[Math Lair] Solutions for Practice Test 6, The Official SAT Study Guide, Section 8

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Here are solutions for section 8 of practice test #6 in The Official SAT Study Guide, second edition, found on pages 728–733. The solutions below demonstrate faster, more informal methods that might work better for you on a fast-paced test such as the SAT. To learn more about these methods, see my e-book Succeeding in SAT Math or the SAT math tips page.

  1. If 3(n − 4) = 18, then n − 4 = 6 and so n = 10. Select (D) 10.
  2. As there are 4 types of stones and 3 types of metals, there are 4 × 3 = 12 combinations of a stone and a metal. Select (D) 12. If you're in doubt as to how to do this one, say that there are stones A, B, C, and D and metals X, Y, and Z, and try to list all combinations. You'll find that there are 12. Select (D) 12.
  3. Convert the sentence into an equation:
    The sum of 3a and3a +
    the square root of
    bb
    is equal to=
    the square of the sum of a and b(a + b
    Putting it altogether, we get 3a + √b = (a + b)². Select (B).
  4. Multiply the left-hand side of the equation by 2:
    2x/8 = 2x/a
    a = 8
    Select (A) 8.
  5. Because s and t lie on a straight line, s + t = 180. Now, u = r = 50, because lines l and m are parallel. So, s + t + u = 230. Select (A) 230.
  6. Simplify the equation and then substitute 300 for x and 1,900 for p(x):
    p(x) = 17x − 10xb
    p(x) = 7xb
    1900 = 7300 −b
    -200 = −b
    b = 200
    Select (E) 200.
  7. Try the extreme values of x and y and see what xy is equal to:
    xyxy
    0−10
    030
    8−1−8
    8324
    So, −8 ≤ xy ≤ 24. Select (E) −8 ≤ xy ≤ 24.