PSAT Math Multiple-Choice Question 361: Answer and Explanation

Question: 361

An engineer is monitoring construction of a 75-foot-long escalator. The difference in height between the two floors being connected was originally supposed to be 40 feet, but due to a calculation error, this figure must be reduced by 25 percent. The angle between the escalator and the floor must not change in order to comply with the building code. What is the change in length in feet between the original escalator measurement and its corrected value?

• A. 18.75
• B. 25
• C. 56.25
• D. 100

Correct Answer: A

Explanation:

A

Difficulty: Medium

Getting to the Answer: Draw a diagram to make sense of the given situation. Your diagram should look similar to what's shown:

The two triangles are similar, which means you can use a proportion to answer the question. First, find the correct height by taking 25% of 40, which is 10, and deducting that from 40 to get 30. Keeping the heights on the left of your proportion and the hypotenuses on the right, you have . Reduce the left side to get ,
then cross-multiply to eliminate the fractions: 225 = 4x. Solving for x yields 56.25. But don't stop yet: the question asks for the difference in escalator length, not the new length. Subtract 56.25 from 75 to get 18.75, which matches (A).