[Math Lair] Solutions for Practice Test 6, The Official SAT Study Guide, Section 4

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Here are solutions for section 4 of practice test #6 in The Official SAT Study Guide, second edition, found on pages 712–717. 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. Start with the first equation, and substitute the second and third into it. You might be able to do this in your head, but I'll show the exact steps below:
    xy = 8
    x − 3z = 8
    x − 3(2) = 8
    x = 14
    Select (E) 14.
  2. Look at the answer choices: The five answers relate m, t, and s using < . If Todd is older than Marta but younger than Susan, then t must be in the middle, and t < s. The only such answer choice is (A) m < t < s. Select that answer.
  3. The arithmetic mean of the areas is the total area (5) divided by the number of regions (2), or 5/2. Select (B) 5/2.
  4. Guess and check: 121 = 11 × 11. Since 11 is a prime number, the only factors of 121 are 121, 11, and 1. Select (A) 121.
  5. This looks gross, but don't panic:
  6. If a number has a factor of 10, its ones digit must be 0. The largest such three-digit number is 990.
  7. If a recipe for chili for 20 people requires 4 pounds of beans, then chili for one person at that rate requires 4/20 = 1/5 pounds. So, chili for 150 people requires 1/5 150 = 30.
  8. Guess and check: Say that n = 10. If 50 percent of n is 5, so if n is increased by 50 percent of itself, the result is 15, which is between 10 and 20. Enter 10. If you weren't as lucky with your guess the first time, select a larger number (if the result was too small) or a smaller number (if the result was too large) and try again.
  9. There are several ways to solve this problem; here's an innovative way of doing so: Because the $2 light bulbs cost twice as much each but only half as many were ordered, then exactly the same amount of money was spent on the $1 bulbs as on the $2 bulbs. Since $600 was spent in total, $300 was spent on the $1 bulbs and $300 on the $2 bulbs. So, there were 300 $1 bulbs and 150 $2 bulbs, or 450 in total.
  10. Substitute xy = 20 in 4(x + y)(xy) = 40:
    4(x + y)(20) = 40
    4(x + y) = 2
    x + y = ½
    Enter 1/2.
  11. If 40% of the voting-age population voted, that would be 40%(1,200 + 1,300) = 40%(2,500) = 1,000. Now, the number of registered voters is 1,000 + 1,200 = 2,200, and the turnout is 1,000/2,200 = 10/22 = 5/11. Enter 5/11.
  12. Looking at the diagram, there are three edges connecting V to another vertex. So, if 11 lines are drawn to the other vertices, 3 will lie on an edge and so 8 will not. Enter 8.