[Math Lair] Solutions for Practice Test 7, The Official SAT Study Guide, Section 9

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Here are solutions for section 9 of practice test #7 in The Official SAT Study Guide, second edition, found on pages 795–800. 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 6 out of 10 cars are red, the probability that a car selected at random is red is 6/10 = 3/5. Select (B) 3/5.
  2. 15 percent of m would equal half of 30 percent of m, or 40/2 = 20. Select (B) 20.
  3. Try a special case: Say that n = −5. Looking at the answers, (A) evaluates to −2.5, (B) evaluates to −10, (C) evaluates to −3, (D) evaluates to −7, and (E) evaluates to 7. The only one that is positive is (E) 2 − n. Select that answer.
  4. Guess and check: Don't try to solve the equation. Instead, try each of the answers as a value for a until you find one that results in a positive integer value for b. If a = 3, then b² = 2, so b is √2, which is not a positive integer. If a = 4, then b² = 9, so b = 3. Select (B) 4.
  5. Convert the sentence into an equation:
    (
    (
    (
    A number nn
    is increased by+
    55
    and[ignore]
    the result is)
    multiplied by×
    55
    This result)
    is decreased by
    55
    Finally[ignore]
    that result)
    is divided by÷
    55
    Putting this all together, we get:
      (((n + 5) × 5) − 5) ÷ 5
    = ((5n + 25) − 5) ÷ 5
    =(5n + 20) ÷ 5
    =n + 4
    Select (D) n + 4.
  6. Look at the answer choices: Check whether n = p for any of the values of p given in choices (A) through (D). For (A), when p = 0, n = 0. Select (A) 0.
  7. Don't get too anxious about the weird symbols (in this answer I've used {x} to denote them), just treat them as if they were functions and solve the equation:
    {a} = {a − 2}
    a² − a = (a − 2)² − (a − 2)
    a² − a = a² − 4a + 4 − a + 2
    4a = 6
    a = 3/2
    Select (C) 3/2.