Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given a diagram of quadrilateral RSTU. Let’s sketch it below:
We are given that RU is parallel to side ST and that RU is longer than ST. We must determine the area of the parking lot. Using the given information we can see that the quadrilateral is a trapezoid; thus, we can use the trapezoid formula to determine the area.
area = height(base 1 + base 2)/2
area = 60(45 + RU)/2
If we can determine the length of side RU, we can determine the area of the parking lot.
Statement One Alone:
RU = 80 meters
Since we know the length of RU, we can determine the area of the parking lot. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C and E.
Statement Two Alone:
TU = 20√10 meters
By filling in the information from statement two into the diagram, we can create a right triangle. We can label the triangle PTU. We also see that WP = 45m. Finally, we can use the Pythagorean theorem to determine the length of side PU.
60^2 + PU^2 = (20√10)^2
3600 + PU^2 = 4000
PU^2 = 400
PU = 20
Thus, we see that RU = 15 + 45 + 20 = 80 meters. Since we know the length of side RU, we can determine the area of the parking lot. Statement two provides sufficient information to answer the question.
Answer: D
