[Math Lair] Solutions for Practice Test 6, The Official SAT Study Guide, Section 2

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Here are solutions for section 2 of practice test #6 in The Official SAT Study Guide, second edition, found on pages 700–705. 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. If each of the packages contained 8 rolls, there would be 5 × 8 = 40 rolls. However, one of the packages contained four additional rolls. So, there are 40 + 4 = 44 rolls. Select (C) 44.
  2. Multiply both sides of the given equation by 2:
    2(x + 3) = 2a
    2x + 6 = 2a
    Select (C) 2a.
  3. Estimate the answer: |u + v| must be > 0, so we can eliminate t and w. u and v seem to be about −½, so |u + v| must be around 1. The only answer near that value is y. Select (D) y.
  4. Try a special case: Say n = ¼. Then, √n = ½, and n2 = 1/16. So, n2 < n < √n. Select (E).
  5. The median of the slopes will be the middle value. From the graph, this is the slope of OC. The slope of OC is rise/run = 3/4. Select (C) 3/4.
  6. From the given information, we can conclude that the plane took off from New York City at 9:00 am PST and arrived at San Francisco at 4:00 pm PST, so it took 7 hours. If a plane left San Francisco at noon PST, it would arrive at New York at 7:00 pm PST. To convert from PST to EST, we need to add three hours, so 7:00 pm PST is 10:00 pm EST. Select (A) 10:00 pm EST.
  7. Look at the answer choices: It may be difficult to see which equations are equivalent as they are, but it's easier if you cross-multiply the equations. Four of the equations result in af = bc, while (A) is the odd one out, resulting in ac = bf. Select (A) a/f = b/c.
  8. Look at I, II, and III individually:
    1. From the question, a [] b = abb. Factoring b out of both terms, the expression becomes b(a − 1). Now, if a and b are positive integers, then this expression can only be equal to zero if a == 1. So, we can eliminate answer choices (B) and (C).
    2. (a + b)[] b
      = b(a + b) − b
      = b(a + b − 1)
      Because a and b must be at least 1, this expression can never be zero.
    3. a[](a + b)
      =a(a + b) − (a + b)
      = (a + b)(a - 1)
      This expression can equal zero only if a == 1. Select (E) I and III.