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Last Updated on September 27, 2023
GMAT students often ask, “Are geometry figures drawn to scale on the GMAT?” or “What can I assume is true on GMAT geometry diagrams?”
Those are great questions because, when we’re presented with a geometrical figure on the GMAT, we must be clear about what the “rules of the game” are and what can and cannot be assumed or inferred based on the figure.
In this article, we’ll cover everything you need to know regarding GMAT geometry figures and what you can assume is true about GMAT diagrams.
Let’s begin with a discussion of what is true about ALL geometric figures on the GMAT.
- Some Basic Facts About All Geometry Diagrams on the GMAT
- Fact 1: Any Information Provided in the Question Stem Will Be Reflected in the Shape
- Fact 2: If a Figure Is Called a Particular Shape, the Figure Has All of the Properties of That Shape
- Fact 3: All Lines That Appear to Be Straight Are Assumed to Be Straight
- Fact 4: We Can’t Make Assumptions About Angle Measurements
- Fact 5: Points Drawn on a Straight Line Are Collinear
- Geometric Figures in GMAT Problem Solving Questions
- Are Geometrical Figures Drawn to Scale in GMAT Data Sufficiency Questions?
- Some Common Assumptions We Can’t Make About Geometric Figures in DS Questions
- Don’t Assume That Shapes That Appear to be Squares are Squares
- Don’t Assume That Lines That Appear Parallel Are Parallel
- Don’t Assume That Two Lines That Look Perpendicular Are Perpendicular
- A Point Appearing at the Center of a Circle Might Not Be at the Center
- Triangles That Appear to Be Right Triangles May Not Actually Have a Right Angle
Some Basic Facts About All Geometry Diagrams on the GMAT
We’ll soon see that many aspects of what we can and can’t assume about geometric figures on the GMAT differ depending on whether we’re working on a Problem Solving (PS) question or a Data Sufficiency (DS) question.
Many aspects of what we can and can’t assume about geometric figures on the GMAT differ depending on whether we’re working on a Problem Solving (PS) question or a Data Sufficiency (DS) question.
However, there are some basic facts about geometric figures that are true in BOTH Problem Solving and Data Sufficiency questions. Let’s discuss these facts.
Fact 1: Any Information Provided in the Question Stem Will Be Reflected in the Shape
In a GMAT PS or DS question, any information provided in the question stem will be reflected in the shape accompanying the question.
KEY FACT:
In a GMAT PS or DS question, any information provided in the question stem will be reflected in the shape accompanying the question.
For example, if we’re given triangle QPR and we’re told that angle QPR is a right angle, we can assume that that information is reflected in the diagram. In other words, the shape accompanying the question will have the right angle symbol drawn on the triangle, as we see here:
Fact 2: If a Figure Is Called a Particular Shape, the Figure Has All of the Properties of That Shape
In a GMAT PS or DS question, if a figure is called a particular shape, then the figure has all of the properties of that shape.
KEY FACT:
In a GMAT PS or DS question, if a figure is named, the figure has all of the properties of that shape.
For example, if we’re told that a figure is a square, we can be sure that the shape is a square and thus has all of the properties of a square.
For example:
In a DS or PS question that said, “What is the perimeter of the square above?” we could be sure that the shape is a square and has all properties of a square.
Fact 3: All Lines That Appear to Be Straight Are Assumed to Be Straight
In a GMAT PS or DS question, all lines and line segments that appear to be straight are assumed to be straight. In other words, if in a figure we see a straight line, the line is straight; it will never be the case that the line is secretly curved. Additionally, if we ever encounter lines that look slightly jagged because they are pixelated on a computer monitor, we can assume that those lines are straight as well.
KEY FACT:
In a GMAT PS or DS question, all lines that appear to be straight are assumed to be straight.
For example, we can assume that the following line is straight:
Because all lines are assumed to be straight in the following diagram, we can assume that x + y = 180.
As a result of our being able to assume that all lines are straight, when presented with the following situation, we can conclude that angle x is 40 degrees.
Fact 4: We Can’t Make Assumptions About Angle Measurements
In GMAT PS and DS questions, we can’t make assumptions about angle measurements based on only how those angles look.
KEY FACT:
In GMAT PS and DS questions, we can’t make assumptions about angle measurements based only on how those angles look.
For example, in the following diagram, we can’t conclude that angle x is 90 degrees because we don’t have any information that the two lines are perpendicular.
Fact 5: Points Drawn on a Straight Line Are Collinear
In both GMAT PS and DS questions, points drawn on a straight line are collinear.
KEY FACT:
In both GMAT PS and DS questions, points drawn on a straight line are collinear.
For example, if we see a straight line, and points w, x, y, and z all exist on the line, then we can be sure that the points actually are on the line.
Let’s now talk in more detail about geometric figures in Problem Solving questions.
