You may find GMAT geometry to be a daunting subject. Then, when you hear there are rules – with exceptions! – about when figures are drawn to scale, you may want to throw up your hands and conclude that these questions are arbitrary complications designed to make our lives miserable.

Today we’ll see that the rules about geometry figures give us clues about how the questions work. They are like GMAT questions: once you understand them, they seem simple.

There is a popular maxim,

"Figures in problem solving questions will be drawn to scale unless otherwise noted, while figures in data sufficiency questions are not necessarily drawn to scale."

The maxim is mostly correct, but let’s look at the exact print from the test makers.

Let’s start with the directions for Data Sufficiency:

Data Sufficiency
Figures: A figure accompanying a data sufficiency problem will conform to the information given in the question but will not necessarily conform to the additional statements given in statements (1) and (2).

These instructions have the same gist as the maxim, but their wording is different. An example shows why:

In the figure above, if RU = 10 and ST= 6, is RS = 10?

(1) TU = 6

(2) SU is perpendicular to RT.

When you look at this diagram, you notice that it sure looks like RU = RS. But the whole point of the data sufficiency question type is that, initially, we don’t have enough information to decide whether RU = RS. It’s our job to examine the data statements and determine whether they give us enough information to say whether RU = RS, always, sometimes, or never.

It’s also part of how data sufficiency questions work that we are supposed to consider the data statements true only when we are considering them. When we look at Statement 1 all by itself, we consider it to be true. But when we are evaluating whether Statement 2 all by itself is sufficient, we don’t consider Statement 1 to be true.

What does that mean? In this question, it means that, when we first consider the figure and the question stem, we don’t know whether or not RT and SU are perpendicular. The figure may or may not be "drawn to scale." We have some information about it (that RU = 10), but we are also missing lots of information – again, that’s the point of Data Sufficiency. It’s almost like a figure in which some angles and lengths are fixed in place, whereas others could be flexed or stretched or bent, and the more information we get in Statements 1 and 2, the more we can pin down and finally determine what we need to know about the figure.

Now you can see why the rules about figures are the way they are for Data Sufficiency questions. The question may give us some information about a figure, and you’ll know those parts of the figure are "to scale," but the other relationships have to be inferred from the data we get, not from how the figure looks. (Although we are allowed to assume that things that look like lines are lines and that angles are greater than zero.)

In this case, the answer is (C).

As usual, the answer choices in Data Sufficiency give us clues. Consider this: when you have a geometry figure for a Data Sufficiency question and the answer is (E), you may have a situation in which it doesn’t even make sense to ask whether the figure has been "drawn to scale," because the dimensions of the figure may still be undefined (it could be drawn one way or another, so there is no scale to draw to).

Problem solving is an entirely different situation:

In the figure above, RS = ?

(A) 6

(B) 8

(C) 10

(D) 12

(E) 14

Here we have all the information we need to get to the answer: we just have to figure out how. Unlike the figure in the Data Sufficiency question, the figure in this Problem Solving question is defined. Problem Solving geometry questions generally contain complete information. This question is about one particular triangle – a "uniquely defined" figure. And for that reason, it makes sense that the figure would be drawn to scale.

Now the GMAC instructions for Problem Solving make sense:

Problem Solving
Figures: A figure accompanying a problem solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible. Exceptions will be clearly noted.

The figure is intended to help – the instructions even say so!

Hopefully these examples have removed the mystery from the rules about figures in geometry questions.

Summary:

Problem solving questions contain complete information to solve the question. Therefore figures are uniquely defined and drawn to scale.

Data sufficiency questions may contain incomplete information to solve the question. Therefore figures may not be uniquely defined and are "drawn to scale" only insofar as we know definite facts about them.

Once these ideas make sense, the exceptions do, too. If a problem solving question about a geometry figure includes an answer choice that states, "Cannot be determined from the information given," then the figure is likely to include an annotation, "Figure not drawn to scale." It doesn’t mean the figure is wildly misshapen; it’s just a statement about whether or not we have complete information.

Video 20 in a series of official excerpts from the Kaplan GMAT program. This video covers multiple figures in geometry. The instructor is Adel Hanash - over 500 students taught and counting.

The quantitative content for the GMAT is definable.  In the next few paragraphs, I’m going to outline what areas of skills you’ll need to be successful on the GMAT.  (Important caveat – these concepts below are the basics of what the GMAT is testing.  For advanced concepts and questions, the test makers have found unique ways of making these more difficult.)

Math Facility #1 – Arithmetic

While arithmetic is foundational in grade school (and a great deal of review for us), we have to ensure we study the fundamentals as well as the more advanced concepts.  The GMAT is testing the following abilities:

·  Manipulate fractions, decimals, and ratios (as well as the need to convert among the three)
·  Understand the properties of individual numbers and the concept of real numbers
·  Work with percentages
·  Calculate and manipulate exponents and roots
·  Understand and apply descriptive statistics (mean, median, mode, standard deviation)
·  Understand and apply properties of sets (Venn diagrams)
·  Know and apply various counting methods (including permutations and combinations)
·  Understand, calculate, and analyze discrete probability

Several Quantitative questions you’ll encounter on test day will require application of more than one of the topics above.  In arithmetic, there are several concepts and equations you’ll have to memorize.

Math Facility #2 – Algebra

Generally, the algebra covered on the GMAT does not test you above High School Algebra 1.  However, it has probably been several years since High School.  These are the concepts you must review for the test:

·  Manipulating algebraic expressions (isolating variables and solving for a variable)
·  Solving equations (linear equations with one or more unknowns and quadratic equations)
·  Solving and manipulating inequalities
·  Applying and solving functions

Math Facility #3 – Geometry

On GMAT geometry, you will not have to build SIN or COS curves nor graph non-linear functions (thank goodness – I struggled doing those equations with a graphing calculator!).  The GMAT geometry is difficult; however, it is limited to the following concepts:

·  Properties of Triangles, Quadrilaterals, and Circles
·  Properties of uniform solids (rectangles and cylinders)
·  Properties of lines (intersecting, perpendicular, and parallel)
·  Properties of angles (a skill that is also part of the lines and geometric shapes)
·  Coordinate Geometry (very basic four quadrant graphing for the standard y=mx+b equation)

Math Facility #4 – ‘Real Life’ Issues

Since the GMAT isn’t a High School equivalency exam, the GMAC added additional concepts that borrower heavily from the items above but add a real-life dimension to the concept.  The GMAT requires that you know a few more equations and concepts; however, at the base level, this is just an additional application of the concepts above.  These additional applications include the ability to calculate the following:

·  Interest (both simple and compound)
·  Discounts and/or Profits
·  Work and Combined Work Problems
·  Rate and Measurement Problems

While this list is comprehensive, it is, by itself, not sufficient.  Since the GMAT doesn’t require a significant amount of outside knowledge, you’ll find these concepts presented in a manner that makes them far more difficult than they seem on paper.  The only way to ensure you are prepared is to practice.  Good luck as you practice these various aspects of the test.