题目信息
In the figure above, what is the perimeter of ΔPQR ?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
参考答案及共享解析
共享解析来源为网络权威资源、GMAT高分考生等； 如有疑问，欢迎在评论区提问与讨论
本题耗时：
已选答案：
正确答案：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Geometry Triangles; Perimeter
Determine the perimeter of ΔPQR by determining PQ + QR + PR.
It is given that PT = 2. Since ΔPTQ is a 45°−45°−90° triangle, it follows that QT = 2 and PQ =
. Since ΔQTR is a 30°−60°−90° triangle and QT = 2, it follows that QR = 4 and TR = 
. PT + TR = PR, so PR, QR, and PQ are known and the perimeter of ΔPQR can be determined; SUFFICIENT.
It is given that RS = 
, but no information is given to determine TS. If, for example, TS = 
, then ΔQTR is a 30°−60°−90° triangle with TS + SR = TR = 
. It follows that QT = 2 and QR = 4. Also, ΔPTQ is a 45°−45°−90° triangle with QT = 2. It follows that PT = 2 (hence PR = 2 + 
) and PQ = 
, so the perimeter of the triangle is 
+ 4 + (2 + 
). However, if TS = 
, then ΔQTR is a 30°−60°−90° triangle with TS + SR = TR = 
. It follows that QT = 3, and QR = 6. Also, ΔPTQ is a 45°−45°−90° triangle with QT = 3. It follows that PT = 3 (hence PR = 3 + 
) and PQ = 
, so the perimeter of the triangle is 
+ 6 + (3 + 
); NOT sufficient.
The correct answer is A;statement 1 alone is sufficient.
Determine the perimeter of ΔPQR by determining PQ + QR + PR.
It is given that PT = 2. Since ΔPTQ is a 45°−45°−90° triangle, it follows that QT = 2 and PQ =
. Since ΔQTR is a 30°−60°−90° triangle and QT = 2, it follows that QR = 4 and TR = . PT + TR = PR, so PR, QR, and PQ are known and the perimeter of ΔPQR can be determined; SUFFICIENT.
It is given that RS = , but no information is given to determine TS. If, for example, TS = , then ΔQTR is a 30°−60°−90° triangle with TS + SR = TR = . It follows that QT = 2 and QR = 4. Also, ΔPTQ is a 45°−45°−90° triangle with QT = 2. It follows that PT = 2 (hence PR = 2 + ) and PQ = , so the perimeter of the triangle is + 4 + (2 + ). However, if TS = , then ΔQTR is a 30°−60°−90° triangle with TS + SR = TR = . It follows that QT = 3, and QR = 6. Also, ΔPTQ is a 45°−45°−90° triangle with QT = 3. It follows that PT = 3 (hence PR = 3 + ) and PQ = , so the perimeter of the triangle is + 6 + (3 + ); NOT sufficient.The correct answer is A;statement 1 alone is sufficient.
加入收藏
在线答疑
题目来源
