In triangle \(ABC\) above, what is the length of side \(BC?\)

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In triangle \(ABC\) above, what is the length of side \(BC?\)

(1) Line segment \(AD\) has length \(6.\)
(2) \(x = 36\)

Answer: A

Source: Official Guide

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Vincen wrote:
Sat Nov 27, 2021 4:48 am
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In triangle \(ABC\) above, what is the length of side \(BC?\)

(1) Line segment \(AD\) has length \(6.\)
(2) \(x = 36\)

Answer: A

Source: Official Guide
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:
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Next, since angles on a line add to 180°, and since ∠BDC = 2x°, we know that ∠ADB = (180 - 2x)°
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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°
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Now that we know ∆BAD has two equal angles (x° and x°), we know that side AD = side BD
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This means AD = BD = BC

Statement 1 tells us that AD = 6, which means BC = 6
The answer to the target question is side BC has length 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 36
Notice 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.
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Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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