[Math Lair] Solutions for Practice Test 8, The Official SAT Study Guide, Section 3

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Here are solutions for section 3 of practice test #8 in The Official SAT Study Guide, second edition, found on pages 830–835. 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. Look at the answer choices: 1/5 is 0.2, while ¼ is 0.25. The only answer in between these two values is (D) 0.21. Select that answer.
  2. If mx · m7 = m28, then x = 21. If (m5)y = m15, then y = 3. 21 + 3 = 24, so select (D) 24.
  3. Cross-multiply, giving ab = 120. Enter 120.
  4. If each term after the first is 1/5 of the term preceding it, the 4th term will be 6/5 and the 5th term will be 6/25. Enter 6/25.
  5. Let x represent the amount of sales for the month:
    1200 + 0.2x = 2500
    0.2x = 1300
    x = 6500
    Enter 6500.
  6. From the Reference Information, the number of degrees of arc in a circle is 360. So, a wedge consisting of 40 degrees of arc is 40/360 = 1/9 of a circle. If the entire circle weighs 2.5 grams, the wedge weighs (1/9)(2.5) = 5/18 gram. Enter 5/18.
  7. Factor the first equation and substitute the second equation in:
    x² − y² = 10
    (x + y)(xy) = 10
    5(xy) = 10
    xy = 2
    Enter 2.
  8. Work backwards: We could find the area of the shaded area if we knew the area of the larger square and the area of the four triangles. Now, the area of the larger square is 3 × 3 = 9, and the area of each triangle is ½(2)(1) = 1. So, the area of the shaded area is 9 − 1 − 1 − 1 − 1 = 5.
  9. If the average of the class of p students is 70, then the total number of marks in the first class is 70p. If the average of the class of n students is 92, then the total number of marks in that class is 92n. The total number of marks in the two classes is 86(p + n). We can use this information to set up an equation:
    70p + 92n = 86(p + n)
    6n = 16p
    p/n = 6/16
    Enter 6/16.