AbeNeedsAnswers wrote: ↑Mon May 06, 2019 7:01 pm
In the figure above, what is the area of region PQRST ?
(1) PQ = RS
(2) PT = QT
C
Source: Official Guide 2020
Solution:
Question Stem Analysis:
We need to determine the area of region PQRST. Notice that the area of the region is composed of triangle PQT and rectangle QRST.
Statement One Alone:
From statement one, we see that RS = 6. Since triangle RST is a right triangle with side RS = 6 and hypotenuse RT = 10, side ST = 8 (notice triangle RST is a 6-8-10 right triangle). Since RS and ST are also the sides of rectangle QRST, the area of rectangle QRST is 6 x 8 = 48. However, we can’t determine the area of triangle PQT, so we can’t determine the area of region PQRST. Statement one alone is not sufficient.
Statement Two Alone:
From statement two, we see that triangle PQT is at least an isosceles triangle and perhaps an equilateral triangle. However, since we don’t know which one it really is, we can’t determine its area. Statement two alone is not sufficient.
Statements One and Two Together:
With the two statements, we see that RS = QT and since RS = 6, QT = 6. Furthermore, PT = QT = PQ = 6. This makes triangle PQT an equilateral triangle. Since we know a side of the equilateral triangle, we can determine its area. Lastly, since we’ve already determined the area of rectangle QRST to be 48, we can determine the area of region PQRST. Both statements together are sufficient.
Answer: C
