Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition![](https://gmatclub.com/forum/download/file.php?id=22575)
In triangle ABC above, what is the length of side BC?
(1) Line segment AD has length 6.
(2) x = 36
Target question: What is the length of side BC? Statement 1: Line segment AD has length 6. BEFORE we deal with statement 1, let's see what information we can add to the diagram.
For example, since ∆BDC has 2 equal angles (of 2x°), we know that side BD = side BC:
![](https://i.imgur.com/koQ77me.png)
Next, since angles on a line add to 180°, and since ∠BDC = 2x°, we know that ∠ADB = (180 - 2x)°
![](https://i.imgur.com/Ssu5edS.png)
Now focus on ∆BAD
Since angles in a triangle add to 180°, we know that ∠ABD = x°
ASIDE: Notice that x° + x° + (180 - 2x)° = 180°
![](https://i.imgur.com/HMG30lu.png)
Now that we know ∆BAD has two equal angles (x° and x°), we know that side AD = side BD
This means AD = BD = BCStatement 1 tells us that AD = 6, which means
BC = 6The answer to the target question is
side BC has length 6Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x = 36Notice that our diagram doesn't any lengths.
We can SHRINK or ENLARGE the diagram and the angles remain the same.
However
the length of side BC changes.
![](https://i.imgur.com/2dsV99t.png)
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent