{"id":10932,"date":"2012-04-16T09:00:00","date_gmt":"2012-04-16T16:00:00","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=10932"},"modified":"2012-04-16T14:51:23","modified_gmt":"2012-04-16T21:51:23","slug":"integer-properties-the-most-common-gmat-question-topic","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/integer-properties-the-most-common-gmat-question-topic\/","title":{"rendered":"Integer Properties: The Most Common GMAT Question Topic"},"content":{"rendered":"

\"\"<\/a>Fact<\/strong>: one of the\u00a0most tested categories of concepts on the GMAT Quantitative section<\/a>\u00a0is Integer Properties<\/p>\n

 <\/p>\n

What are the \u201cproperties of integers\u201d?<\/h2>\n

<\/strong>Probably none of these are brand new to you \u2014- in fact, you probably learned about all these in grade school.\u00a0 Here\u2019s a list.<\/p>\n

a) factors and multiples; GCF and LCM<\/p>\n

b) quotient and remainder<\/p>\n

c) even & odd<\/p>\n

d) prime numbers<\/p>\n

e) consecutive numbers and other consecutive sets (odds, evens, multiple of 5, etc.)<\/p>\n

f) special properties of 1 (e.g. 1*(any number) = that number)<\/p>\n

g) special properties of 0 (e.g. (any number) + 0 = that number, (any number)*0 = 0)<\/p>\n

 <\/p>\n

Again, nothing here is anything that is not covered in grade school, but the trick is: you have to have this all at your fingertips when you take the GMAT.\u00a0 These interrelated concepts lend themselves effortlessly to a myriad of PS & DS questions, and you need to handle them deftly with precision.\u00a0 See this post\u00a0https:\/\/magoosh.com\/gmat\/2012\/gmat-math-factors\/<\/a>\u00a0for tips about factors, multiples, GCF, and LCM. \u00a0For more tips, see below.<\/p>\n

 <\/p>\n

What are integers?<\/h2>\n

Integers are positive and negative whole numbers.\u00a0 They are the set:<\/p>\n

{ . . . -3, -2, -1, 0, 1, 2, 3, . . .}<\/p>\n

They go on forever in the positive and negative direction.\u00a0 They do not include fractions, decimals, and numbers like pi. One way for non-mathy folks to remember the integers: the word \u201cinteger\u201d shares a root with the word \u201cintegrity\u201d \u2014 both come from the Latin word for \u201cwhole, wholeness.\u201d\u00a0 If I have integrity, there is a wholeness among my intention, my speech, and my actions; people who lack integrity say one thing and do another.<\/p>\n

Big GMAT idea: \u00a0if the GMAT makes a numerical statement (e.g. x < 3), do not assume x is an integer unless that is specified.\u00a0 That\u2019s one of the biggest DS traps, assuming the only possibilities are integers when there are many more possibilities allowed.\u00a0 Here\u2019s a trippy advanced math idea: the infinity of non-integers is infinitely bigger than the infinity of integers.\u00a0 (Read\u00a0https:\/\/en.wikipedia.org\/wiki\/Infinity<\/a>\u00a0if you are up for an adventure learning about infinity \u2014 well beyond what you need to know for the GMAT).<\/p>\n

 <\/p>\n

Even and Odd<\/h2>\n

First of all, here are three addition rules:<\/p>\n

1) (even) + (even) = (even)<\/p>\n

2) (odd) + (odd) = (even)<\/p>\n

3) (even) + (odd) = (odd)<\/p>\n

Those also work if the addition sign is changed to a subtraction sign.<\/p>\n

Now, three multiplication rules<\/p>\n

1) (even)*(even) = (even)<\/p>\n

2) (odd)*(odd) = (odd)<\/p>\n

3) (even)*(odd) = (even)<\/p>\n

(These rules are\u00a0not<\/em><\/strong>\u00a0the same if the multiplication sign is changed to division!) If you have trouble remembering these six rules, you can always use even = 2 and odd = 3 to remind yourself.\u00a0 (Yes, 1 is also odd, but I recommend not using that as a test number only because it has so many special properties.)<\/p>\n

Keep in mind: zero is an even number.\u00a0\u00a0 Keep in mind, also: negative numbers can be even and odd, just like their positive compatriots.\u00a0 Fractions and non-integers cannot be even or odd: it\u2019s exclusively an integer property.<\/p>\n

 <\/p>\n

Prime<\/h2>\n

Every number has 1 as a factor.\u00a0 Every number has itself as a factor.\u00a0 A number is prime if it has only those two factors, i.e., no factors other than 1 and itself.\u00a0 Only positive integers are said to be prime; we do not apply the distinction \u201cprime\u201d or \u201cnot prime\u201d to negative integers, zero, or to non-integers.<\/p>\n

Here is a list of the first few primes:<\/p>\n

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, . . .<\/p>\n

The primes go on forever in an irregular pattern, the nature of which involves the hardest unanswered question in math today, the Riemann Hypothesis \u2014 again, well beyond what you need to know for the GMAT.\u00a0 It would be good to memorize that list of the first ten prime numbers: that will help you a lot on the GMAT.\u00a0 Notice that, for a variety of reasons with which we need not concern ourselves here, 1 is not a prime number.\u00a0 Notice, also: 2 is the only even prime number: all other even numbers are divisible by 2.\u00a0 That\u2019s a very handy distinction, especially in GMAT DS: 2 is the only even prime number.<\/p>\n

See the factors post for more information about prime numbers.<\/p>\n

 <\/p>\n

Know Them Cold<\/h2>\n

Probably there\u2019s nothing brand new in this post.\u00a0 Probably you have at least a dim memory, if not a perfectly clear understanding, of everything here.\u00a0 Whatever here is rusty, whatever is less than perfectly fluent, you need to practice until you know it cold.\u00a0 The GMAT is relentless in asking about these properties, and if you can nail them every time, you will be well on your way to a stunningly successful GMAT Quantitative section.<\/p>\n

 <\/p>\n

Here are a couple of practice questions:<\/p>\n

1)\u00a0https:\/\/gmat.magoosh.com\/questions\/880<\/a><\/p>\n

2)\u00a0https:\/\/gmat.magoosh.com\/questions\/317<\/a><\/p>\n

3)\u00a0https:\/\/gmat.magoosh.com\/questions\/864<\/a><\/p>\n

 <\/p>\n

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

Fact: one of the\u00a0most tested categories of concepts on the GMAT Quantitative section\u00a0is Integer Properties   What are the \u201cproperties of integers\u201d? Probably none of these are brand new to…<\/p>\n","protected":false},"author":133,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,783,243,718,717,736],"tags":[],"class_list":["post-10932","post","type-post","status-publish","format-standard","hentry","category-gmat","category-magoosh-blog","category-blog","category-data-sufficiency-gmat","category-problem-solving-gmat","category-quant-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/10932","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=10932"}],"version-history":[{"count":2,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/10932\/revisions"}],"predecessor-version":[{"id":10990,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/10932\/revisions\/10990"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=10932"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=10932"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=10932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}