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The GMAT Quant section tests a variety of mathematical concepts, including algebra, geometry, and arithmetic. Generally speaking, the test-makers are not looking to trick or confuse you. Most GMAT math problems are rather straightforward. Read on to find out the specific arithmetic topics covered, tips for success, and plenty of practice problems!<\/p>\n
<\/a> <\/a> The nine essential arithmetic concepts you need to look out for on the GMAT are these: Now let’s take a quick tour through these various areas. Some of the topics overlap a bit. And you may need to combine ideas to solve more challenging problems, but here are the basics.<\/p>\n <\/a> This includes the fundamental operations such as addition, subtraction, multiplication, and division. For example, typical problems may test your mastery of order of operations<\/a>, or spotting common factors<\/a> to cancel in complicated fractions. It’s important to have good number sense<\/a> too.<\/p>\n <\/a> A good number of GMAT math problems rely on your knowing your number properties<\/a>. Primarily, we’re talking about properties of integers<\/a>. So, be prepared to analyze evens and odds, consecutive integers and multiples<\/a>, prime numbers, positives and negatives, and all the related concepts.<\/p>\n For example, did you know that 1 is not<\/em> a prime number<\/a>? On the other hand, 0 is definitely an integer<\/a>!<\/p>\n <\/a> Fractions are incredibly important and useful. However, they often get a bad rap. But as long as you remember the fundamental rules, then fractions can be your friends!<\/p>\n Check out this helpful resource for more info about fractions on the GMAT!<\/a><\/p>\n <\/a> Ratios are nothing more than fractions in disguise! But they are often used just to compare the parts<\/em> of a whole with each other.<\/p>\n For example, if you tell me that the ratio of boys to girls in your classroom is 3 : 5, then I know that 3\/8 of the class are boys and 5\/8 are girls (note how I just added 3 and 5 to get the denominator of 8).<\/p>\n Proportions are equations that compare two fractions or ratios. <\/p>\n Here is a great resource to fill in the details: GMAT Quantitative: Ratio and Proportions<\/a><\/p>\n <\/a> Percents represent yet another way of talking about fractional amounts. It literally tells you how many out of a hundred (per cent<\/em> = per hundred<\/em>). If you want to find p<\/em>% of a number A<\/em>, just multiply p<\/em> × A<\/em>. Percent change<\/em> involves adding or subtracting a percentage of the original amount — for example, 50% more of 40 is equal to 40 + (0.50)(40) = 60.<\/p>\n Here’s more on the topic of percents:<\/p>\n <\/a> Knowing your Laws of Exponents and Roots<\/a> will definitely help you to get through the GMAT Quantitative section. Here are a few links to get you started.<\/p>\n But what about those “impossible” problems with huge tricky exponents, in which they ask for the units digit of the answer? Don’t fall into the trap of trying to work out the number exactly — that will eat up too much precious time. Instead, review these methods: GMAT Quant: Difficult Units Digits Questions<\/a>.<\/p>\n <\/a> GMAT statistics problems generally ask you to work out the average (arithmetic mean), median, mode, range, and interpret standard deviation. Further topics to be aware of include descriptive statistics<\/a> and statistical significance<\/a>.<\/p>\n Often, the problems can be done without much of computation. For example, did you know that if you multiplied all of the data by the same number, \\(k\\), then the mean, median, mode, and standard deviation also gets multiplied by that same factor \\(k\\)? By contrast, adding the same number \\(k\\) to all of the data only changes the mean, median, and mode, while leaving the standard deviation the same!<\/p>\n <\/a> The term combinatorics<\/strong> is just a fancy word for counting<\/em>. So it can’t be that<\/em> hard, right? Well, just be careful. Does the order of items make a difference? Can the same item be counted more than once in a list?