CHAPTER DRILL ANSWERS AND EXPLANATIONS
Algebra Strategies Drill 1: No Calculator Section
5. C Plug in the answers. If you start with (B), the length is 8, and the width is half that, or 4. Area is
length × width. The area of this rectangle is 8 × 4, which is nowhere near 128. Eliminate (A)
and (B), as both are too small. Try (C): If the length is 16, the width is 8. So, does 128 = 16 ×
8? You could write it all out, since you can’t use your calculator, but you can also estimate. 16
× 10 = 160, so 16 × 8 would be about 130. The number in (D) is too large and will give a
weird fraction, so (C) is correct. Alternatively, write an equation. The equation is area = w ×
2 w. So, 128 = 2w^2 . Divide by 2 to get 64 = w^2 . Take the square root of both sides to find w = 8.
The length is twice this width, so length = 2 × 8 = 16, and the answer is (C).10. B A question with unknown variables indicates a good place to plug in. You need numbers for x
and y that will give you a negative product. Try x = 1 and y = –2. If you plug these into the
statements in the Roman numerals, you find that (I) is false, but (II) and (III) are true. You can
eliminate any answer choice that contains (I). This leaves (B) and (D). Now try different
numbers to see if you can eliminate another choice. If you try x = –1 and y = 2, you find that (II)
is false and (III) is still true. This leaves you with (B), which is correct.13. D Plug in the answers, starting with (B). If x = 16, the left side of the equation is = = 2.Does that equal 2 ? No—it’s too small. Choice (C) is ugly to work with, so try (D) next. If itis too big, (C) is your answer. For (D), x = 32, and the left side of the equation becomes . It’s a match, so (D) is correct. You could also solve this
algebraically. Multiply both sides by 2 to get . Square both sides to get x = 16 × 2 =- Choice (D) is correct.
15. C We’ve got variables in the answer choices, which means this is a perfect Plug In problem.
Since we can’t use calculators, let’s make up an easy value for x, such as 2. 9x + 3x+1 then
becomes 9^2 + 32+1 = 81 + 27 = 108. We plugged in x = 2, so let’s use that to find y: y = 3x, so y
= 3^2 = 9. Now plug in y = 9 to each answer choice to see which one gives you 108. Choice (C)
is y(y + 3), which is 9(12) = 108, which is the correct answer.Algebra Strategies Drill 2: Calculator-Permitted Section
8. C Two variables tells you this is a great place to plug in. Let’s pick numbers that make the math
easy. You can try x = 30 and y = 2. So in 2 hours there are 4 periods of 30 minutes each: 12 × 4
= 48. Alex can fold 48 napkins in 2 hours. 48 is your target. Plugging into your answer choices
gives you (C).