SAT Math Multiple Choice Question 232: Answer and Explanation

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Question: 232

7.

In figures I and II above, two stacks of identical carpenter's sawhorses are shown, with heights of 92 and 60 inches, respectively. The height, in inches, of a stack of k sawhorses is given by the function h(k) = 16k + 12, where k is a positive integer and k ≥ 1. The number 12 in the function represents which of the dimensions shown in Figure III ?

  • A. a, the height of one sawhorse
  • B. b, the distance from the bottom of one sawhorse to the bottom of the next highest sawhorse
  • C. c, the distance from the top of one sawhorse to the bottom of the next highest sawhorse
  • D. d, the width of a sawhorse at the top

Correct Answer: C

Explanation:

C Start by using Process of Elimination to eliminate (D) because the entire question is about finding the height, and (D) has nothing to do with height. The difference between the left and middle stacks is 2 stacked sawhorses. The height added to the stack of sawhorses by adding two to thestack can therefore be calculated as 92 - 60 = 32. Therefore, the added height of one stacked sawhorse is 32 ÷ 2 = 16. From this information, keep subtracting the 16 inches added to the top of a stack by each additional sawhorse until you get down to one sawhorse in the stack. If three sawhorses are 60 inches tall, two will be 60 - 16 = 44 inches tall and one sawhorse will be 44 - 16 = 28 inches tall. Choice (A), the height of one sawhorse, can now be eliminated. Another way to think about the height added to the stack of sawhorses by each additional sawhorse is to think of it as the distance between the top of one sawhorse and the top of the next. Since all the sawhorses are the same height, this distance is also the distance from the bottom of one sawhorse to the bottom of the next. Since this distance is 16, eliminate (B). Therefore, the answer must be (C). The height of one sawhorse is 28, which is b + c, so the overlap, c, is 28 - 16 = 12.

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