[Math Lair] Solutions for Practice Test 3, The Official SAT Study Guide, Section 5

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Here are solutions for section 5 of the third practice test in The Official SAT Study Guide, second edition, found on pages 525–530. 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. If Dave owns 44 comic books, then Fred and Norman own a total of 84 comic books. So, the average number of comic books owned by the two is 84 ÷ 2 = 42. Select (A) 42.
  2. Solution 1: Solution 2:
  3. Solution 1: If something is directly proportional to 1⁄x², it is inversely proportional to x². Since x is inversely proportional to y, x² is inversely proportional to y². Select (E) y².

    Solution 2:
  4. This is a fairly simple proportion question. If the bird flew 62 miles in 4 hours, it flew 62 × ¾ = 46.5 miles in 3 hours. Enter 46.5.
  5. Draw a diagram: Draw a diagram similar to the following:
    [diagram for question 10]
    Now, PQ, PR, PS, and PT are all radii of the circle. Since the radius of the circle is 1, the sum of these four lengths is 4.
  6. Solution 1: If a and b are positive integers, so is ab. All positive integers are divisible by 1, so regardless of what the value of ab is, a possible value for a is 1. Enter 1.

    Solution 2: 10,000 = 104, so ab = 4. By trial and error, find values for a and b. For example, a = 2, b = 2. Enter 2.
  7. When x = 5 and y = −1:
    2(5) − 3(−1) = c
    c = 13
    Enter 13.
  8. Convert the sentence into an equation:
    SentenceEquation
    five5
    times·
    a numberx
    is the same as=
    the numberx
    added to+
    five5
    This results in:
    5x = x + 5
    4x = 5
    x = 5⁄4
    Enter 5/4.
  9. Since there are 1 1s, 2 2s, 3 3s, and so on, there will be 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 terms in the sequence before a 12 appears. Adding these terms up (you may be able to find a shortcut way of doing so) results in 66. There is a little trick here, though. The 12 appears after these 66 terms, so it is the 67th term. Enter 67.
  10. The pattern in the paper repeats every 4 inches. Every 4 inches, the length of the notched edge increases by 3 + 1 + 1 = 5 inches. So, after 80 inches, the length will be (80 ÷ 4) × 5 = 100.
  11. Enter 1/2.