[Math Lair] Solutions for Practice Test 5, The Official SAT Study Guide, Section 8

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Here are solutions for section 8 of practice test #5 in The Official SAT Study Guide, second edition, found on pages 667–672. 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: Look for a number that is even, positive, and less than 5. The only one is (B) 4. Select that answer.
  2. Solve the equation:
    8 + √k = 15
    k = 7
    k = 49
    Select (B) 49.
  3. 35 out of 35 + 14 + 1 = 50 people were in support of the library, so the fraction of those in support is 35/50 or 70/100 or 7/10. Select (A) 7/10.
  4. Look at the graph for adjacent bars that have very different values. Two large changes occur between 1982 and 1983, and 1984 and 1985. Looking at those two a little more closely, the difference between 1984 and 1985 is the greater difference. Select (D) 1984 and 1985.
  5. Look at the answer choices: Looking at the graph, g(k) = 1 between k = −1 and k = 0. Look for an answer choice between those two numbers. The only such choice is (B) −0.5. Select that answer.
  6. If 2a·2b·2c = 64, then 2abc = 64. Since 64 = 26, then abc = 6. If a, b, and c are different positive integers that multiply to 6, one must be 1, one must be 2, and one must be 3. So, 2a + 2b + 2c = 21 + 2² + 2³ = 2 + 4 + 8 = 14. Select (A) 14.
  7. Set up an inequality:
    30 < h < 50
    -10 < h − 40 < 10
    |h − 40| < 10
    Select (D) |h − 40| < 10.
  8. By the definition in the question, the statement −2 <> (n, 0) is true if n < −2 < 0. If n < −2, the only possible value among those listed is I. −3. Select (A) I only.
  9. If x + y is even, then (x + y)² is even. So, if (x + y)² + x + z is odd, then x + z must be odd, because if it were even, we would be adding two even numbers, resulting in an even number. So, if x + z is odd, then one or the other of x and z, but not both, must be odd. So, if z is even, then x must be odd. Select (C) If z is even, then x is odd.
  10. Try a special case: Say that x = 0.5 or ½. Then: If desired, you can try other cases if you feel that you need to verify that I, II, and III are always true. Select (E) I, II, and III.
  11. Draw a diagram: Sketch the five functions in the answer section on the graph given. The graphs for (B), (C), and (D) are nowhere near the vast majority of the dots, so these answers are obviously wrong. This leaves us with (A) t(p) = 44 and (E) t(p) = p + 44. Now, (A) lies above 5 dots and below 7, and (E) lies above 10 dots, on one dot, and above one dot. Because (A) appears to be more in the middle of the data, it is the better choice. Select (A) t(p) = 44.