19 . D Assign a number to represent the value of a. When choosing a value for a, make sure that the
number you choose does not cause either dimension of the parallelogram to be negative. Try
a = 10, which means that the base would be 13, and the height would be 5. The formula for
area of a parallelogram is A = bh, so A = 13 × 5 = 65. When you substitute a = 10 into each
of the answer choices, only (D) gives has a value of 65.
20 . G Since the distributing and subtraction can be complex, try picking values for x and y. If x = 2
and y = 3, then (2(2) + 5(3)) − (3(2) − 2(3)) = (4 + 15) − (6 − 6) = 19 − 0 = 19. Plug these x
and y values in to the answer choices to find that only (G) yields a value of 19. If you chose
(J), be careful: You may have forgotten to distribute the negative sign.
21 . B Choose values for a, b, and c, and substitute those values into the given equation. Then
substitute the same values into the answer choices and figure out which choice has the same
value. Try a = 2, b = 3, and c = 4. This makes the original expression = = −.
Only (B) has the same value: = = = − . If you chose (C) be
careful: The c will not divide out of the equation equally if it is not multiplied by the a as
well as the b.
22 . J Use the provided answer choices to determine the correct number of 45¢ comic books. Start
in the middle: this will help with POE. With (H), the total value of the 45¢ comic books
would be $0.45 × 15 = $6.75. Since 15 of the comic books are 45¢, the other 15 would be
10¢ comics. So, the total value of the 10¢ comic books would be $0.10 × 15 = $1.50, and the
total value for all 30 comic books would be $6.75 × $1.50 = $8.25, which is less than $9.65,
the value given in the problem. Therefore, there must be more comic books at 45¢. For (J),
the total value would be $0.45 × 19 + $0.10 × 11 = $6.65. If you chose (F), be careful: This
is the number of 10¢ comics.
23 . E If you’re not sure how to factor this problem, try the numbers from the answer choices. Start
in the middle to help with POE. If a = 3, then (3)^2 + 9(3) = 36 ≠ 0, so eliminate (C). You can
also eliminate (A) and (B) because those values will be too large. Try (E). If a = −9, then
(−9)^2 + 9(−9) = 0, which works. Choice (E) is therefore the only possible answer.
26 . H You can isolate b in the given equation, but you can also plug in a value for a and find the
corresponding value for b. Try a = 4. If a = 4, then, 7(4) − b = 2(4) + 3b, 28 − b = 8 + 3b,
−4b = −20, and b = 5. Now, plug in 4 for a in each answer choice. Choices (F) and (K) are
incorrect because if you want to solve for b, you cannot have b in your expression. Choice
(G) forgets to divide by a negative, and (J) results from incorrectly combining the b terms.
