{"id":19367,"date":"2019-10-11T16:31:32","date_gmt":"2019-10-11T23:31:32","guid":{"rendered":"https:\/\/magoosh.com\/gre\/?p=19367"},"modified":"2019-10-11T16:31:32","modified_gmt":"2019-10-11T23:31:32","slug":"gre-arithmetic-overview-and-practice","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gre\/gre-arithmetic-overview-and-practice\/","title":{"rendered":"GRE Arithmetic: Overview and Practice"},"content":{"rendered":"

\"student<\/p>\n

Achieving a high score on the GRE (Graduate Record Examination) is one of the major steps in landing a spot in the graduate school of your choice. But often, students struggle with the GRE math<\/a> section.<\/p>\n

The GRE Quantitative test has four main mathematical areas: Arithmetic, Algebra<\/a>, Geometry<\/a>, and Data Analysis<\/a>.<\/p>\n

This post is all about GRE arithmetic. But don\u2019t let the name fool you! Arithmetic means much more than just adding and subtracting numbers. It covers a lot of ground, including general properties of numbers and how they are put together.<\/p>\n

In this post, we\u2019ll explore the various GRE arithmetic topics, which include things like divisibility, remainders, exponents, roots, percents, ratios, and sequences of numbers. We\u2019ll also work through a few GRE arithmetic practice questions. Each example will be tagged as QC (quantitative comparison), MC (multiple choice), or NE (numeric entry). If you want to learn more about the question types on the GRE test, check out What Kind of Math is on the GRE?<\/a><\/p>\n

Table of Contents<\/h2>\n

Numbers and Their Properties<\/a>
\nOperations on Numbers<\/a>
\nRatios, Percents, and Proportions<\/a>
\nSequences<\/a><\/p>\n

<\/a><\/p>\n

Numbers and their Properties<\/h2>\n

Remember your times table?<\/p>\n

\"times
Image by brgfx<\/a><\/em><\/figcaption><\/figure>\n

 
\nEach column or row displays the first ten multiples<\/strong> a given number. For example, the numbers 3, 6, 9, 12, 15, etc. are multiples of 3, or equivalently, those numbers are divisible by 3. (Of course, there are infinitely many more multiples\u2014just imagine continuing each column or row forever!)<\/p>\n

Numbers like 2, 3, 5, 7, 11, 13, 17, and 19, that are only divisible by 1 and themselves, are called the primes<\/strong>. There are infinitely many of those too! Primes are important because they are like the \u201cLego pieces\u201d that fit together to make up all the other numbers out there.<\/p>\n

\"magoosh Watch our video to brush up on Divisibility Rules<\/strong><\/a>. You should also familiarize yourself with concepts such as prime factorizations<\/a> of whole numbers, least common multiple (LCM)<\/a>, and greatest common factor (GCF) in the math section of the GRE.<\/p>\n

Example (MC)<\/u>: If an integer is divisible by both 12 and 27, then the integer must be divisible by which of the following?<\/p>\n

(A) 48
\n(B) 54
\n(C) 81
\n(D) 108
\n(E) 324<\/p>\n

Answer<\/u>: (D)<\/p>\n

Explanation<\/u>: This question is really asking for the LCM of 12 and 27. First, get the prime factorizations of each number.<\/p>\n

12= 22<\/sup>\u00d73
\n27=33<\/sup><\/p>\n

If an integer is divisible by both 12 and 27, then it must have at least two factors of 2 and three factors of 3. The LCM is 22<\/sup>\u00d733<\/sup>\u00a0= 4\u00d727 = 108.<\/p>\n

By the way, you could eliminate answer choices (A), (B), and (C), because each one fails to be divisible by one of the two numbers, 12 or 27. What about choice (E)? Isn\u2019t that divisible by both 12 and 27? Well yes, it\u2019s a common multiple, but it\u2019s not the least<\/i> common multiple.<\/p>\n

\"magoosh Try to avoid mindless calculator use by developing a good number sense and an aptitude for mental math. Check out this video on Number Sense<\/a><\/strong> and practice mental math with these problems<\/a>. Also, check out these GRE Math Basics Quick Tips<\/a>!<\/p>\n

Example (QC<\/span>):<\/p>\n

n<\/i> is a positive integer<\/p>\n\n\n\n
Quantity A<\/center><\/th>\n
Quantity B<\/center><\/th>\n<\/tr>\n
The remainder when n<\/em> is divided by 7.<\/td>\n
The remainder when n<\/em>+21 is divided by 7.
<\/td>\n<\/tr>\n<\/table>\n

Answer<\/span>: The two quantities are equal.<\/p>\n

Explanation<\/span>: Quantitative comparison questions on the GRE ask you to decide whether one quantity is bigger than the other, the same, or cannot be determined.<\/p>\n

The clue is that 21 is a multiple of 7, so when n<\/em>+21 is divided by 7, the additional 21 will not contribute anything to the remainder.<\/p>\n

