A Guide to GMAT Geometry

 
 
 

Most of the students when they hear the word “Geometry”, they think of trigonometry, they think about theorems etc. But in GMAT it’s quite different.

 
 
In this article, let’s discuss about what is tested in GMAT geometry and what could be the best preparation strategy for GMAT Geometry?
 
Even though it carries only approximately 3 to 6 questions in GMAT, it has its own importance in GMAT.For these 3- 6 questions, you are expected to know the basic formulae and shapes. GMAT also tests your visualizing skills.
 
 
Below mentioned three things are must for a GMAT student who wants to fair really well in Geometry:
 
1. Draw for the questions even if the figures are not provided. If the figures are provided then re-draw the figure.
 
2. Know the basic shapes like triangle, quadrilaterals, circles, rectangular solids and basic properties of straight lines in co-ordinate geometry really well.
 
3. Do not make any assumption unless or otherwise it is specified in the question.
 

 
Let’s understand what GMAT has to say about the figures in Geometry.
 
GMAT Directions for Geometry (GMAC™)
 
Figures:
 
1. For problem solving questions, figures are drawn as accurately as possible. Exceptions will be clearly noted.
 
2. For data sufficiency questions, figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
 
3. Lines shown as straight are straight, and lines that appear jagged are also straight.
 
4. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
 
5. All figures lie in a plane unless otherwise indicated.
 
So, how should a student approach a question on Geometry?
 
In GMAT particularly for a DS questions, one should not solve a question based on the diagram or figure given in the question. Try to draw your own figure based out of the information provided in the question and the statements.
 
For a PS question, mostly the diagram will map to the question provided unless stated otherwise.
That is, they will give a note below a figure stating “Figure is not drawn to scale”, In that case one should be really careful about the diagram and try to redraw according to the information given to the question.
 
To just to give an example of this, take a look at the below question,
 
In the figure given, if PR is a line segment, what is the sum of the lengths of the curved paths from P to Q and from Q to R?
XQ = QY = 5 centimeters.
Every point on arc PQ is 5 centimeters from point X, and every point on arc QR is 5 centimeters from point Y.
 
 

Explanation:
 
Given is a figure that looks like two semi circles of equal areas with center X and center Y respectively. However we cannot assume any of this as we are not told this in the question.
Here anybody could easily fall for the diagram, and say X and Y are centers, which is what we have to be very careful and look at the question and the statements, and search for anything with suggests that X and Y are centers. Here statement II only suggest that X and Y are centers.
Statement I is insufficient: XQ=QY=5.
 
This would have been sufficient if we were given X and Y are the center of the circles. If they were centers then XQ and QY were radius of the circle and we could have calculated the length of the arc. However as we do not know if they are centers they could be any arbitrary points. Hence not sufficient.
 
 
Statement II is sufficient:
 
The meaning of the statement is that X and Y are the centers of the 2 semi circles each with radius of 5. We can calculate length of arc by 2* Pie* Radius.
Hence it is sufficient.
 
So the Answer is B.
 
 

Let’s look at another figure:

Here let’s say the question is ABCD is a quadrilateral and all sides are equal.
 
Here basic assumption students may end up doing is considering this is a square. Because all sides are equal and each angle looks like it is 90 degrees. But here one should be really careful about this.
 
It looks like each vertex angle is 90 degrees, does not mean that it is a square. If somewhere in the question if they have specified each vertex angle is 90 degrees then you can take the figure as a square otherwise not.
 
You have to seriously look for other information in the question. Because you cannot assume anything like angles and lengths based out of a diagram.
 
Tips for Co-ordinate Geometry:
 
Best part about GMAT co-ordinate geometry question is they test your visualizing skills in straight lines than the formulae. Very rarely they test curve like parabola. Even if they test curves you can still solve it by plugging in and drawing it out.
 
If you look at it, lines alone could easily have 20 odd formulae; one cannot be mugging up all these to do well in GMAT.
 
Just keep the following tips in mind while solving a co-ordinate geometry questions:
 
 
1. A student will be provided with a scratch pad during the exam which has grid lines. So make good use of this and draw x-y plane in the scratch pad and consider each small square as x and y units.
 
2. When finding the intercepts, slopes and distance try to use the grid lines to solve rather than formulae. Formulae would be handy only for easy questions but not for hard questions. You need to develop the skills of finding the distance, slope and intercepts using the x-y plane.
 
3. Use the answer choices, so that you can do some POE (Process of Elimination) when it comes to a hard question. That would save lot of time.
 
 
If you follow the above points while practicing the questions it would definitely help you in the actual GMAT exam.
 
To sum it up, GMAT geometry is the easiest topic one could expect. So don’t go about learning all the unnecessary formulae. That is definitely not going to help. Try to keep it simple. Practice as many questions keeping in mind the above points.
 
I hope this article helped you in understanding – how to take on GMAT geometry and shine through.

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