Geometric Figures in GMAT Problem Solving Questions
When a geometric figure appears in a GMAT Problem Solving question, we can assume that the figure is drawn to scale, unless we’re told otherwise. In other words, unless we’re told, “figure NOT drawn to scale” or something similar, then we can assume that the figure IS drawn to scale.
KEY FACT:
When a geometric figure appears in a Problem Solving question, we can assume that the figure is drawn to scale, unless we’re told otherwise.
Take a look at the directions that GMAC provides for Problem Solving questions.
“All figures accompanying problem-solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.”
Most of the figures accompanying Problem Solving questions are drawn to scale. What does “drawn to scale” really mean? Drawn to scale means that a figure will be helpful when we’re visually approximating.
Now, the only time that a figure in a PS question is not drawn to scale is when we’re told, “Diagram Not Necessarily to Scale,” or given some similar warning. If we don’t see a warning, then we can be sure that the shape is drawn to scale, and we can make accurate decisions about the shape.
When the warning appears, it’s important not to draw any conclusions about the shape (without additional factual information) regardless of how it appears.
Let’s now discuss the fact that, even when geometrical figures in Problem Solving questions are NOT drawn to scale, those figures can’t be overtly deceptive.
Diagrams Not Drawn to Scale in Problem Solving Questions Can’t Be Overtly Deceptive
Even when we’re told that a diagram in a Problem Solving question is not drawn to scale, it’s helpful to remember that diagrams can’t be overtly deceptive.
KEY FACT:
Even when we’re told that a diagram in a Problem Solving question is not drawn to scale, the diagram cannot be overtly deceptive.
For example:
- We can’t be provided with a figure with four lines that looks like a square, only later to find out that — sorry — the figure is actually a triangle. If the figure has four lines and looks like a square, it’s a four-sided figure (but not necessarily a square).
- We can’t be provided with a shape that looks like a triangle but later be told — sorry — it’s actually a circle.
- If a figure shows two lines intersecting, they intersect. We can’t be later told that — sorry — the lines don’t really intersect. Now, we cannot assume specifics about the intersection. For example, we wouldn’t be able to conclude that the lines are perpendicular or that the lines intersect at a 45-degree angle. However, we would know that the lines do intersect.
- If one shape is inside of another shape, we can’t be later told that — sorry — the shape that is drawn inside is actually not inside. If a shape appears inside another, it’s inside.
- All angles have a measure greater than zero. In other words, we can’t be presented with what looks by all conventions to be an angle only to later be told that the angle was not actually an angle.
- If we’re presented with five points on a line, we can’t later be told that — sorry — there are actually four points. If we see five points, there are five points.
So, as we see, there are some “basic rules of fairness and civility” on the part of the test-writers that apply regardless of whether a diagram is drawn to scale or not. Each of these basic rules of fairness and civility also applies to all figures in DS questions, which we’ll soon discuss.
KEY FACT:
In both Problem Solving and Data Sufficiency questions, there are some “basic rules of fairness and civility” whether a diagram is drawn to scale or not. Be sure to understand these rules.
Let’s now discuss whether geometrical figures are drawn to scale in GMAT Data Sufficiency questions.
Are Geometrical Figures Drawn to Scale in GMAT Data Sufficiency Questions?
In Data Sufficiency questions, figures are not drawn to scale, and a figure reflects only the information provided in the question stem. The figure will not necessarily reflect the information provided in the statements.
KEY FACT:
In Data Sufficiency questions, figures are not drawn to scale, and a figure reflects only the information provided in the question stem. The figure will not necessarily reflect the information provided in the statements.
Let’s look at the instructions given to us 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). Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc. exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.”
So, for example, if a Data Sufficiency question stem tells us that a figure is a rectangle, then we can be sure that the figure is a rectangle. However, just seeing a shape that looks like a rectangle does not allow us to conclude that the shape is, in fact, a rectangle.
On the other hand, if either statement (1) or statement (2) tells us that two angles are supplementary (add to 180 degrees), for example, that information won’t necessarily be reflected in the figure.
Now, it’s important to understand that the reason a Data Sufficiency figure is not drawn to scale is not that the figure is meant to be deceptive. Rather, it is simply impossible to draw a Data Sufficiency diagram to scale.
Remember that our job in a Data Sufficiency question is to determine whether we have enough information to answer the question. Therefore, it only makes sense that, when we begin a DS question, before we’ve been provided with the statements, there will be multiple ways in which the figure can be drawn. In other words, multiple possibilities exist. Of course, these multiple possibilities are the essence of DS questions. Our job is to determine whether, by using statements (1) and (2), we can narrow the possibilities down to only one.
In a DS Question, a Figure Will Always Be a True Representation of at Least One Possible Situation
In a Data Sufficiency question, it’s helpful to remember that a figure provided will always be a true (drawn-to-scale) representation of at least one possible situation.
