[Math Lair] Solutions for Practice Test 7, The Official SAT Study Guide, Section 3

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Here are solutions for section 3 of practice test #7 in The Official SAT Study Guide, second edition, found on pages 768–773. 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. Simplify the expression 2 · (x/y) · y² by cancelling out the y's, giving 2xy. Since xy = 10, 2xy = 20. Select (E) 20.
  2. If x + y = 30, then x = 30 − y. Since x > 8, then 30 − y > 8. Rearranging this equation, we get 22 > y. Select (B) y < 22.
  3. Convert the sentence into an equation:
    When[ignore]
    twice2 ·
    a numberx (or any variable)
    is decreased by
    33
    the result is=
    253253
    This gives us 2x − 3 = 253. Solving the equation, 2x = 256 or x = 128. Enter 128.
  4. Substitute a = 2 and c = 3 into the equation:
    2b + b = 2 2·3
    3b = 8
    b = 8/3
    Enter 8/3.
  5. List the factors of n: 1, p, r, s, pr, ps, rs, prs. There are 8 in total. Because p, r, and s are all prime, they can't be broken down any further, so there are only 8 factors. Enter 8.
  6. This problem looks be a little bit time-consuming, but there is a shortcut if you read the problem carefully: