{"id":16459,"date":"2013-01-28T09:00:08","date_gmt":"2013-01-28T16:00:08","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=16459"},"modified":"2013-02-11T16:34:02","modified_gmt":"2013-02-11T23:34:02","slug":"gmat-number-properties","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/gmat-number-properties\/","title":{"rendered":"GMAT Number Properties"},"content":{"rendered":"

\"\"The single most-tested topic on the GMAT Quantitative Section is something called \"Number Properties.\"\u00a0 In a way, this statement, while absolutely true, is a bit deceptive.\u00a0 It's like saying the biggest category at a particular zoo is mammals: even if that is completely true, that statement alone doesn't give us a particular clear idea of what kinds of critters we are likely to encounter at the zoo.\u00a0 Much in the same way, \"number properties\" is a vast category, just like \"mammals\", and simply knowing that you will have to know \"number properties\" doesn't necessarily narrow down specifically what you will have to know.\u00a0 This post is designed to give an overview of this vast topic.<\/p>\n

 <\/p>\n

Numbers<\/h2>\n

Let's first talk about the constituents of this realm.\u00a0 When I say the word \"numbers\", what do you think?\u00a0 If the only thing that comes to mind is (1, 2, 3, 4, 5, \u2026), then, with all due respect, you are thinking like a second-grader.\u00a0\u00a0 Not surprisingly, such thinking will get you in trouble on the GMAT.\u00a0 If, when I say the word \"numbers\", you immediately think not only of those numbers but also their negative counterparts, as well as zero, positive & negative fractions, positive & negative decimals, squareroots, pi, etc. etc., then you are thinking like a mathematician.\u00a0 One very simple trick for success on GMAT math problem: whenever you hear the word \"number\", automatically force yourself to think exhaustively of every possibility.<\/p>\n

Numbers live on what grade-school teachers call the \"number line\" and what mathematicians call the \"real number line\", a continuous infinity of values.\u00a0 (The more you think about the idea of continuous infinity, the more it boggles the mind!)\u00a0 The real-number line is a real of perfect fairness ---- the number -137\/8 is just as much a legitimate member of the number line as is 4. If you have any prejudice that, for example (1, 2, 3, 4 \u2026.) are the only \"worthy\" numbers and all the rest are somehow exceptions or illegal aliens or something like that, you have to retrain your mind to see the perfect fairness and equal worthiness of each and every number on the real number line.<\/p>\n

It's particular important if you are choosing numbers plugging in, say to test algebraic expression in a\u00a0Data Sufficiency<\/a>\u00a0question, to remember to\u00a0test numbers of all categories<\/a>.<\/p>\n

 <\/p>\n

Categories of numbers<\/h2>\n

In addition to knowing the infinite implications concerning the word \"number\", two further terms you should know are \"integers\" (\u2026 -4, -3, -2, -1, 0, 1, 2, 3, 4, \u2026) and \"positive integers\" (1, 2, 3, 4, \u2026).\u00a0 On a rare occasion, the GMAT will also have a question concern \"negative integers\", which are just the negative counterparts of the positive integers.\u00a0 Notice:\u00a0while zero is an integer, it is neither positive nor negative<\/em><\/strong>.\u00a0 The word \"integer\" is etymologically related to the word \"integrity\": both come from the Latin word for wholeness.\u00a0 Each integer is, as it were, a unique wholeness, a complete package in and of itself.<\/p>\n

The \"parts\" between the \"wholes\" can be represented in two ways:\u00a0fractions<\/a>\u00a0and\u00a0decimals<\/a>.\u00a0 Both can be either positive or negative.\u00a0 Mathematicians have both systems for these \"partial\" numbers because each system has its own advantages under certain circumstance.\u00a0 Technically, \"fractions\" and \"decimals\" don't cover exactly the same turf, because, as I discuss in that post on decimals, fractions include only the\u00a0rational numbers<\/strong>, whereas decimals include both rationals and\u00a0irrational numbers<\/strong>, an infinitely bigger set.\u00a0 Thus, even though there's an infinity of fractions between 0 and 1 as well as an infinity of decimals between 0 and 1, the infinity of decimals is infinitely bigger than the infinity of fractions (one of the many mind-boggling things about the continuous infinity of the real number line!) Irrational numbers include\u00a0roots<\/a>, which the GMAT loves to test.<\/p>\n

 <\/p>\n

More on positive integers<\/h2>\n

The positive integers (1, 2, 3, 4, \u2026.) are also called the \"counting numbers\", and mathematicians call them the \"natural numbers\", but \"positive integers\" seems to be the term the GMAT consistently uses.\u00a0\u00a0 These numbers have a bunch of special properties just to themselves:\u00a0primes<\/a>,\u00a0odd & even<\/a>, multiples,\u00a0factors<\/a>,\u00a0remainders<\/a>, etc.<\/p>\n

One of the hardest things the GMAT will ask you to do with positive integers is to\u00a0count<\/a>.\u00a0 This may sound paradoxical, as counting is one mathematical thing even the most inveterate math-phobe can do, but here, by \"counting\", I mean problems like: \"There are three boys in blue shirts, five boys in green shirts, and four girls in blue dresses.\u00a0 How many ways can they sit in seven seats if blah blah blah<\/em>?\"\u00a0 Those arrangements and sets and combinations ---- that's what the GMAT will have you count.\u00a0 Also, remember the trick of\u00a0inclusive counting<\/a>, which the GMAT loves to test.<\/p>\n

 <\/p>\n

Summary<\/h2>\n

Number properties is a huge topic: if you follow all those links, you will have a good understanding of the lay of the land.\u00a0 It's also good to know the\u00a0most common math mistakes<\/a>\u00a0on the GMAT.\u00a0 Finally, here's a very easy practice question, to get you warmed up to thinking about this topic as it appear in test-format questions:<\/p>\n

1)\u00a0https:\/\/gmat.magoosh.com\/questions\/2621<\/a><\/p>\n

This post was written by Mike McGarry, GMAT expert at Magoosh<\/a>, and originally posted here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

The single most-tested topic on the GMAT Quantitative Section is something called “Number Properties.”\u00a0 In a way, this statement, while absolutely true, is a bit deceptive.\u00a0 It’s like saying the…<\/p>\n","protected":false},"author":133,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,783,243,736],"tags":[],"class_list":["post-16459","post","type-post","status-publish","format-standard","hentry","category-gmat","category-magoosh-blog","category-blog","category-quant-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/16459","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/users\/133"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=16459"}],"version-history":[{"count":4,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/16459\/revisions"}],"predecessor-version":[{"id":16964,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/16459\/revisions\/16964"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=16459"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=16459"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=16459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}