{"id":6747,"date":"2022-08-30T12:35:28","date_gmt":"2022-08-30T12:35:28","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/business-school-insider\/?p=6747"},"modified":"2022-08-30T17:26:03","modified_gmt":"2022-08-30T17:26:03","slug":"land-score-number-properties-gmat","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/gmat\/land-score-number-properties-gmat\/","title":{"rendered":"Number Properties on the GMAT"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">How long has it been since you learned about odd and even numbers? What about the differences between positives and negatives? And when did you learn the definition of an integer or a prime number?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Most of us learned all of these things before we were 10 years old. But as you may have noticed, the GMAT tests these concepts\u2014collectively known as <\/span><b>number properties<\/b><span style=\"font-weight: 400;\">\u2014in ways that make them seem absolutely foreign. Here is some example question stems drawn from Data Sufficiency problems:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Is <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> even?<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Is <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> &lt; 0?<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Is <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> an integer?<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">In Problem Solving, algebra problems are frequently set up such that you will answer incorrectly if you <\/span><b>assume<\/b> <i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> must be an integer or that it must be positive.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Number properties are all about categories and rules; certain kinds of numbers behave the same way in all cases. The GMAT will reward you for using the Core Competencies of Pattern Recognition and Critical Thinking to draw inferences about how numbers behave, based on certain characteristics or \u201cproperties\u201d they possess. That\u2019s why number properties questions appear on the Quant section with greater frequency than other topics.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Here are some definitions to brush up on and some tips for mastering the number properties concepts tested most frequently on the GMAT.<\/span><\/p>\n<p><div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-0  el_before_av_heading  avia-builder-el-first  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Integers<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\n<span style=\"font-weight: 400;\">The term <\/span><i><span style=\"font-weight: 400;\">integer<\/span><\/i><span style=\"font-weight: 400;\"> refers to positive whole numbers, negative whole numbers, and zero. When an integer is added to, subtracted from, or multiplied by another integer, the result is always an integer. (An integer divided by an integer may or may not result in an integer; it depends on whether the first number is a <\/span><i><span style=\"font-weight: 400;\">multiple<\/span><\/i><span style=\"font-weight: 400;\"> of the second.) <\/span><b>Picking Numbers<\/b><span style=\"font-weight: 400;\"> makes questions about integers and non-integers easier to tackle.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Zero is a special case. It is an integer, and it is even, but it is neither positive nor negative. <\/span><i><span style=\"font-weight: 400;\">Zero has no sign<\/span><\/i><span style=\"font-weight: 400;\">. One is also somewhat special; 0 and 1 behave differently from all other integers when you multiply them, with one important exception: odd and even rules. Zero behaves the same as all other even integers when adding, subtracting, or multiplying, and 1 behaves the same as all other odds in these situations.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">When \u201cinteger\u201d is a central word in a question, <\/span><b>you know have a number properties question<\/b><span style=\"font-weight: 400;\">. Questions that focus on the rules governing integers force test-takers to discriminate between different categories of numbers (whole numbers versus fractions or decimals). These questions also contain an important trap that you must learn to avoid: <\/span><b>Never assume a number is an integer<\/b><span style=\"font-weight: 400;\"> unless you\u2019re told that it is. The absence of information in a <a href=\"https:\/\/www.kaptest.com\/gmat\/practice\/gmat-practice\">GMAT question<\/a> can be just as important as its inclusion.<\/span><\/p>\n<p><div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-1  el_after_av_heading  el_before_av_image  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Odd and Even<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\n<span style=\"font-weight: 400;\">The terms <\/span><b>odd<\/b><span style=\"font-weight: 400;\"> and <\/span><b>even<\/b><span style=\"font-weight: 400;\"> apply only to integers. Even numbers are integers that are divisible by 2, and odd numbers are integers that are not. Odd and even numbers may be negative; 0 is even. The product of an even number and any integer will always be even. Here are the rules that govern odd and even:<\/span><br \/>\n<div  class='avia-image-container  av-styling-    avia-builder-el-2  el_after_av_heading  el_before_av_hr  avia-align-left '  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\"  ><div class='avia-image-container-inner'><div class='avia-image-overlay-wrap'><img class='wp-image-0 avia-img-lazy-loading-not-0 avia_image' src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2017\/11\/Screen-Shot-2016-09-26-at-12.12.06-PM-300x127.png\" alt='' title=''   itemprop=\"thumbnailUrl\"  \/><\/div><\/div><\/div><br \/>\n<div  style='height:10px' class='hr hr-invisible   avia-builder-el-3  el_after_av_image  el_before_av_heading '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\nNotice that there are no universal rules for dividing odds and evens.