I got the answer as C.

From Statement 1: you can figure out that x=30, 2x=60 and the remaining angle (<ADC) must be 90. You can also figure out that the smaller triangle (DBC) is 30-30-120 because BC=BD. Due to this, you can also figure out that the other triangle is an equilateral triangle (triangle ADB). You get that from 90-30 leaves 60 and since you know the angle DAB is 60, the remaining angle must be 60.

However, there are no numbers given, so you cant figure out the length of BC.

Statement 2: Simply gives you the length of AD and you cannot figure out any of the angles (even though it appears ADC is 90, it doesn't have to be.

Putting both statements together you can figure out that AD=DB=AB and therefore also equals BC.

Hope that made sense.

A quick way to think about most geometry question is to access 2 things: angles and lengths.

If the question asks for exact length, then you must be provided with some baseline length. Statement 1 is obviously not sufficient since it doesn't provide length.

Statement 2 doesn't provide enough about the angles, since all you learn is that the bottom triangle is iscoles. You are not told whether the entire figure is a right triangle yet, so it's insufficient.

The answer is B.

Explanation.

Since BC = BD, this gives us two x's in the lower section triangle. Then 180-2x = the third angle within the lower section triangle.

Now to determine the top section triangle it should be 2x+180-2x. This is because the angle must equal 180. Knowing this we have 2 2x's and therefore have two equal sides. Knowing one of those sides gives us the answer. This is why it is B.

chris6 wrote:The answer is B.

Explanation.

Since BC = BD, this gives us two x's in the lower section triangle. Then 180-2x = the third angle within the lower section triangle.

Now to determine the top section triangle it should be 2x+180-2x. This is because the angle must equal 180. Knowing this we have 2 2x's and therefore have two equal sides. Knowing one of those sides gives us the answer. This is why it is B.

The part I bolded above does not make sense to me. Please clarify. I understand how you got 180-2x as the angle of DBC, but you cannot figure out any of the numbers without statement 1. (at least to my simple mind)

Anyone else have clarification?

i agree with chris ..answer should be B

2010gmat wrote:i agree with chris ..answer should be B

any chance you want to give an explanation?

Can we get an instructor or moderator to comment?

a. --> tells us nothin...simply knowing the measures of angles wont fetch the length of line hence insuff

b. bd = bc --> <dbc = <dcb = x

<adb = exterior angle = two int opp angles = x + x = 2x

<adb = <bad = 2x --> bd = ad

but bd = bc

ad = bc

= 1

hnce suff

2010gmat wrote:a. --> tells us nothin...simply knowing the measures of angles wont fetch the length of line hence insuff

b. bd = bc --> <dbc = <dcb = x

<adb = exterior angle = two int opp angles = x + x = 2x

<adb = <bad = 2x --> bd = ad

but bd = bc

ad = bc

= 1

hnce suff

Thats a good explanation! Thanks.