[Math Lair] Solutions for Practice Test 4, The Official SAT Study Guide, Section 6

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Here are solutions for section 4 of the fifth practice test in The Official SAT Study Guide, second edition, found on pages 650–655. The following solutions 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 s + t = 3, then s + t − 6 = 3 − 6 = −3. Select (A) −3.
  2. Look at the diagram for a point that appears to be either much closer to P or much closer to Q. C is such a point. Select (C) C.
  3. Solution 1: Guess and check: Look for a fraction equal to ¾ with a numerator 5 less than the denominator. ¾ = 6/8 = 9/12 = 12/16 = 15/20. 15/20 is equal to ¼ and has a numerator 5 less than the denominator. Its denominator is 20, so select (D) 20.
    Solution 2:
  4. Solution 1: Solution 2:
  5. Solution 1: Solution 2:
  6. The family needs 5 × 4 = 20 bottles of water. If the water is sold only in 3-bottle packages, they will need 20/3 = 6.666... packages. However, they can't buy .666... of a package, so round up to the nearest integer, 7. Enter 7.
  7. Guess and check:
  8. If 2f(p) = 20, then:
    2f(p) = 20
    2(p + 1) = 20
    p + 1 = 10
    p = 9
    So, f(3p) = (3p + 1) = (3(9) + 1) = 28.
  9. The amount of orange juice added in the mixture is (4/5)(1/3) = 4/15 cup. There was 1/5 cup of orange juice to begin with, so the total amount is 4/15 + 1/5 = 7/15. Enter 7/15.
  10. Convert the sentence into an equation:
    If[ignore]
    aa
    ++
    2b2b
    is equal to=
    125 percent125%
    of·
    4b4b
    Putting it all together, we get:
    a + 2b = 125% · 4b
    Solving this equation for a/b, we get:
    a + 2b = 125% · 4b a + 2b = 5b a = 3b a/b = 3
    Enter 3.
  11. If there are 9 equal intervals between 0 and 1 on the number line, the one labelled &sqrt;x is equal to 6/9, or ⅔. So, if &sqrt;x = ⅔, then x = 4/9. Enter 4/9.