23 . B Draw a diagram with numbers 1−8 evenly spaced around a circle. On the first run, the paper
is delivered to houses 1, 4, and 7; on the second run, the paper is delivered to houses 2, 5,
and 8; and on the third run, the paper is delivered to houses 3 and 6. Therefore, by the third
lap, the paper has been delivered to all the houses.
24 . J In the equation of a line, y = mx + b, the y-intercept is given by constant b, thus line q has a y-
intercept of 500. The y-intercept of line m is 10 less than line q, so subtract 10 from 500 to
get 490. Choice (K) incorrectly adds 10; (H) calculates the y-intercept as 10 times less,
rather than 10 less than that of line m. Choices (F) and (G) use the slope rather than the y-
intercept.
25 . B Simplify the expression by multiplying −9a^5 to each term in the parentheses. Remember
MADSPM. When bases are multiplied, exponents are added. Therefore, the equation should
look like this: −9a^5 (8a^7 − 4a^3 ) = −72a(5+7) + 36a(5+3) = −72a^12 + 36a^8 . Choices (D) and (E)
incorrectly multiply the exponents. Choice (C) doesn’t distribute the negative sign to the
second term. Choice (A) incorrectly subtracts non-combinable terms inside the parentheses
and then multiplies −9a^5.
26 . G Consider PEMDAS and first combine the terms inside the absolute value: −4|−9 + 2| = −4|
−7|. Then take the absolute value of −7, which is +7, and multiply by −4 to get −28. Choices
(F) and (K) incorrectly take the absolute value of −9 and 2 first and then combine. Choice
(H) adds rather than multiplies −4 and +7. Choice (J) neglects to take the absolute value of
−7.
27 . B Given YZ is parallel to XV, ΔWXV and ΔWYZ are similar triangles, thus they have
proportional sides. First, use Pythagorean theorem WX^2 = 6^2 + 8^2 to calculate WX is 10, or
remember that this is one of the special right triangles. Then set up the proportion
to find YZ: , and YZ is 18 inches. Choices (A), (C), and (E) do not use
the correct proportions; (D) is the length of WZ, not YZ.
28 . H Plug in a w value from the table, and eliminate equations that do not give the corresponding h
value. When you plug in w = 0, (G), (J), and (K) do not give h = 7. When you plug in w = 1,
(F) gives h = 8, not 10, so it can also be eliminated.
29 . A Simplify the expression by distributing the coefficients on both sides of the inequality: 4(n −
3) < 5(n + 2) becomes 4n − 12 < 5n + 10. Combine like terms to get −n < 22 and divide by
−1, remembering to flip the inequality sign. Choices (B), (C), (D), and (E) all result from
either neglecting to distribute the coefficient completely through the parentheses or mixing up
