In triangle ABC (attached), what is the length of BC?
1) Line segment AD has length 6
2) x=36
Thank you,
Prerna
1) Line segment AD has length 6
2) x=36
Thank you,
Prerna
- Attachments
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Cheers,
Brent
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Another DS problem
Source: Beat The GMAT — Data Sufficiency |
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Brent@GMATPrepNow
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Hi prernamalhotra,
Brent has already explained the "math" behind this question, so I won't rehash that here. Instead, I'll show you a quick way to figure out that the "left" triangle is isosceles: TEST VALUES....
Since the variable X shows up in both triangles, the angles will relate to one another - you just have to figure out HOW they relate.
If X = 10, then 2X = 20 and the angle "next to" 2X = 160. So, the third angle in the "left" triangle is 10; we have a 10/10/160, which is ISOSCELES.
If X = 20, then 2X = 40 and the angle "next to" 2X = 140. So, the third angle in the "left" triangle is 20; we have a 20/20/140, which is ISOSCELES.
IF X = 25, then 2X = 50 and the angle "next to" 2X = 130. So, the third angle in the "left" triangle is 25; we have a 25/25/130, which is ISOSCELES.
This proves a pattern. Whatever we pick for X, we end up with an ISOSCELES triangle.
With this information, it becomes really easy to deal with Fact 1 (you can point to all of the Isosceles triangle sides - they all equal 6) and Fact 2 (it has no information on the lengths of sides, so it can't be enough to answer the question).
You can TEST VALUES in may questions to discover patterns and get the correct answer, so keep it in mind when you see variables in a prompt.
GMAT assassins aren't born, they're made,
Rich
Brent has already explained the "math" behind this question, so I won't rehash that here. Instead, I'll show you a quick way to figure out that the "left" triangle is isosceles: TEST VALUES....
Since the variable X shows up in both triangles, the angles will relate to one another - you just have to figure out HOW they relate.
If X = 10, then 2X = 20 and the angle "next to" 2X = 160. So, the third angle in the "left" triangle is 10; we have a 10/10/160, which is ISOSCELES.
If X = 20, then 2X = 40 and the angle "next to" 2X = 140. So, the third angle in the "left" triangle is 20; we have a 20/20/140, which is ISOSCELES.
IF X = 25, then 2X = 50 and the angle "next to" 2X = 130. So, the third angle in the "left" triangle is 25; we have a 25/25/130, which is ISOSCELES.
This proves a pattern. Whatever we pick for X, we end up with an ISOSCELES triangle.
With this information, it becomes really easy to deal with Fact 1 (you can point to all of the Isosceles triangle sides - they all equal 6) and Fact 2 (it has no information on the lengths of sides, so it can't be enough to answer the question).
You can TEST VALUES in may questions to discover patterns and get the correct answer, so keep it in mind when you see variables in a prompt.
GMAT assassins aren't born, they're made,
Rich
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To determine how the angles affect each other, PLUG IN FOR THE ANGLES.
Be sure to satisfy both the rules of geometry and the constraints in the question stem.
The figures above show two valid combinations of angles.
In each case, AD = BD = BC.
Question rephrased: What is the length of AD or BD?
Statement 1: AD = 6.
SUFFICIENT.
Statement 2: x=36.
No information about the any of the lengths.
INSUFFICIENT.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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theCodeToGMAT
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As a general rule with DS, you should REPHRASE the question as much as possible. The other experts have taken you through the proof, so I won't repeat that. I just want to emphasize that when it comes to geometry DS, rephrasing is particularly difficult. The GMAT will try to trick you into thinking that you need information you already have.
If you start plugging the statement information into the diagram to begin with, you may think that you need the angle information from statement 1. You must INFER EVERYTHING from the diagram before you look at the statements to avoid these traps.
If you start plugging the statement information into the diagram to begin with, you may think that you need the angle information from statement 1. You must INFER EVERYTHING from the diagram before you look at the statements to avoid these traps.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