<strong><strong><br \/>\n<\/strong><\/strong><\/p>\n<p><div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-4  el_after_av_hr  el_before_av_image  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Positive and Negative<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\n<span style=\"font-weight: 400;\">Positive numbers are greater than zero, falling to the right of 0 on a number line. Negative numbers are less than zero, falling to the left on a number line.<\/span><strong><strong>\u00a0<\/strong><\/strong><br \/>\n<div  class='avia-image-container  av-styling-    avia-builder-el-5  el_after_av_heading  el_before_av_hr  avia-align-left '  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\"  ><div class='avia-image-container-inner'><div class='avia-image-overlay-wrap'><img class='wp-image-0 avia-img-lazy-loading-not-0 avia_image' src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2017\/11\/Screen-Shot-2016-09-26-at-12.12.13-PM.png\" alt='' title=''   itemprop=\"thumbnailUrl\"  \/><\/div><\/div><\/div><br \/>\n<div  style='height:10px' class='hr hr-invisible   avia-builder-el-6  el_after_av_image  el_before_av_heading '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<span style=\"font-weight: 400;\">When multiplying or dividing two numbers that have the same \u201csign\u201d (positive or negative), the result is always positive. When multiplying or dividing two numbers with different signs, the result is always negative.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Some <a href=\"https:\/\/www.kaptest.com\/gmat\/practice\/gmat-practice\">GMAT questions<\/a> hinge on whether the numbers involved are positive or negative. These properties are especially important to keep in mind when Picking Numbers on a Data Sufficiency question. If both positives and negatives are permissible for a given question, <\/span><b>make sure you test both possibilities<\/b><span style=\"font-weight: 400;\">, since doing so will often yield significant (different) results. Take the same approach that you\u2019ve been learning to use for other number properties: <\/span><b>Spend some time memorizing the rules, but always keep your eye out for strategic opportunities to pick numbers.<\/b><\/p>\n<p><span style=\"font-weight: 400;\">The special properties of \u22121, 0, and 1 make them important numbers to consider in Data Sufficiency questions, as well as for the \u201ccould be\/must be\u201d kinds of Problem Solving questions. Because numbers between \u22121 and 1 behave differently than do other numbers, they are good numbers to pick when testing whether one expression always has to be less than or greater than another.<\/span><\/p>\n<p><div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-7  el_after_av_hr  el_before_av_heading  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Divisibility Rules<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\n<span style=\"font-weight: 400;\">Because the GMAT tests math concepts most of us learned in elementary school, it can be challenging to recall some of these basic quantitative building blocks. Boost your ability to do mental math with these tips for remembering how to divide numbers in your head.<\/span><br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h4  blockquote modern-quote  avia-builder-el-8  el_after_av_heading  el_before_av_heading  '><h4 class='av-special-heading-tag '  itemprop=\"headline\"  >Rules for Twos, Fives, and Tens<\/h4><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\n<span style=\"font-weight: 400;\">The easiest of the divisibility rules are the rules for 2, 5, and 10:<\/span><\/p>\n<ul>\n<li><span style=\"font-weight: 400;\">If a number is even, it is divisible by 2.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">If a number ends in 0 or 5, it is divisible by 5.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">If a number ends in 0, it is divisible by 10.<\/span><\/li>\n<\/ul>\n<p><div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h4  blockquote modern-quote  avia-builder-el-9  el_after_av_heading  el_before_av_heading  '><h4 class='av-special-heading-tag '  itemprop=\"headline\"  >Rules for Threes, Sixes, and Nines<\/h4><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\n<span style=\"font-weight: 400;\">If the sum of a number\u2019s digits is divisible by 3, the number is divisible by 3. For example,\u00a0<\/span><span style=\"font-weight: 400;\">432<\/span><span style=\"font-weight: 400;\">\u00a0\u2192\u00a0<\/span><span style=\"font-weight: 400;\">4+3+2=9,<\/span><span style=\"font-weight: 400;\">\u00a0so 432 is divisible by 3. But\u00a0<\/span><span style=\"font-weight: 400;\">253<\/span><span style=\"font-weight: 400;\">\u00a0\u2192\u00a0<\/span><span style=\"font-weight: 400;\">2+5+3=10<\/span><span style=\"font-weight: 400;\">, so 253 is not divisible by 3.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">If a number is even AND the sum of its digits is divisible by 3, it is divisible by 6:\u00a0<\/span><span style=\"font-weight: 400;\">432<\/span><span style=\"font-weight: 400;\">\u00a0\u2192\u00a0<\/span><span style=\"font-weight: 400;\">4+3+2=9,<\/span><span style=\"font-weight: 400;\">\u00a0and 432 is even (divisible by 2), so it is divisible by 6.