Practice Test #3, Quant Section 2, Question 1

[jakehunter46]

The area of triangle ABD is larger than the area of triangle BCD.

Quantity A
length of AD

Quantity B
length of CD

(Not sure if the image pasted above) Nonetheless, I don't believe there is enough information here to solve. The solution argues that because the heights are equal, (1/2)(AB)(H)>(1/2)(BC)(H). Which leaves AB>BC, which I understand. But who is to say the the heights (H) are equal? In order for the height to be equal, it must be given that the larger figure, (ADC) is indeed a triangle. It looks like a triangle, but we need to be told that. We are told nothing about angle DBC, which is drawn to look like 90 degrees, but if it were to be, say 100 degrees, then the heights aren't equal, and CD could be greater than AD.

Thoughts?

[jakehunter46]

x

[nareshchowdary28]

As the area of ABD > area of BCD it is clearly indicating that

1/2 * AB*BD > 1/2 *BC*BD
so
AB> BC
so if AB>BC definitely AD > CD

and more over if AB > BC and B is right angle the hypotenuse of ABD is > hypotenuse of BCD

it is clearly quantity A is bigger.

Tom, Please correct me if anything wrong in my understanding.

[jakehunter46]

None of that is in dispute if the larger figure (ADC) is a triangle. But that has to be given, and it isn't. All that is given is the area of triangle ADB is greater than triangle BCD. As I see it, the picture can be redrawn as such:


Here, the area of triangle ADB is still larger than triangle BCD but DC is longer than AD. If we are given that the larger figure ADC is a triangle, then we know AC is a straight line, and AD>CD. But not knowing the parameters of the larger figure allows us to manipulate it in compliance with what's given. I still think this has to be D, not enough information to solve.

[jgabry]

hey jake,

even though you can't assume objects are drawn to scale on the gre, you can assume that lines drawn as straight are straight. this is actually mentioned in the gre official math conventions (although it took me a while to even discover that the document even existed).

if you go to this link:

http://www.ets.org/s/gre/pdf/gre_math_conventions.pdf

and scroll to page 4 you will see mentioned that "you should assume that lines shown as straight are actually straight". there is also a sample geometric figure along with a list of assumptions that can be made, including one about 3 points assumed to lie on a straight line and forming the base of a triangle.

hope that helps!

[tommywallach]

Hey Jake,

The whole discussion here has been great, and jgabry is absolutely right. There are lots of things you shouldn't trust, but lines, weirdly, are not one of them. I agree with you that this is annoying (why lines, but not angles?), but it's the way of the GRE-world. Blame ETS. : )

-t