For example, let’s take a DS diagram that shows two line segments — XY and BC — that appear to be parallel, and one segment — XY — as drawn, is clearly longer than the other. In such a case, we can’t conclude from the figure alone that XY must be longer than BC. However, we can be sure from the figure alone that, given the information in the question stem, at least one situation exists in which XY is longer than BC.
Here are two more examples based on this idea:
Example DS Question: In the triangle above, is a2 + b2 = c2?
We see that the diagram above represents one possible depiction of a given triangle. If we determine that the triangle is in fact a right triangle, then the diagram is pretty accurate as it stands. However, if the triangle is NOT a right triangle, then the triangle could be quite a different-looking triangle.
Another example:
Example DS Question: If lines x and y are parallel and lines m and n are parallel, is the measure of angle b greater than the measure of angle a?
In the given diagram, we see that angle a appears larger than angle b, providing one possible scenario related to the question asked. However, it also may be possible, depending on the information provided in the statements, that angle a is actually smaller than angle b, meaning of course that the diagram provided is not an exact representation of the indicated scenario. Once again, this situation is totally OK, because one DS diagram cannot portray all possible scenarios.
Let’s see how the diagram would look if we wanted to illustrate that angle a is smaller than angle b.
Let’s now discuss some common incorrect assumptions that people make about geometric figures in Data Sufficiency questions.
Some Common Assumptions We Can’t Make About Geometric Figures in DS Questions
Although we know that geometric figures found in Data Sufficiency questions are quite possibly not drawn to scale, people sometimes get these DS questions wrong simply because they, without realizing it, make assumptions that they’re not able to make.
To help ensure that you don’t make such assumptions when answering Data Sufficiency questions, let’s look at some of these bad assumptions.
Don’t Assume that Shapes That Appear to Be Squares Are Squares
In a Data Sufficiency question, the only way to be sure that a four-sided figure is a square is to have conclusive evidence that the shape is actually a square.
KEY FACT:
In a Data Sufficiency question, the only way to be sure that a four-sided figure is a square is to have conclusive evidence that the shape is actually a square.
For example, consider the following two shapes that appear to consist of four equal sides and four right angles. Are both shapes squares? They appear to be, right?
Actually, they are not both squares. The shape on the left has four equal sides and all 90-degree angles, so it’s a square. In the shape on the right, although it has four 90-degree angles and appears to have all equal sides, sides EF and GH are greater than sides EG and FH.
Don’t Assume That Lines That Appear Parallel Are Parallel
In a Data Sufficiency question, the only way to be sure that lines that appear parallel actually are parallel is to have conclusive evidence that those lines are parallel.
KEY FACT:
In a Data Sufficiency question, the only way to be sure that lines that appear parallel actually are parallel is to have conclusive evidence that those lines are parallel.
For example, consider the following geometric figure. Are the lines parallel? Your eyes may be telling you that they are, but the truth is that the lines are very close to being parallel, but they are not parallel.
If we were presented with the figure above in a Data Sufficiency question, we could not conclude that the lines are parallel unless we were provided with factual information telling us that they are.
Don’t Assume That Two Lines That Look Perpendicular Are Perpendicular
In a Data Sufficiency question, if two lines appear to be perpendicular, we cannot conclude from the figure alone that the lines are in fact perpendicular.
KEY FACT:
In a Data Sufficiency question, the fact that two lines appear to be perpendicular does not allow us to conclude from the figure alone that the lines are actually perpendicular.
Consider the following diagram. Are the lines perpendicular?
The lines are close to being perpendicular, but they are not perpendicular. We’d require factual information to conclude that the lines are perpendicular.
A Point Appearing at the Center of a Circle Might Not Be at the Center
In a Data Sufficiency question, when presented with a circle, we cannot assume that a point that appears to be located at the center of the circle actually is located at the center of the circle.
KEY FACT:
In a Data Sufficiency question, when presented with a circle, we cannot assume that a point that appears to be located at the center of the circle actually is located at the center. of the circle.
For example, refer to the diagram below, with point O near the center of the circle.
We’d require factual information to conclude point O is located in the center of the circle.
Triangles That Appear to Be Right Triangles May Not Actually Have a Right Angle
In a Data Sufficiency question, although a triangle may appear to have a right angle, unless we have proof that the triangle contains a right angle, we can’t assume that the triangle is a right triangle.
KEY FACT:
In a Data Sufficiency question, although a triangle may appear to have a right angle, unless we have proof that the triangle contains a right angle, we can’t assume that the triangle is a right triangle.
Refer to triangle ABC below. Although the triangle may appear to be a right triangle, angle BAC is actually slightly greater than 90 degrees.
You now have all the information you need about whether geometry figures are drawn to scale on the GMAT. Next, check out this helpful article on terminating and repeating decimals on the GMAT.
