SAT Math Multiple Choice Question 429: Answer and Explanation

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Test Information

Question: 429

City Cost per Square Foot
Detroit $62.45
Atlanta $74.19
New York City $288.58
San Francisco $420.99

9. In real estate, location is often the number one determinant of home prices. The table above shows the average price per square foot of houses in four cities. Assuming an average home size of 1,500 to 2,000 square feet, which inequality represents how much more in dollars a house in New York City would cost than in Detroit?

  • A. x ≥ 226.13
  • B. 62.45 ≤ x ≤ 288.58
  • C. 93,675 ≤ x ≤ 432,870
  • D. 339,195 ≤ x ≤ 452,260

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Heart of Algebra / Inequalities

Strategic Advice: The best way to answer this question is to pretend you are a homebuyer. How much more per square foot would your house cost in New York than Detroit? If the house was 1,500 square feet, how much more would this be? If the house was 2,000 square feet, how much more would this be?

Getting to the Answer: Based on the data in the table, a house would cost $288.58 – $62.45 = $226.13 more per square foot in New York than in Detroit. If the house was 1,500 square feet, it would cost 1,500(226.13) = $339,195 more. If the house was 2,000 square feet, it would cost 2,000(226.13) = $452,260 more. So, the house would cost somewhere between $339,195 and $452,260 more, which can be expressed as the compound inequality 339,195 ≤ x ≤ 452,260.

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