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

Hello! Thanks for the very good video and explanation. I want to understand how you had concluded E to be the midpoint of BD, making BE = 5. Appreciate the help!
gmat-admin's picture

We know that ∠ECD = ∠BAE = 60°
Also, EC = EA
And AB = DC
So, we can conclude that ∆BAE and ∆DCE are identical, which means EB = ED

Does that help?


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.


Hi Brent. How do you concluded that the side BD should intersect the point E if we cannot assure that the figure is not drawn to scale? I think I misunderstood or overlooked something.
gmat-admin's picture

Good question!

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

You are right to say that the geometrical figures in Data Sufficiency questions are not necessarily drawn to scale. However, there are some assumptions we can make. For example, if a point (like point E) APPEARS to be on a line (like line BD), then we can ASSUME that the point is on the line.

For more on what can and cannot be assumed (regarding geometrical figures on the GMAT), watch this video: https://www.gmatprepnow.com/module/gmat-geometry/video/863


I appreciate it a lot.

gmat-admin's picture

gmat-admin - July 22, 2018
Sure, just email me at info@gmatprepnow.com

Great videos. Thanks Brent.

hi brent thumbs up for the great videos..i have a doubt in the second question. you say that when we can lock down the figure the answer will be c ...what if x=70degrees..
gmat-admin's picture

Thanks for the kind words. I'm delighted to hear you like the videos!

If x = 70, then ∠EAC = ∠ECA = 70°
This information will still "lock in" the length of AB.
So, the correct answer would still be C.

For the second link (where the area of the triangle is half the area of the rectangle) can we generalize that WHEN a triangle and a rectangle have the same base and height the
A(triangle) = 1/2 A(rectangle)
gmat-admin's picture

Question link: https://gmatclub.com/forum/what-is-the-area-of-the-shaded-region-in-the-...

Yes, if a triangle and rectangle have the same base and height, then the area of the triangle will be 1/2 the area of the rectangle.

In the second link from the bottom we are asked to find x + y. But following the concept of locking a particular length or angle I am not sure how we got the correct choice.

In the solution provided, when we combine the two statements, Line 1 and Line 2 are fixed. BUT isn't the horizontal line that creates angle X and Y on line 1 and Line 2 yet free to move?

I hope I am being clear with my doubt. Would you like me to post the doubt on the club (as a follow up to your post)?
gmat-admin's picture

Question link: https://gmatclub.com/forum/what-is-the-value-of-x-y-in-the-figure-above-...

You're absolutely right to say that that line it's not fixed.
This means the INDIVIDUAL angles, x and y, can have infinitely many values, which also means the INDIVIDUAL angles j and k will also have infinitely many values.
However, the SUM of angles j and k must be 220 (since angles in a quadrilateral always add to 360°)
If the SUM of angles j and k = 220, we can be certain that the SUM of angles x and y is 140°

Does that help?

Yes, by the quadrilateral property I was able to understand this sum BUT I tried the concept of "locking" the image and seeing if I could solve the sum. Don't you think for this specific sum we cannot completely rely on this concept? I found this approach quite practical but I don't believe we can use it for every sum? can we? Because when I thought of using this approach I chose option E since I thought "the horizontal line is not fixed"
gmat-admin's picture

The strategy doesn't work with every geometry question. This is why I preface my solutions by saying that "For geometry Data Sufficiency questions, we’re TYPICALLY checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement."

The strategy usually works when we're trying to find an INDIVIDUAL angle or length. That said, the strategy still works with this question.
Once we know that the combined statements "lock" in 2 of the 4 angles in the quadrilateral, the SUM of the two remaining angles is definitely locked in to be 220°, which means the sum of angles x and y is locked in to be 140°

So because the first example has no side lengths at all in it it means that it's answer E (even when the shape is locked in) but with the second example, the answer is C because the shape is locked in and we have at least one specific length value. Is that correct? Thanks Brent!
gmat-admin's picture

That's 100% correct.

What a revolutionary way of teaching. Thanks Brent.
One question at video 6:20 for statement 2, Can't 30° force point E fixed on BD, therefore making statement 2 sufficiecnt? Can't really see how AC = 10 here make any effect in order for it to be C ? Have I missed something here? Thanks Brent
gmat-admin's picture

You're correct to say that statement 2 locks in angle x, but if we don't know any of the lengths in the diagram, there's no way to find the length of side AB.
For example, if side AC has a length of 1cm, the length of side AB will be quite small.
On the other hand, if side AC has a length of 10,000 km, the length of side AB will be quite very large.

Does that help?

Crystal clear now and thanks Brent for the great clarification.

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