Let\u2019s double-check our thinking with a particular value, say n<\/em>=36. The value 7 divides into 36 a total of 5 times, with a remainder of 1. What about n<\/em>+21=57? Well, this time 7 goes into it 8 times, but the remainder is still 1.<\/p>\n

<\/a><\/p>\n

Operations on Numbers<\/h2>\n

When you start to look at operations on numbers, it may seem that there are a ton of formulas to remember. In reality, there are just a few essential GRE arithmetic formulas and properties to master.<\/p>\n

Integer<\/h3>\n

We\u2019ve already used the term integer <\/strong>in this post, but in case you’re wondering exactly what an integer<\/a> is…Briefly, integers are just the real numbers that do not have any fractional part (which do include negatives and zero).<\/p>\n

Fractions<\/h3>\n

\"magoosh For some solid fraction review, check out our videos on Intro to Fractions, <\/a><\/strong>Fraction Properties<\/a><\/strong>, and GRE Division, Mixed Numerals, and Negatives. <\/a><\/strong>Be sure you\u2019re also familiar with the properties of negative numbers and absolute value<\/a>.<\/p>\n

Exponents<\/h3>\n

\"magoosh Our Intro to Exponents<\/a><\/strong> video is a good primer. The general properties are key here: for example, a negative number raised to an even power gives you a positive, while a negative raised to an odd power keeps the quantity negative:<\/p>\n

(-)even <\/sup><\/em>= (+)
\n(-)odd <\/sup><\/em>= (-)<\/p>\n

Example (MC)<\/span>: What is the sum of the digits of 28<\/sup>+(-3)5<\/sup>+(-4)2<\/sup>?<\/p>\n

(A) 5
\n(B) 7
\n(C) 11
\n(D) 12
\n(E) 14<\/p>\n

Answer<\/span>: (C)<\/p>\n

Explanation<\/span>: 28<\/sup>+(-3)5<\/sup>+(-4)2 <\/sup>= 256 – 243 + 16 = 29. Add the digits to get the correct answer of 11.<\/p>\n

Here is some more GRE Exponents Basics Practice<\/a>.<\/p>\n

Roots<\/h3>\n

\"magoosh
\nYou\u2019ll also need to understand how to work with square roots and higher roots on the GRE. Here\u2019s a helpful video on Simplifying Roots<\/a><\/strong>.<\/p>\n

 
\nExample (NE)<\/span>: If \u221aa<\/em><\/span>=4 and \u221bb<\/em><\/span>=a<\/em>, what is the value of b<\/em>?<\/p>\n

Answer<\/span>: 4096<\/p>\n

Explanation<\/span>: \u221aa<\/em><\/span>=4 means \u201cthe square root of a number is 4.\u201d You can guess and check, or better yet, translate the equation into: a<\/em>=42<\/sup>, which is 16.<\/p>\n

Then plug in a to the second equation: \u221bb<\/em><\/span>=16, and rewrite as: b <\/em>= 163 <\/sup>= 4096.<\/p>\n

<\/a><\/p>\n

Ratios, Percents, and Proportions<\/h2>\n

\"magoosh When you need to compare two or more things, often a ratio, percent, or proportion is the best tool to use. For the basics of working with percents, check out this Intro to Percents<\/strong><\/a> as well as this video on Percent Changes<\/a><\/strong>.<\/p>\n

Example (QC)<\/span>:<\/p>\n

N<\/em> is a positive real number.<\/p>\n\n\n\n
Quantity A<\/center><\/th>\n
Quantity B<\/center><\/th>\n<\/tr>\n
The result of a 20% increase of N<\/em>, followed by a 20% decrease.<\/td>\n
N<\/em>
<\/td>\n<\/tr>\n<\/table>\n

Answer<\/span>: Quantity B is bigger.<\/p>\n

Explanation<\/span>: Don\u2019t be fooled; the quantities are not the same! Let\u2019s work out the percent increase: N<\/em>+0.20N<\/em>=1.2N<\/em>. Call that result M<\/em>. <\/p>\n

Now work out the percent decrease: M<\/em>-0.2M<\/em>=0.8M<\/em><\/p>\n

Together, the two changes give: 0.8M<\/em>=0.8(1.2N<\/em>)=0.96N<\/em>, which is less than N<\/em>.<\/p>\n

\"magoosh Ratios and Proportions are basically about comparing fractions. Here are a few videos to get you started: Intro to Ratios <\/a><\/strong>and Proportions on the GRE<\/a><\/strong>.<\/p>\n

 
\nOften, ratios or proportions show up in application questions, such as Distance-Rate-Time<\/a> problems.<\/p>\n

Example (MC)<\/span>: Stacy needs to drive 75 miles on a highway with a speed limit of 65 mph. If she starts at 3:00pm, and drives the speed limit, at what time can she expect to arrive at her destination?<\/p>\n

(A) 3:56
\n(B) 4:03
\n(C) 4:07
\n(D) 4:09
\n(E) 4:13<\/p>\n

Answer<\/span>: (D)<\/p>\n

Explanation<\/span>: Use (Distance)=(Rate)(Time).<\/p>\n

D=RT<\/em>
\n75 mi<\/em>.=(65 mph<\/em>)T<\/em>
\nT=75\/65=1.1538 hr.<\/p>\n

So, that\u2019s an hour plus a fraction of the next hour. Multiply the fractional part by 60 to find the minutes: (0.1538)(60)=9.2<\/p>\n

The closest answer choice is 4:09, which is an hour and 9 minutes after 3pm.<\/p>\n

<\/a><\/p>\n

Sequences<\/h2>\n

\"magoosh A sequence is just a list of numbers. Here are a couple videos that may help you to understand sequences: Intro to Sequences <\/a><\/strong>and Series and Counting<\/strong>.<\/p>\n

 
\nThere are not many sequence problems on the GRE\u2014maybe one will show up in a math section, but there could be none! So don\u2019t spend too much time agonizing over all the formulas, techniques, and challenging theory in this topic. As long as you know the basics, you should be fine.<\/p>\n

Example (NE)<\/span>: A sequence is defined by the rule, \u00a0t<\/em>1<\/sub>=3, t<\/em>2<\/sub>=2, and for n\u22653, tn<\/sub><\/em>=tn-<\/sub><\/em>1<\/sub>+2tn-<\/sub><\/em>2<\/sub>. What is the value of t<\/em>5<\/sub>?<\/p>\n

(A) 6
\n(B) 5
\n(C) 8
\n(D) 12
\n(E) 28<\/p>\n

Answer<\/span>: (E)<\/p>\n

Explanation<\/span>: You have to work out t<\/em>3<\/sub> and t<\/em>4<\/sub> first.<\/p>\n

t<\/em>3<\/sub>=t<\/em>2<\/sub>+2t<\/em>1<\/sub>=(2)+2(3)=8
\nt<\/em>4<\/sub>=t<\/em>3<\/sub>+2t<\/em>2<\/sub>=(8)+2(2)=12
\nt<\/em>5<\/sub>=t<\/em>4<\/sub>+2t<\/em>3<\/sub>=(12)+2(8)=28<\/p>\n

Keep Practicing!<\/h2>\n

This GRE Arithmetic overview could not cover everything, so don\u2019t forget to sharpen your skills by doing plenty of GRE Math Practice Questions<\/a> as well as a GRE practice test or three! Training with a great test prep resource gives you the best chance of success on test day!<\/p>\n","protected":false},"excerpt":{"rendered":"

Achieving a high score on the GRE (Graduate Record Examination) is one of the major steps in landing a spot in the graduate school of your choice. But often, students struggle with the GRE math section. The GRE Quantitative test has four main mathematical areas: Arithmetic, Algebra, Geometry, and Data Analysis. This post is all […]<\/p>\n","protected":false},"author":223,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[41,25],"tags":[],"ppma_author":[12283],"class_list":["post-19367","post","type-post","status-publish","format-standard","hentry","category-arithmetic","category-math"],"acf":[],"yoast_head":"\nGRE Arithmetic: Overview and Practice - Magoosh Blog \u2014 GRE\u00ae Test<\/title>\n<meta name=\"description\" content=\"GRE arithmetic might seem easy, but it's more than just adding and subtracting numbers. 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Shaun has taught and tutored students in mathematics for about a decade, and hopes his experience can help you to succeed!","sameAs":["http:\/\/valdosta.academia.edu\/ShaunAult","https:\/\/twitter.com\/ShaunAultMath"],"url":"https:\/\/magoosh.com\/gre\/author\/shaunault\/"}]}},"authors":[{"term_id":12283,"user_id":223,"is_guest":0,"slug":"shaunault","display_name":"Shaun Ault","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/f10cdb687137bc0ad4e885404588101b7cd4aa01ae2be48abda61f14fa3715e2?s=96&d=mm&r=g","user_url":"http:\/\/valdosta.academia.edu\/ShaunAult","last_name":"Ault","first_name":"Shaun","description":"Shaun earned his Ph. D. in mathematics from The Ohio State University in 2008 (Go Bucks!!). He received his BA in Mathematics with a minor in computer science from Oberlin College in 2002. In addition, Shaun earned a B. Mus. from the Oberlin Conservatory in the same year, with a major in music composition. Shaun still loves music -- almost as much as math! -- and he (thinks he) can play piano, guitar, and bass. Shaun has taught and tutored students in mathematics for about a decade, and hopes his experience can help you to succeed!"}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/posts\/19367","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/users\/223"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/comments?post=19367"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/posts\/19367\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/media?parent=19367"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/categories?post=19367"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/tags?post=19367"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/ppma_author?post=19367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}