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">If the sum of a number\u2019s digits is divisible by 9, the number is divisible by 9:\u00a0<\/span><span style=\"font-weight: 400;\">432<\/span><span style=\"font-weight: 400;\">\u00a0\u2192\u00a0<\/span><span style=\"font-weight: 400;\">4+3+2=9,<\/span><span style=\"font-weight: 400;\">\u00a0so 432 is divisible by 9;\u00a0<\/span><span style=\"font-weight: 400;\">837<\/span><span style=\"font-weight: 400;\">\u00a0\u2192\u00a0<\/span><span style=\"font-weight: 400;\">8+3+7=18,<\/span><span style=\"font-weight: 400;\">\u00a0so 837 is divisible by 9.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">An interesting side note about 9: All multiples of 9, when their digits are summed, eventually yield 9. For example,\u00a0<\/span><span style=\"font-weight: 400;\">837<\/span><span style=\"font-weight: 400;\">\u00a0\u2192\u00a0<\/span><span style=\"font-weight: 400;\">8+3+7=18,<\/span><span style=\"font-weight: 400;\">\u00a0and\u00a0<\/span><span style=\"font-weight: 400;\">1+8=9<\/span><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h4  blockquote modern-quote  avia-builder-el-10  el_after_av_heading  el_before_av_hr  '><h4 class='av-special-heading-tag '  itemprop=\"headline\"  >Rules for Fours<\/h4><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\n<span style=\"font-weight: 400;\">If the last two digits of a number are a multiple of 4, the entire number is a multiple of 4. You don\u2019t add the digits together; if the last two are a multiple of 4 that you recognize, you can trust you have a multiple of 4. Because 100 is divisible by 4, all that matters is the last two digits. For example, 2,348,632 is divisible by 4 because the last two digits, 32, is divisible by 4.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">I\u2019m not aware of any useful ways to determine divisibility by 7 or 8, so your best bet for those is to learn their multiples instead.\u00a0<\/span>Most of us have forgotten our multiplication tables, so there is no shame in needing to refresh them. Take care to learn the multiples of 13 as well. Because most people brush up on multiples through 12, the GMAT loves to throw in 13 to catch you off guard.<\/p>\n<p><span style=\"font-weight: 400;\">Spend some time reviewing number properties. Being aware of and comfortable with the behaviors of numbers will take you a long way toward landing your best GMAT score on Test Day.<\/span><br \/>\n<div   class='hr hr-short hr-center   avia-builder-el-11  el_after_av_heading  el_before_av_testimonials '><span class='hr-inner ' ><span class='hr-inner-style'><\/span><\/span><\/div><br \/>\n<div   data-autoplay='1'  data-interval='5'  data-animation='fade'  data-hoverpause='1'  class='avia-testimonial-wrapper avia-grid-testimonials avia-grid-2-testimonials avia_animate_when_almost_visible   '>\n<section class ='avia-testimonial-row'><div class='avia-testimonial av_one_half flex_column no_margin avia-testimonial-row-1 avia-first-testimonial' ><div class='avia-testimonial_inner'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/BlogPosting\" itemprop=\"blogPost\" ><div class='avia-testimonial-image'  itemprop=\"image\"  ><\/div><div class='avia-testimonial-content '  ><div class='avia-testimonial-markup-entry-content'  itemprop=\"text\" ><p>Jennifer Mathews Land has taught for Kaplan since 2009. She prepares students to take the GMAT, GRE, ACT, and SAT and was named Kaplan\u2019s Alabama-Mississippi Teacher of the Year in 2010. Prior to joining Kaplan, she worked as a grad assistant in a university archives, a copy editor for medical websites, and a dancing dinosaur at children&#8217;s parties. Jennifer holds a Ph.D. and a master\u2019s in library and information studies (MLIS) from the University of Alabama, and an AB in English from Wellesley College. When she isn\u2019t teaching, she enjoys watching Alabama football and herding cats.<\/p>\n<\/div><\/div><div class='avia-testimonial-meta'><div class='avia-testimonial-arrow-wrap'><div class='avia-arrow'><\/div><\/div><div class='avia-testimonial-meta-mini'  itemprop=\"author\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Person\" ><strong  class='avia-testimonial-name'    itemprop=\"name\" >Jennifer Land<\/strong><\/div><\/div><\/div><\/div>\n<\/section><\/div><\/p>\n\n<p class=\"p1\"><div  class='avia-builder-widget-area clearfix  avia-builder-el-14  el_after_av_sidebar  avia-builder-el-last '><div id=\"text-76\" class=\"widget clearfix widget_text\">\t\t\t<div class=\"textwidget\"><p><span data-sumome-listbuilder-embed-id=\"70f62512b89832cc8e7fcd96b9d03245c2794cf0b7170fa257f26acec72436d9\"><\/span><\/p>\n<\/div>\n\t\t<\/div><div id=\"text-77\" class=\"widget clearfix widget_text\">\t\t\t<div class=\"textwidget\"><p><span data-sumome-listbuilder-embed-id=\"71160db829b51adcc3539815988485f372b020407413c2957efe50cfe72ea639\"><\/span><\/p>\n<\/div>\n\t\t<\/div><\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>How long has it been since you learned about odd and even numbers? What about the differences between positives and negatives? And when did you learn the definition of an integer or a prime number? Most of us learned all of these things before we were 10 years old. But as you may have noticed, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27645,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[55],"tags":[44,56],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/6747"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=6747"}],"version-history":[{"count":5,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/6747\/revisions"}],"predecessor-version":[{"id":41224,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/6747\/revisions\/41224"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/27645"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=6747"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=6747"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=6747"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}