Question 248 Data Sufficiency 2018 GMAT Quantitative Review
Question 248 Data Sufficiency 2018 GMAT Quantitative Review
Video explanation[PQID: DS02940]: What is the area of rectangular region R? Each diagonal…
Comments
Tom Walkersays
I used the same logic as you, but for the combination I just visualized a 3:4:5 triangle. Knowing that the perimeter is 14 is not enough to solve the question (for the reasons you stated), but when we add the known hypotenuse of 5, we know that only a 3:4:5 triangle can meet both conditions.
It so happens that the GMAT writers mostly use familiar triangles. What students need to make sure is that they can also deal with situations where the solution is not necessarily one of the familiar triangles. For example, in this question, I could change statement 1 to: Each diagonal of R has length $9$, and statement 2 to: The perimeter of R is $20$. In this case, the answer would still remain D, but the corresponding right triangle is not one of the “nice” right triangles.
I used the same logic as you, but for the combination I just visualized a 3:4:5 triangle. Knowing that the perimeter is 14 is not enough to solve the question (for the reasons you stated), but when we add the known hypotenuse of 5, we know that only a 3:4:5 triangle can meet both conditions.
It so happens that the GMAT writers mostly use familiar triangles. What students need to make sure is that they can also deal with situations where the solution is not necessarily one of the familiar triangles. For example, in this question, I could change statement 1 to: Each diagonal of R has length $9$, and statement 2 to: The perimeter of R is $20$. In this case, the answer would still remain D, but the corresponding right triangle is not one of the “nice” right triangles.