[Math Lair] Solutions for Practice Test 1, The Official SAT Study Guide, Section 8

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Here are solutions for section 8 of the first practice test in The Official SAT Study Guide, second edition, found on pages 413–418. The following solutions illustrate faster, less formal methods that may work better than formal methods 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. Read the question and understand what it is asking: Read the question through a first time so you know what to look for. Then read the question through a second time, looking for the relevant information in each sentence: Since Chadd, Steph, and Owen are not the oldest, Daria must be the oldest. Select (B) Daria.
  2. Solution 1: Solution 2:
  3. Solution 1: Multiply both sides of the equation by 9:
    9k = 3x
    Therefore, the answer is (B) 9k.
    Solution 2: Solution 3:
  4. Solution 1: Solution 2:
  5. Solution 1: We can select any one of 5 colors for color 1. Having done that, we can select any one of 4 colors for color 2. The answer is 4 × 5 = 20. Select (B) 20.
    Solution 2: While this solution takes more time, you could list out all of the possibilities. Say that the colors are Red (R), Orange (O), Yellow (Y), Green (G), and Blue (B). The possibilities are:
    RO (Red=color 1, Orange=color 2), RY, RG, RB, OR, OY, OG, OB, YR, YO, YG, YB, GR, GO, GY, GB, BR, BO, BY, BG.
    There are 20 possibilities. Select (B) 20.