SAT Math Multiple Choice Question 532: Answer and Explanation

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Question: 532

7. The Great Pyramid of Giza, built in the 26th century BC just outside of Cairo, Egypt, had an original height of 480 feet, 8 inches, before some of the stones in which it was encased fell away. Inside the pyramid is a 53.75-foot passage, called the Dead End Shaft, which archeologists have yet to discover the purpose of. Suppose a museum is building a scale model of the pyramid for patrons to explore. Because of the museum's ceiling height, they can only make the pyramid 71 feet, 6 inches tall. About how long should the museum's Dead End Shaft be?

  • A. 8 feet
  • B. 12 feet
  • C. 30 feet
  • D. 96 feet

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Strategic Advice: Pay careful attention to the units. You need to convert all of the dimensions to inches and then set up and solve a proportion.

Getting to the Answer: There are 12 inches in one foot, so the real pyramid's height was (480 × 12) + 8 = 5,760 + 8 = 5,768 inches; the length of the passage in the real pyramid is 53.75 × 12 = 645 inches; the museum's pyramid height will be 71 feet, 6 inches, or 858 inches; and the length of the museum's passage is unknown. Set up a proportion and solve for the unknown. Use words first to help you keep the measurements in the right places:

The museum should make its passage about 96 inches, or 96 ÷ 12 = 8 feet long.

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