woohoo921 wrote:
CrackverbalGMAT wrote:
Solution:
In the triangles ABC1and DC2E, let the height be "h" in each of the triangles.
This height is "h" for both as the distance b/w C1 and AB = h = distance b/w C2 and DE.
The area = 1/2 (AB)*h for triangle ABC1 and 1/2 DE*h for triangle DC2E
So, we are being asked if 1/2 (AB)*h < 1/2 DE*h?
=> Is AB <DE ?
St(1):-The radius of Circle 1 is less than the radius of Circle 2.
The height being same we have 1/2(C1A)*h and 1/2 (C2D)*h as areas of the triangles.
C1A <C2D is given and thus answer to the question stem is yes.(Sufficient)
St(2):- AB<DE
This is exactly asked as a question. Thus (Sufficient) (option d)
Devmitra Sen(GMAT Quant Expert)
CrackverbalGMATHow can you assume that the heights are the same?
Hey
woohoo921,
Thanks for posting your query.
You’re missing a very important piece of information given in the question. This is common in questions with too much information but should not happen if you wish not to lose points to avoidable mistakes. 😊
Always read very carefully! For this question, let me help you:
READING THE QUESTION AGAIN: Below is the question stem of this DS question. I have bolded the part that I want you to focus on. Read and then try to infer what the bolded part could mean. Let’s go!
“The figure above shows Line L, Circle 1 with center at \(C_1\), and Circle 2 with center at \(C_2\). Line L intersects Circle 1 at points A and B, Line L intersects Circle 2 at points D and E, and points \(C_1\) and \(C_2\) are equidistant from line L. Is the area of Δ\(ABC_1\) less than the area of Δ\(DEC_2\)?” EXPLANATION: I hope you tried inferring on your own. Let me elaborate now -
- The bolded statement in the question is what you missed completely. We are given that points \(C_1\) and \(C_2\) are equidistant from line L. To understand the meaning of this, you first need to understand how the distance between a point and a line is calculated.
- Here’s the definition – the distance between a point and a line is equal to the length of the perpendicular drawn from the point to the line.
- In our question, this means that if we draw \(C_1M\) perpendicular to AB (M lying on AB), then \(C_1M\) is the distance between \(C_1\) and line L.
- Similarly, that if we draw \(C_2N\) perpendicular to DE (N lying on DE), then \(C_2N\) is the distance between \(C_2\) and line L.
- Per our given information (the bolded part), we have \(C_1M = C_2N\). -----------(1)
Now, note that \(C_1M\) and \(C_2N\) are precisely the
heights of triangles \(ABC_1\) and \(DEC_2\)! And hence, from (1), we get that the heights of these two triangles are equal.
And that’s it!
TAKEAWAYS - Read a question piece by piece and keep translating English to Math as you go.
- Keep making inferences as you gather more and more information while reading questions or solving them.
Hope this helps!
Best,
Shweta
Quant Product Creator,
e-GMAT _________________