SAT Math Multiple Choice Question 431: Answer and Explanation

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Question: 431

11.

The figure above shows the route that Max currently takes to work and back home every day. The city is planning to build an expressway that would cross through the city to help alleviate commuter traffic. Assuming an average gas consumption of 20 miles per gallon and a 5-day workweek, how many gallons of gas will Max save per week by taking the expressway to and from work each day instead of using his current route?

  • A. 2
  • B. 4
  • C. 8
  • D. 10.25

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Additional Topics / Geometry

Strategic Advice: It will save valuable time on Test Day if you can recognize the Pythagorean triple in this problem. If not, just use the Pythagorean theorem to find the length of the expressway.

Getting to the Answer: The roads form a right triangle with the expressway as the hypotenuse. The two legs are Max's current route. He travels on one road for 9 miles and the other for 40. You might recognize this as a Pythagorean triple: 9, 40, 41. Even if you don't, you can always use the Pythagorean theorem to solve for the length of the hypotenuse.

Now that you know the length of the expressway, it's time to analyze what the question is actually asking.

The question asks how much gas he will save given that his car gets 20 miles per gallon. His current round-trip route is 2(9 + 40) = 2(49) = 98 miles, which will use 98 ÷ 20 = 4.9 gallons of gas per day, which is equal to 5(4.9) = 24.5 gallons per workweek. The round-trip expressway route is 2(41) = 82 miles, which will use 82 ÷ 20 = 4.1 gallons of gas per day, which is equal to 5(4.1) = 20.5 gallons per workweek. Thus, he will save 24.5 – 20.5 = 4 gallons of gas per week by taking the expressway.

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