
b(15), then divide both sides by 15, b = 92.4. Round down to get (A).
42 . F Nathan read of his book in the first month. That leaves him to read in the
remaining 4 months. To find how much he must read in each of the remaining 4 months,
divide the amount left by the number of months, .