<\/p>\n Combinations questions ask how many ways that groups can be made out of a pool of distinct items. For example, how many 4-person committees are possible if chosen from a group of 7 people? Order doesn’t matter.<\/p>\n Permutations questions, on the other hand, are all about order. For instance, in how many ways can 4 people line up against the wall? If you are thinking 24, then you already know your factorials<\/a>. <\/p>\n Check out GMAT Permutations and Combinations<\/a> for more!<\/p>\n <\/a> GMAT Probability questions come in many flavors. From problems that involve counting<\/a> to geometric probability<\/a> and problems based on dice<\/a>, you have to be prepared for just about anything.<\/p>\n But there are just a few fundamental concepts to keep in mind. The main idea behind probability is that it’s a fraction of the desired outcomes<\/em> over the total number of outcomes<\/em>. To get started, check out this article: GMAT Probability Rules<\/a>.<\/p>\n Also, you can expect probability to be a favorite topic for GMAT data sufficiency questions — for practice, see GMAT Data Sufficiency Practice Questions on Probability<\/a>.<\/p>\n <\/a> Here are three tips for the GMAT arithmetic section — two fairly general pointers and one specific content area pitfall to avoid.<\/p>\n You can avoid a ton of work and headache by simply estimating. A careful approximation may allow you to eliminate answer choices and avoid lengthy computations at the same time. That’s a win-win!<\/p>\n For example, if you have to multiply 98 × 103 for some reason, then just estimate 100 × 100 = 10000. <\/p>\n GMAT Arithmetic questions do not require extensive mathematical expertise to solve. In fact, most questions rely on either basic number properties or recognizing a simple pattern. For an example of the latter, consider the following example:<\/p>\n What is the remainder when \\(5^{31}\\) is divided by 3?<\/em><\/p>\n Clearly, we cannot work out the expression directly. Calculators are not permitted on the Quant section, and this power is way too large to compute by hand. But let’s look for a pattern. First consider small powers.<\/p>\n \\(5^1 = 5\\). Remainder: 2<\/p>\n \\(5^2 = 25\\). Remainder: 1<\/p>\n \\(5^3 = 125\\). Remainder: 2<\/p>\n \\(5^4 = 625\\). Remainder: 1<\/p>\n It seems as though every odd power yields a remainder of 2 when you divide by 3, and so since the exponent 31 is odd, we’ll guess (correctly): 2.<\/p>\n There’s a standard set of traps<\/em> that the GMAT test-makers rely on in powers and roots questions. <\/p>\n If \\(b > 0\\), then the equation \\(x^2 = b\\) always<\/strong><\/em> has two solutions, the positive and negative square root of \\(b\\). <\/p>\n For example, if one of the two equations in a Data Sufficiency problem is \\((x + 1)^2 = 25\\), then that statement cannot be sufficient by itself (unless further information was given in the setup before the statements). Instead, you have to be aware that both \\(x +1 = 5\\) and<\/strong><\/em> \\(x+1=-5\\), or \\( x = 4, -6\\) are the solutions.<\/p>\n
\n <\/p>\nTable of Contents<\/h2>\n
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\n <\/p>\nWhat kind of arithmetic is tested on the GMAT?<\/h2>\n
\n(Click on the concept to go to that section directly)<\/em><\/p>\n\n
\n <\/p>\nArithmetic Operations<\/strong><\/h3>\n
\n <\/p>\nNumber Properties<\/strong><\/h3>\n
\n <\/p>\nFractions<\/strong><\/h3>\n
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\n <\/p>\nRatio and Proportions<\/strong><\/h3>\n
\n <\/p>\nPercents<\/strong><\/h3>\n
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\n <\/p>\nPowers and Roots of Numbers<\/strong><\/h3>\n
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\n <\/p>\nStatistics<\/strong><\/h3>\n
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\n <\/p>\nCombinatorics<\/strong><\/h3>\n
\n <\/p>\nDiscrete Probability<\/strong><\/h3>\n
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\n <\/p>\nGMAT Arithmetic Tricks: 3 Tips for Success<\/h2>\n
Tip #1: It’s All About Number Sense<\/strong><\/h3>\n
Tip #2: Look for Patterns<\/strong><\/h3>\n
Tip #3: Be Careful with Roots and Squares<\/strong><\/h3>\n