The GMAT Math Sections - Problem Solving and Data Sufficiency

The GMAT Quantitative Test consists of two types of questions, mathematics problem solving and data sufficiency. Math problem solving can range from asking you to solve a simple equation, to giving you a word problem that forces you to both understand English, figure out the equation to use, and solve it. For this reason, we recommend practicing your mental arithmetic, since calculators aren't allowed. If you are an international student it is stringly recommended to practice the Quantitative section in English.

Data sufficiency problems are weird little problems that give you an equation and two pieces of data. They then ask you whether you can solve the problem with only the first piece of data, only the second piece of data, with either one of the first and second pieces of data, only with both pieces of data, or not at all. The easy part about these questions is that you don't actually have to solve the problem to get the correct answer. The hard part though, is that they tend to be confusing.

Today's GMAT quantitative section tests arithmetic, algebra, geometry, number theory, and probability. This is a big change from four years ago when number theory and probability were not on the exam at all. It's important when you study, therefore, to make sure you have recent software and textbooks for the quantitative portion of the exam.

The GMAT Quantitative Ability Section

(Estimation, rounding, process-of-elimination, and other time-saving shortcuts)

Q: Does the GMAT reward test-takers who know certain shortcuts for arithmetical calculations and for manipulating numbers?

It depends on the type of shortcut. On the one hand, a GMAT test-taker who can perform complex arithmetical calculations quickly, like Dustin Hoffman in Rainman, would hold absolutely no advantage. Number-crunching is simply not what the GMAT is about. For example, on the GMAT you won't be required to use columnar multiplication or long division to combine multiple-digit numbers deal with unwieldy numbers to determine root and exponential values carry decimal points beyond one or two places. On the other hand, if by "shortcuts" you mean the combining of multiple computational steps, then the GMAT does indeed reward test-takers who know how to use shortcuts.

Q: Can you provide a few examples of the sorts of shortcuts GMAT test-takers can use to their advantage?

A GMAT question might require you to remove radical (root) signs from a fraction's denominator. If so, it's useful to know that you can accomplish this simply by "copying" the radical term to the numerator, and removing the radical sign from the denominator. So to rework the expression , you can omit the intermediary steps of multiplying both numerator and denominator by the root value, then canceling:

Here's another useful shortcut: If two fractions are equal, you can "factor out" terms across numerators or denominators, and set the fractions' "cross-products" equal to each other. So in the following equation you can solve for x in three quick steps (also using the shortcut involving radicals I just mentioned):

Q: In preparing for the GMAT, should test-takers memorize certain formulas or computational tables?

Yes, but the learning curve is neither steep nor long. In gearing up for the GMAT you need to learn only a handful of formulas, all of which involve geometry:

area of certain triangles: right, isosceles, equilateral
area and circumference of a circle
area of a right cylinder
area and perimeter of a square, rectangle, rhombus, and trapezoid
angle measures of any polygon

Understanding the Pythagorean Theorem (for determining the area of a right triangle and the relationship among its three sides) will be especially helpful on the GMAT.

In gearing up for the GMAT you should also memorize tables for determining
fraction-percent-decimal equivalents
certain square roots and cube roots that are integral values (no decimals)
squares of integers up to 15, along with 25
prime numbers up to 100
divisibility (for factoring numbers)

Q: For the GMAT, would you suggest memorizing conversion tables for units of measurement - such as weight, length, and monetary units?

For the GMAT, there's no need to memorize conversion tables. GMAT questions will not require you to convert across systems of measurement - for example, meters to yards. Although conversions within a system (e.g., ounces to pounds) are sometimes required, the GMAT question itself will provide the conversion information you need to do the conversion - for example, "1 pound = 16 ounces."

But what every test-taker should be concerned about is making sure their calculated solution is expressed in terms of the specific unit of measurement called for in the question. A GMAT question might express units in pounds, then ask for a solution in terms of ounces. If you neglect to convert - by either multiplying or dividing a key figure by 16 at some point in your calculations - you'll come up with the wrong solution, of course. And if the question is in the Problem Solving format, chances are that your wrong solution will appear among the four incorrect answer choices!

Q: Do the test-takers frequently resort this ploy - determining common errors and listing wrong-answer choices that reflect those errors? If so, how can test-takers avoid falling victim to this ploy?

Yes, the test-makers incorporate this ploy into nearly every GMAT Problem Solving question. To increase the difficulty level of a question, they load a question with three or four of these sucker-bait choices; to decrease the difficulty level, they reduce the number to one or two.

The best way to avoid falling prey to this ploy is to predetermine, if possible, the sort of answer choice you're looking - in other words, determine what meets the criteria for a viable correct response. If the question asks for a numerical solution - without variables - ask yourself how large or small a number would make sense as the correct answer in the context of the problem:

a single-digit number?
a very small fractional number?
a large percentage?

In so-called "story" problems - questions in a real-world setting - you can often define parameters for a viable answer choice based on common sense, then eliminate at least one answer choice based on those parameters. This technique also helps if you're in a time crunch during the Quantitative section. If you can eliminate one or two answer choices without doing any pencil-work, simply because they are unrealistic in size, this will help increase your odds.

When using this technique, keep in mind that numerical answer choices are always listed in ascending order of size (except for questions that ask which of the five choices is largest/smallest in value). In other words, the smallest value among the five choices will be listed first among the five, while the largest value will be listed last. So if you determine parameters up front, and only the first two listed choices fall within them, chances are that the last two listed choices are both wrong. Thus defining parameters can help speed up the elimination process a bit.

Q: The process-of-elimination technique you just mentioned applies only to the Problem Solving format. What about the Data Sufficiency format? Is there any such technique that might be useful in handling questions in this format?

Yes; the Data Sufficiency format does suggest a particular process of elimination. Let's first look at the five answer choices for every Data Sufficiency question:

(A) statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

(B) statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient

(D) EACH statement ALONE is sufficient to answer the question asked

(E) statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

These five answer choices suggest the following process of elimination:

1. Consider statement (1) by itself. If you can answer the question based on (1) alone, eliminate (B), (C) and (E) as viable choices.

2. Consider statement (2) by itself. If you can answer the question based on (2) alone, eliminate (A), (C) and (E) as viable choices.

3. If you were able to answer the question based on (1) alone and based on (2) alone, the correct response is (D).

4. If you were not able to answer the question based on either statement alone, the correct response must be either (C) or (E).

As you can see, built into the Data Sufficiency format is the opportunity to make reasoned guesses when you're in a time crunch or have trouble analyzing one of the two numbers statements.

Q: Are there any visual shortcuts to answering GMAT geometry questions that are accompanied by pictures of geometric figures? In other words, can the test-taker analyze these questions by estimating lengths and sizes visually?

Before answering your question, I need to point out two basic ground rules that you'll see as part of the directions for the Quantitative section:

In Problem Solving questions, assume that figures are drawn to scale unless a figure indicates that it is not drawn to scale.

In Data Sufficiency questions, figures are not necessarily drawn to scale, unless otherwise indicated.

So with respect to Data Sufficiency questions, the answer to your question is clearly "no." But the answer is also "no" for Problem Solving questions. Why?

The test-makers draft geometry questions so as to eliminate any advantage of visual measurement. For example, you're unlikely to encounter a question that asks you to compare one linear length in a figure with another? And if you do, the test-makers will intentionally distort the figure's proportions and indicate that the figure is not drawn to scale. The bottom line is: Don't rely on your eye to answer Quantitative questions, regardless of whether its format is Problem Solving or Data Sufficiency.

There is one important exception, however, to this "bottom-line" advice. Handling a Data Interpretation question in the Problem Solving format might necessarily require certain visual measurements - for instance, determining the height of a certain bar on a bar graph, or the vertical position of a point on a line chart.

by Mark Alan Stewart - www.businessweek.com