[Math Lair] Solutions for Practice Test 10, The Official SAT Study Guide, Section 5

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Here are solutions for section 5 of practice test #10 in The Official SAT Study Guide, second edition, found on pages 965–970. 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. By inspection, x = 39 and x − 2 = 37. Select (B) 39.
  2. The difference between the cost of the new refrigerator and the cost of fixing the new one is 900 − 300 = $600. If it saves $15 per month, it will save an amount of $600 in $600/($15/month) = 40 months. Select (D) 40.
  3. If the perimeter of equilateral triangle DEF is 10, the perimeter of equilateral triangle ABC is 30. So, each side of triangle ABC = 30/3 = 10. Select (B) 10.
  4. If the machine mints coins at the rate of one coin per second, and there are 60 seconds in a minute and 60 minutes in a second, it mints 3,600 coins per hour. If it works 10 hours a day, it mints 36,000 coins per day. So, it will take 360,000/36,000 = 10 days to mint 360,000 coins. Select (A) 10.
  5. The arithmetic mean of x and 3x is (x + 3x)/2 = 4x/2 = 2x. Since the arithmetic mean is 12, 2x = 12, or x = 6. Select (C) 6.
  6. Solve for n:
    3x + n = x + 1
    n = −3x + x + 1
    n = −2x + 1
    n = 1 − 2x
    Select (D) 1 − 2x.
  7. Look at the answer choices: List the first few members of each of the sets in the answers:
  8. Guess and check: Try each value, starting with the smallest, to see if it makes √5k/3 an integer:
  9. Examine each integer greater than 20 but less than 30: Out of those numbers, three of them, 21, 22, and 26 meet the criteria in the problem. Select (D) 3.
  10. Try a special case: Say that k = 2. Then: Only (E) is an even integer that is twice the value of an odd integer. Select (E) 4k + 2. Note: If you tried an odd integer (e.g. 1), you might find that (A), (C), and (E) all result in an even integer twice the value of an odd integer. In that case, just try another integer, testing only (A), (C), and (E) this time.