[Math Lair] Solutions for 2014 SAT Practice Test, Section 8

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SAT Practice Test Solutions:
2014–15 SAT Practice Test
2013–14 SAT Practice Test
The Official SAT Study Guide, second edition
SAT Math Tips

Here are solutions for the section 8 of the 2014–15 SAT practice test (which was also the 2012–13 practice test); you can find the test at the College Board's web site or in the Getting Ready for the SAT booklet. The following solutions illustrate faster, less formal methods that may work better than formal methods 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 Heather ran 3 miles in 30 minutes and she ran 45 minutes at the same rate, then she would have ran 3 × (45/30) = 4.5 miles. Select (C) 4.5.
  2. Divide both sides of the equation by 2:
    mk = 3
    . Select (A) 3.
  3. Look for a pattern: The first student kept ½ of the rope. The second student kept ½ × ½ = ¼ of the rope. The third student kept ¼ × ½ = 1/8 of the rope. It appears that each possible value is ½ of the previous value. So, the next value must be 1/8 × ½ = 1/16. Select (C) 1/16.
  4. Solution 1: Solution 2: Note that it's also possible to solve the problem by transforming the figure in other ways than the one illustrated here.
  5. Solution 1: Solution 2: