Only (H) correctly yields the target value of 5.
27 . A Use the formula for area of a parallelogram, A = bh. Since the answer choices are all
possible values for the height of the parallelogram, substitute each choice to figure out which
value yields an area of 60 in^2 . With (C), the height would be 12 in., which means that the
base is 19 in. because the height is 7 in. shorter than the base. Use the formula for area of a
parallelogram to find A = b · h = 19 · 12 = 228 in^2 , which is greater than the target area of
60. Eliminate (C), (D), and (E), because you’ll need a shorter height. Choice (A) gives a
height of 5, which results in a base of 12 and an area of 12.5 = 60. If you chose (C), be
careful: This is the base of the parallelogram, and the problem is asking for the height.
33 . E If you substitute a value for y, you can avoid some of the common algebraic errors. Let y = 2.
Substitute this into the given expression to get .
When you substitute y = 2 into each of the answer choices, only (E) has a value of 2. If you
got one of the other answers, make sure you applied the square to the 4 in the numerator.
35 . C To figure out when Miguel will catch Brian, you need to know the time at which their total
distances will be the same. Use the numbers in the answer choices to figure out how far each
of them traveled and see whether the totals are equivalent. If you try (C), they both have run
for 8 seconds. In that time, traveling at 5 meters per second, Miguel will have traveled 8 × 5
= 40 meters. Brian, given a 20–meter lead and running at a speed of 2 meters per second,
will have traveled 20 + (8 × 2 ) = 20 + 20 = 40 meters as well. Since their total distances
are equal, Miguel needs 8 seconds to catch Brian. If you chose (B), you may have found only
the time it takes Miguel to run 20 m, but remember, Brian is moving also.
47 . B Since the question only tells you that b has to be an integer, choose any integer for b and then
solve the problem. Try b = 2. The two values are then 3(2) = 6 and 7(2) = 14, which have a
difference of 14 − 6 = 8. The correct answer must divide evenly into 8, so the answer is (B).
If you’re not convinced, try another value for b. You’ll find that it yields the same final
answer.
49 . D First, to make the question easier to understand, replace the values for the base and height
with actual numbers. Set b = 3 and y = 2. This means that the base of the parallelogram is 3
feet, and the height of the parallelogram is b + y = 2 + 3 = 5 feet. Using the formula for the
