Lesson: Geometry Data Sufficiency Questions

Comment on Geometry Data Sufficiency Questions

Why shouldn't we estimate lengths and angles when most figures on the gmat are drawn to scale? Actually, it's a great idea to estimate lengths and angles if you cannot answer the question using traditional methods. Most books on the gmat tell you to do this.
gmat-admin's picture

There are 2 kinds of math questions on the GMAT: Problem Solving questions and Data Sufficiency questions. In a Problem Solving question, the diagram will be drawn to scale unless stated otherwise. In a Data Sufficiency question, the diagrams are not necessarily NOT drawn to scale.

In the other videos (e.g., https://www.gmatprepnow.com/module/gmat-geometry/video/885), we note that (at 0:50) one can use estimation for a Problem Solving question.

In the video above, we deal with strategies pertaining to Data Sufficiency geometry questions. Since the diagrams in Data Sufficiency questions are not necessarily NOT drawn to scale, we advise you to avoid estimation.

At 5:04, the statement looked sufficient. We can measure AE and EC by the pythagorean with 45:45:90 triangle measure. By knowing AC is 10 AE and EC are 10√2.BE is half 10 which is 5. so we only have AB left from the triangle ABE. Apply the pythagorean again and you get AB. what do you think?
gmat-admin's picture

Your conclusion is based on having a 45-45-90 right triangle, but none of the information supports that there must be such a triangle. If you examine the video at 4:28 and at 4:51, you'll see that we can freely change the angles in diagram. So, we can't be certain of any 45-45-90 right triangles.

Hi Brent,

First of All i would like to Thank you for these videos. Your website is definitely an excellent resource for preparing for GMAT. Thank you once again.

Coming to my doubt pertaining to this video.
In the last rectangle example,You have concluded that "the statements force the diagram into one possible shape and thus there will be only one value of AB" and thus both the statements are sufficient.
Agreed, Now I have two questions,
1) suppose instead of X = 30, if its given that "0 < x < 90". Can we still conclude that both the statements are Sufficient. Or since there will be different soltutions for every different value of x we cant conclude that.
2) If by chance this question is asked in Problem solving section, how to find the value of AB?
gmat-admin's picture

Great questions!
1) The target question asks for the length of AB. So, unless we can answer that question with one (and only one) numerical value, the statement is not sufficient. So, if statement 1 were 0 < x < 90, that statement would be insufficient.

2) If combine the statements, we see that angle BAE = 60 degrees. This means angle BEA = 30 degrees.
So, triangle BAE is a 30-60-90 right triangles. This is a special kind of right triangle. To learn more about it, see https://www.gmatprepnow.com/module/gmat-geometry/video/870).
We also know that side BE (the side opposite the 60-degree angle) has length 5.
In the "base" 30-60-90 right triangle, the side opposite the 60-degree angle) has length root3
So, we can see that triangle BAE is 5/root3 times bigger than the "base" 30-60-90 right triangle.

In the "base" 30-60-90 right triangle, the side opposite the 30-degree angle has length 1.
In our diagram, side AB is opposite the 30-degree angle.
We already determined that triangle BAE is 5/root3 times bigger than the "base" 30-60-90 right triangle.
So, side AB = (5/root3)(1) = 5/root3

Thank you.


just a question regarding the triangle.

Are you sure that we can conclude C when the value we are looking for is fixed ?

I mean the question is what is the length of BA and not whether there is only one possible solution ?

I mean of course we could figure it out since we are dealing with 2 30°-60°-90° triangles and therefore BA should be 5*root of 3

But if we can choose C by simply saying there is only one possible value than this would make it easier =)

hope its clear
gmat-admin's picture

Hi David,

You're referring to the question that starts at 2:55 in the video.

"I mean the question is what is the length of BA and not whether there is only one possible solution?"

When it comes to Data Sufficiency, those two questions are the same. We might combine them to ask "Is there only one answer to the question "What is the length of BA?"

Think of it this way. Once we know that the combined statements LOCK the figure in place, we COULD just draw a super precise version of the diagram and then just measure it with a super precise ruler. So, even without employing any knowledge of 30-60-90 right triangles, we COULD still answer the target question with certainty.

Does that help?

The explanation is great, however, it don't think it is solvable in 2 mins. What is the faster method of evaluating a problem like this. Or what would be some tricks to recognize the key points faster..say rules of thumb

gmat-admin's picture

If you're referring to the question that starts at 2:55 in the video, I think the question is very solvable in under 2 minutes. The "trick" is to avoid performing lengthy calculations whenever possible.

Hi Brent,
In fact your explanation is great, thank you for the amazing input you put.
Just wondering about some possible typos in your answer here:
1- Since we cannot answer the target question with certainty, statement 1 is SUFFICIENT
2- Since we cannot answer the target question with certainty, statement 2 is SUFFICIENT
I think you meant to say INSUFFICIENT in both statements.

"Since we can" instead of "Since we can not" in the following statement:
Since we can not answer the target question with certainty, the combined statements are SUFFICIENT

Unless I am missing something.
Please correct me if I am mistaken.
gmat-admin's picture

Question link: http://www.beatthegmat.com/is-there-a-simpler-way-to-solve-this-question...

Thanks for the heads up! I have edited my response.


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